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                     \begin{center}
        \begin{large}{\bf Explaining Incomplete Contracts as the
Result of  Contract-Reading Costs}
\\
             \end{large}
                 \bigskip
  September 3, 2001. Retexed 13 Dec. 2006.  \\


PUBLISHED IN: 
 the BE Press journal, {\it  Advances in Economic Analysis and Policy.} Vol. 1: No. 1, Article 2 (2001). \url{http://www.bepress.com/bejeap/advances/vol1/iss1/art2}.


 
                    \bigskip
                    Eric Rasmusen \\
                    \vspace*{ .2in}
                    {\it Abstract} \\
 \vspace*{ -.1in}
\end{center}

	 Much   real-world contracting involves adding finding new clauses to add
to a basic
agreement, clauses which may or may not increase the welfare of both parties. The
parties must
decide which complications to propose, how closely to examine the other side's
proposals, and
whether to accept them.     This suggests a   reason    why contracts are
incomplete in the
sense of lacking Pareto-improving clauses:   contract-reading costs  matter  as
much as
contract-writing  costs. Fine print that is  cheap to write can be expensive to
read carefully
enough to understand the value to the reader, and especially to verify the
absence of
clauses artfully written to benefit the writer at the reader's expense. As a
result,
complicated clauses may be rejected outright  even if they really do benefit both
parties, and
this will deter  proposing such clauses in the first place.

\noindent {\small \hspace*{20pt}    Professor of Business
Economics and Public Policy and Sanjay Subhedar Faculty Fellow,
Indiana University, Kelley School of Business, BU 456, 1309 E. 10th
Street, Bloomington, Indiana, 47405-1701. Office: (812) 855-9219. Fax:
812-855-3354. Erasmuse@indiana.edu.   
}

{\small  I  thank Maria Arbatskaya, William Bright,  Lutz Busch,
 Peter Cramton, Kenneth Elzinga,  T. Lynn Fisher, Benjamin Hermalin,
 Michihiro Kandori,   Felice Martinello, Wolfgang Pesendorfer, J. Mark
 Ramseyer, David Waterman, two anonymous referees   and participants
 in seminars at Brock University, CIRANO (Montreal),  Indiana
 University,  the  U. S. Department of Justice, Kyushu University, the
 University of Manitoba, Otaru University of Commerce,  the Central
 Bank of Turkey, Virginia Polytechnic Institute,  the University of
 Virginia, and the American Law and Economics Association for helpful
 comments. I thank  Harvard Law School's Olin Center   and the
 University of Tokyo's Center for International Research on the
 Japanese Economy for their hospitality.   Not  all of those I thank
 have seen this draft, and they bear no responsibility for errors.}


 \newpage

 

 \bigskip
 
\begin{center}
{   1.  INTRODUCTION} 
 \end{center}

 Why are contracts incomplete? The contracts we observe in the world
often  fail to  specify what happens in many important contingencies 
and they are not always  crafted    to  provide each party with the
optimal incentives. This has been often remarked upon, notably in     Stewart
Macaulay's
classic 1963 article,
``Non-Contractual Relations in Business: A Preliminary Study.''  

	Some contractual incompleteness can be explained easily enough. Important
aspects of the agreement   are unobservable to one of the parties  (information is
asymmetric) or   too costly to prove in court (information is ``unverifiable'')
.\footnote{If
information is symmetric but  unverifiable---observed by both
parties to the contract but unobservable to the court--- then it may still be
useful
to design an agreement around that information, as  the mechanism design literature
tells us.  This possibility   brings into question unverifiability as an
explanation for
contract incompleteness, a controversy discussed in Jean Tirole (1999).} These
things can then
induce a ``second-best'' effect:  the parties   decide to omit from the contract
certain of
even  the  observable variables for fear of unduly concentrating   incentives on
just what is
included.\footnote{This is the idea in Bengt Holmstrom and Paul Milgrom (1991).
Suppose an
employment contract specifies that a salesman will (a) work 40 hours per week, and
(b) be paid
based on his sales volume. This contract omits the variable ``time spent helping
other
salesmen'', which is unobservable to the employer or to the court. As a result, the
salesman
will spend zero hours helping other salesmen, and a better contract might omit part
(b).    }
Or, it may be desirable to leave something out of the contract so   it can be used
as a threat
by a  party who would otherwise be vulnerable to opportunism by the other party (B.
Douglas
Bernheim \& Michael Whinston, 1998).\footnote{ Bernheim and Whinston's article
provides a
bridge to a  separate literature,  on renegotiation
in contracts.  Many of these articles in that literature have ``incomplete
contracts'' in the
title  but they are
about the   consequences, not the  causes, of incompleteness.  Examples are Oliver
Hart \& John
Moore's 1988
``Incomplete Contracts and Renegotiation,''  Tai-Yeong Chung's 1991 ``Incomplete
Contracts,
Specific Investments, and Risk Sharing,''  and Christoph Lulfesmann's 2001
``Incomplete
Contracts, Non-Contractible Quality, and Renegotiation.''      A  second-best
explanation for
incomplete contracts in the spirit of this literature would    be that future
renegotiation on
unverifiable variable $X$   makes it undesirable to include verifiable variable $Y$
in the
initial contract. I do not recall seeing this   in a formal model, however, and
mention it only
as a conjecture. }

	Asymmetric information can also lead to incomplete contracts in a different
way: Party
A's fear that if he proposes an addition to the contract Party B  will  deduce that
he has
private information  and either be more reluctant to trade   or somehow use that
information
against him. If a professional athlete asks for extra health insurance from his
employer, for
example the employer may deduce, rightly or wrongly, that the athlete is not
feeling well  and
propose a lower salary. If an industrial buyer asks for a minimum monthly quantity
guarantee in
a long-term contract, the seller may deduce---again, rightly  or wrongly---that the
buyer does
not have alternative sources of supply, and   raise the price. This idea can be
found in a
number of contexts, including the models of Ian Ayres and  Robert Gertner (1992),
Benjamin
Hermalin and Michael Katz (1993),  and Kathryn Spier (1992).

 	On  a simpler level, there is a cost to deciding which
contingencies are important and to writing the  contract  clauses
themselves. And even if the parties   write a simple contract,
if the dispute goes to   court, the court will    ``fill in the
blanks'' using default rules designed to work well for the typical
contract. In a sense, it is impossible to write an incomplete
contract, because the courts will always find some way of interpreting
a contract for every contingency. With the addition of the law's
implicit default rules, even a very short contract is
extraordinarily complex in its legal implications.

  


 	Thus, we do have a number of explanations for why important
variables are left out of contracts---unobservability,
unverifiability, second-best incentives, fear of signalling
undesirable characteristics,  contract-writing costs, and
legal default rules. These explanations are far superior to the old
phrases, ``bounded rationality'' and ``transaction costs,'' in that
they explain which contracts will be most complete, but for that very
reason they leave us with many contracts which ought to be complete
but are not.\footnote{Any of the
explanations for incompleteness just given  could fit under the
heading of either ``bounded rationality'' or ``transaction costs,''
since those headings   amount to little more than  
residuals for whatever makes behavior different from in the 
simplest maximizing models.}  Often the contingencies omitted in the
contract are
easily verifiable in court---disasters, accidents,   changes in market prices, and
so forth.
Often  there is no problem of distorted incentives.  Writing down details of the
agreement has
low cost   if the contractual situation is repeated and there are economies of
scale, as when a
retailer sells to a thousand consumers. Once the contract is written, writing
extra sentences
adds little to the cost.  And though courts do their best to fill in the blanks,
existing legal
default rules will be tailored for the average contract and thus will not fit every
contract.
And if the courts have not encountered a particular blank in a contract before,
they will  make
up a new default rule, which adds uncertainty to the original agreement.

	    I  will  suggest a new explanation: contract-reading costs. The problem
is not in
the social cost of discovering or writing a new contract term, nor is there any
problem with
incentives, commitment,  or enforcement  once the contract is formed. Rather, the
problem is
that Party A cannot  understand    the implications of language proposed by Party B
unless he
expends effort reading the contract carefully. Contracts are thus incomplete
because both
parties must agree to them, the problem lying in the    contract-forming process
that I will
call negotiation.  Economists usually think of contract formation as bargaining
over splitting
a pie, but it can increase the size of the pie, which is what we think extra
contract terms
could do.

  Examples abound.   If I     negotiate with a contractor about building a house,
we do not
just talk about the price, and   our talk about the details of the contract is not
just
redistributive.   We could eliminate almost all the contracting costs if the
government were to
require  that houses  be of a  single standard design, but that would not be
efficient. I have
my  particular preferences about  the windows, woodwork, floor type,   color,  and
time of
completion, and the  contractor has his own individual costs for each feature. Much
of my
concern will not be about whether I can  extract a good price at the expense of the
contractor,
but whether I   am agreeing  to buy features  of the house that  I really want.
Rather than
agree to builder proposals that sound attractive, I may wish to leave some features
out of the
contract, to be determined by default legal rules.

 	Labor contracting is dominated by negotiation of this kind. It may be that
a union and  an employer have agreed upon a wage, but that does not
end the collective bargaining.  The employer may also 
offer an extension to the health insurance benefits, in exchange for a
wage concession. Possibly, the benefit to the union is greater than
the lost wages, in which case the change would benefit both sides. Or,
maybe the  workers could do better by rejecting the new insurance.
The union negotiator's uncertainty is not over the minimum offer
acceptable to  the company, but over whether the health insurance
helps both sides.  

	 Or consider mergers and acquisitions, notoriously complicated deals.
Suppose company A  is selling off a division to  company B. They have
agreed on a price, but now company A asks that a clause be added to
the deal under which it would buy  back a certain amount of the output
of the division each year at a specified price. The  clause might
benefit company B, or might hurt it.   Again, the uncertainty is not
over the minimum that company A would accept, but over whether the
contract benefits both sides or not. It may be quite clear that the
clause benefits company A by exactly five million dollars, but it may
be unclear what the cost   is to company B.  

 	On a less grand level, suppose that Mr.  Smith is selling  a
load of lumber to Mr. Jones.  After the  deal has been made,   Smith
says, ``Throw in an extra \$50  and I'll  deliver the lumber to your
house.  It's no big deal for me, and you'll save a lot of effort.''
Jones's uncertainty is not over the cost of delivery to Smith, which
is of no interest to him. Rather, it is over the net benefit to himself.
 The cost of hiring a deliveryman might   be \$80, in which case Smith is
right that both Smith and Jones would benefit from the proposal, or it might
be \$30, in which case Smith gains but Jones loses.As an alternative, the contract
might be
left incomplete, with  delivery
  left for later decision. 

	 All four examples involve   the conflict between production
and distribution    which is emphasized in the nonformal
literature on bargaining, where it is called the  conflict
between ``creating value'' and ``claiming value''  (see the 1992 survey by   James
Sebenius).  This difference has been recognized
but not modelled. At the start of their  1993 survey of bargaining models 
John   Kennan and  Robert Wilson list three costs of bargaining:
\vspace*{-12pt}
\begin{quotation}
 \begin{small}
   ``Costly delays and failures to agree when gains from trade exist represent two
kinds of inefficiencies; a third is that  an agreement is inefficient if its terms
fail to realize all the potential gains from trade, as in the case that a firm's
contract with a union specifies inefficient work rules or numbers of workers.''
 \end{small}
\end{quotation}
\vspace*{-12pt}

  Kennan and Wilson go on to survey the bargaining literature at
length, but while costly delays and failures to agree receive ample
attention in the next fifty-eight pages, failure to realize  all the
potential gains from trade does not resurface.

 I  will explore contract-reading costs as a reason for  the failure to realize
all the  gains from trade. A complicated contract is
relatively easy to write, but it is difficult to read. By reading I do
not, of course, mean simply staring at   words, or even looking at
each word and understanding what it means in isolation. Rather, the
problem is to read the contract and understand its implications. Even
unsophisticated parties to contracts know that by signing their name
they are making themselves vulnerable, and that the other parties are
self-interested.  Reading is a skill, and requires effort even by those who are
expert in it.
As
George Stigler  points out   in  his 1980 article on privacy,   
 apparently free information is actually   costly once we include the effort of
understanding
how to use it. His
example is what might seem the paradigm of information as a public good: the
mathematical
theorem.
\begin{small}
\begin{quotation} 
``Consider the highly useful solution of the quadratic equation ($x= -
b \pm \sqrt{b^2 -4ac}/2a$). It was discovered by numerous
mathematicians, probably at small cost.[Footnote omitted] To make it
available to our society, we invest perhaps a day of every high school
student's life in instructing them in its use. The social costs of
nonrecovery of the original discovery are contemptibly negligible
compared to  any inefficiencies in the dissemination of the theorem.''
(Stigler, 1980, Appendix A)
 \end{quotation}
\end{small}
   Like mathematical  theorems, legal clauses can be copied from
books. The clauses can   easily be  read out loud  and   even  
memorized without great difficulty. But that does not mean   they
are easy to understand.    And even small 
  reading costs have wide-ranging implications, as we will see below. 


	Previous research has not touched upon contract-reading costs, though it
has come close
enough that the formal analysis of the next section will not require any new
modelling
technology.  The central idea of the present paper---that a party's
proposal of a more complex contract should be viewed with suspicion
because  of possible underlying implications---
is related to the articles by Ayres \& Gertner (1992), Hermalin \& Katz
(1993),  and Spier (1992) cited earlier, in which  complex contract
proposals signalled undesirable characteristics of the proposer,
leaving him worse off than if he had remained silent. Here, however,
complex contract proposals  will signal nothing    about the proposer, though they
may signal
something about the contracts  themselves.
  If the proposals  are rejected, the proposer will be no
worse off than if he had remained silent, except for having expended
contract-writing costs. Moreover,   the party to
whom a proposal is made will have the opportunity to obtain information
directly  by incurring the contract-reading cost   rather than just by
deduction.

	The closest     model to the present one is perhaps    that of
Avery  Katz (1990). Katz  is not concerned with negotiation {\it per
se}, but with the legal rules involving the fine print in contracts
(incidentally, the same issue as in the 1993 article by Benjamin Hermalin and
Michael
Katz cited earlier). The courts must decide how much   fine print   to
enforce. If they enforce none of it, they must specify how the
contract binds the parties, because the writing in the contract has
been abandoned. If they enforce all of it, each    party must read the
terms carefully or abandon   detailed contracts  in favor of
short but ambiguous ones. The legal
rules should be designed to induce the parties to monitor what each
inserts into the contract.

Attention in the present paper, however, will be on what the contractors
will do  rather than  on what   the courts should do. Courts will make no
effort here to determine what is fair  or whether both parties fully
understood their agreement.  Rather, if both parties agree to the
contract,  the  courts will enforce it as written, even if it is clear later that
one party
did not read it carefully.

  The framework    will be  an   auditing model. In such a model,   one player
takes an action
which the other player can
either audit or let pass.  Here, the action will be  to insert an
extra clause in the contract, a clause which     might benefit both
players, creating value, or   just benefit the offeror, claiming
value.  The other player must decide whether to trust the offer or
read it carefully.  It will be costly both to offer and to read
clauses, so this will be a model   both of contract-writing  
  and      contract-reading costs.

	 The strategic problem   is  thus   different from  in
bargaining or mechanism design. In bargaining,  a player's concern  is
to determine how much the pie is worth to the other player  so he can
offer  a share just big enough for the deal to go through. In
mechanism design, the mechanism tries to elicit from each player his private
information: the
value of the pie to himself. In the    model here,  the proposing player
will   have
an incentive to offer the clause regardless of his private information, and the
other player
will have no private information to elicit.
  In addition, every new term of a  complicated  mechanism
would just multiply the original problem, by creating new possibilities for
redistribution that would themselves have to be examined carefully.

	  Early applications of auditing  were to arms control
verification, as in Melvin Dresher (1962). Rudolf Avenhaus, Bernhard
von Stengel \& Shmuel Zamir (2002) survey the literature in Volume III
of the {\it The Handbook of Game Theory}  with systematic attention to
the variety of auditing situations---only one possible violation but
$n$ periods of possible reading, $m$ possible violations and $n$
possible readings, and so forth. One strand of the applied literature, which began
with Stan
Baiman \&  Joel Demski (1980),  examines  the incentives for high effort by a
worker
whose
income is observed and can be used as the basis for an audit investigation. Another
strand,
which began with Robert Townsend (1979),  investigates the mechanism design
question
of how a
provider of capital can elicit truthful reports of   financial condition from  the
user of
capital. Since the problem is one of mechanism design, the players can contract in
advance on
penalties for lying and bonuses for telling the truth.  This kind of auditing, in
which lying
is penalized, certainly is helpful for negotiation. If someone makes a false claim
that can be
proved in court, the deal can be voided and criminal penalties may even be
applicable. It does not apply, however, to   negotiating proposals   in which
Party A
makes a
proposal for Party B's consideration without specific  claims verifiable in court
as to how
much Player B will benefit. If a housebuilder says  that his customer will   like
purple paint
and that turns out to be false, how is a court to tell whether the customer's
complaint is
justified?   The model used below will not have penalties for lying, and so will
have more of
the flavor of auditing in politics (e.g., Rasmusen, 1993), where a player's claim
can be
checked and disproved, but the only penalty is that he has wasted his effort in
making the
claim.

	

	Section 2  will construct the model of negotiation without
solving for the equilibrium.   Sections 3 and  4 will find the
equilibria in the simple but important  cases when precommitment is possible---in
Section 3 when  a player can precommit to  honesty; and in Section 4 
when he can precommit to reading all clauses carefully. Section 5 is
the heart of the analysis,  setting out  the two equilibria of the
game without precommitment. Section 6 contrasts the basic complete-
information model with a model of incomplete information.  Section 7,
perhaps the most important part of the paper, interprets the model's
results at length. Section 8 is a short summary.

\bigskip

\newpage
 
\begin{center}
 {2. THE MODEL}
 \end{center}

 Two parties, the ``offeror'' and the ``acceptor,''   are trying to agree  on the
details of  a
contract after having  already agreed to its basics. The basic contract will not
affect the
model  and is included only to emphasize that some parts of the deal may not
require
negotiation.  Let us assume that as  part of the bargaining process behind the
original deal,
the players  split the anticipated gains from trade equally, including the gains
they
anticipate from the  details added by a new clause  in the negotiation subgame
being modelled
here. We will denote the expected payoffs of the subgame starting with the offer of
a new
clause  by $\pi_{offeror} $ and $ \pi_{acceptor}$.

      The offeror has the option of not offering any  clause at all, for a payoff
of 0.
Instead, he can    offer a   ``sincere'' clause  which yields  him  $x_s$ if
accepted,  or a
``misleading'' clause which yields  him  $x_m$. The  cost to him of making an offer
is  a
contract-writing cost of  $c_{ws}>0$  or $c_{wm}>0$, depending on the type of
clause.  We will
not make any assumption on the relative sizes of  $c_{ws} $ and $c_{wm}$; it might
be more
costly to discover and propose a mutually beneficial sincere clause, or to discover
and
disguise a one-sided clause. We will, however, assume that
    \begin{equation} \label{e00}
      x_m-c_{wm}>x_s-c_{ws}>0.  
    \end{equation}
         The first inequality in (\ref{e00}) says that the offeror
would prefer a misleading   clause to a sincere one if both   had equal
probabilities of acceptance, even given the contract-writing costs.
The second inequality says that either type of clause helps the
offeror  if accepted.

      The acceptor's benefit  is $y_s>0$ from a sincere clause  and $-
y_m<0$ from a misleading one.    He cannot costlessly identify which 
clause has been offered. Instead, he   can accept  it outright, reject
it outright, or read it at contract-reading cost $c_r$ to  discover
whether it is sincere or misleading. Let us   assume that
    \begin{equation} \label{e00a}
      x_s + y_s -c_{ws} >x_m-y_m-c_{wm}.   
    \end{equation}
    Assumption (\ref{e00a})  says that the  sincere clause is
efficient; there is no side payment that the offeror would be willing
to make that would  induce the acceptor to knowingly accept a
misleading clause.

\noindent
 The order of play is thus
\vspace*{-8pt}
    \begin{enumerate}
\item[(0)]
  Offeror and acceptor split the expected    social  surplus   of $E(\pi_{offeror}
+\pi_{acceptor} )$ from the    negotiation subgame equally,  using  the appropriate
side
payment  of
 \begin{equation} \label{e01a}
 S =E(\pi_{offeror} )  -\frac{E(\pi_{offeror}+\pi_{acceptor}   )}{2}
\end{equation}
 from offeror to acceptor, where $S $ might be negative. 

\item[(1)]    The offeror offers a sincere clause at cost $c_{ws} $  or a
misleading clause at
cost  $c_{wm}$.

\item[(2)]  The acceptor reads the clause at cost $c_r$, discovering whether it is
sincere or
misleading, or does not read it.

\item[(3)]  The acceptor accepts or rejects the clause.

\item[(4)]  The contract is finalized, payoffs are received, and the effect of the
clauses is
discovered.


   \end{enumerate}
  

This is a game of complete information. At the start of the game the
players possess exactly the same information, and the only way
information becomes asymmetric is that once the offeror offers a
clause  he knows what kind of clause he offered.  There do not exist
different  types  of offerors, and there is nothing for the
acceptor  to learn about the offeror or the state of the world during
the game.   We will, however, see in Section 6 how an
incomplete
information version of this model would work.

 \bigskip
 
  \begin{center}
  {   3.  \\
 THE VALUE OF A REPUTATION FOR HONESTY: \\
 WHAT  IF THE OFFEROR CAN PRECOMMIT?    }
 \end{center}

 What happens if the offeror can precommit to offer only sincere clauses? The
acceptor will then not bother to read the clause  and will accept it outright. The 
payoffs    are
 \begin{equation} \label{e0a}
 \pi_{offeror}   =    x_s-c_{ws}  
 \end{equation}
 and 
\begin{equation} \label{e0b}
 \pi_{acceptor}  =     y_s,    
 \end{equation}
 for a total social surplus   of  
\begin{equation} \label{e0c}
   \pi_{offeror}  +\pi_{acceptor}    =    x_s  + y_s -c_{ws}.
 \end{equation}
  The social surpluses in this and the  scenarios below  are tabulated later in
Table 1 in Section 5 for comparison.   The social surplus in this scenario is the
highest possible, because reading contracts   is unnecessary and the sincere
clauses are always offered.

   It is hard to see how someone could literally commit to offering
only sincere clauses  but in some cases  plausible ways to  reach the
same outcome are available. If the offeror repeatedly    negotiates
over time  with one or different acceptors, he may wish to preserve a
reputation for sincerity. If he ever offered a misleading contract, it
would be accepted, but if he tried to enforce it, he could lose his
reputation.    

\bigskip
 
\begin{center}
   {   4. \\
 THE VALUE OF A REPUTATION FOR READING CONTRACTS CAREFULLY:  
 WHAT   IF THE ACCEPTOR CAN PRECOMMIT?  }
 \end{center}

 What happens if the acceptor can precommit to read the clause? The offeror   
will respond by offering a sincere clause, even if he himself cannot precommit as
in
Section 3.
The   payoffs   are
  \begin{equation} \label{e0d}
 \pi_{offeror}   =    x_s-c_{ws}  
 \end{equation}
 and 
\begin{equation} \label{e0e}
 \pi_{acceptor}  =     y_s -c_r,  
 \end{equation}
 for a total social surplus   of 
\begin{equation} \label{e0f}
  \pi_{offeror}  +\pi_{acceptor} = x_s  + y_s -c_{ws} -c_r.
 \end{equation}
     Given that the side-payment $S$ at the start of the game splits the gains from
trade, the
acceptor is   willing to precommit to reading if  expression  (\ref{e0f}) is
positive. It will
be positive if the contract-reading cost $c_r$ is not too large, a reasonable
condition, but one   not
  assumed
 as part of  the model.


    The acceptor may be able to do even better, however, as Wolfgang Pesendorfer
pointed out to me.  Suppose  he can precommit to read with  auditing probability
$\alpha$; e.g., he precommits to read the clause with  a probability of 90 percent.
This is cheaper   than the  100 percent probability   used above 
and it will  still deter the offeror from trying to sneak by a misleading clause if 
  \begin{equation} \label{e0g}
 \pi_{offeror} (sincere)   =    x_s-c_{ws}  \geq  \pi_{offeror} (misleading)   =
(1-\alpha) x_m + \alpha (0) -c_{wm},
 \end{equation}
 which requires that
   \begin{equation} \label{e0h}
\alpha \geq    \frac{(x_m -c_{wm})-(x_s -c_{ws})}{x_m}.       
 \end{equation}
 Assumption (\ref{e00}) ensures that the right-hand side of (\ref{e0h}) is between
zero and one. If $\alpha$ is set at    the  lowest level which makes
inequality (\ref{e0h}) true  then the   payoffs  are
  \begin{equation} \label{e0i}
 \pi_{offeror}   =    x_s-c_{ws}  
 \end{equation}
 and 
\begin{equation} \label{e0j}
 \pi_{acceptor}  =     y_s -\left( \frac{(x_m -c_{wm})-(x_s -c_{ws})}{x_m} \right)
c_r,
 \end{equation}
 for a total social surplus    of 
\begin{equation} \label{e0k}
  \pi_{offeror}  +\pi_{acceptor}     =   x_s  + y_s -c_{ws} -
\left( \frac{(x_m -c_{wm})-(x_s -c_{ws})}{x_m} \right)c_r.
 \end{equation}

The use of  the probability $\alpha$   does not imply that the equilibrium is in
mixed
strategies.   Precommitment to an auditing probability is distinct from a mixed
strategy 
because the acceptor must read with positive probability   even though he knows
that in
equilibrium the offeror  will never offer a misleading clause.\footnote{ For more
on the
distinction between auditing and mixing, see Rasmusen (2001), pages 79-81}  Without
precommitment, if    the acceptor announced he was following the strategy just
described it
would not be an equilibrium. If the offeror believed the announcement and   offered
a sincere
clause, the acceptor would change his mind and reset the reading probability to
zero when the
time came to pay the reading cost.

 Precommitment might take the form of paying for contract reading in advance of the
negotiation---by hiring an in-house lawyer and being careful to not have other uses
for his
time, for example. An interesting alternative   would be for the offeror to pay for
the lawyer,
bundling together the offer of a new clause and the reading of the clause.  ``He
who pays the
piper calls the tune,'' however, and such an arrangement might not be trusted by
the acceptor.

The usual substitute for precommitment, reputation,  runs into more difficulty here
than  in
Section 3, where I suggested it as way for the offeror to make his honesty
credible. Here in
Section 4, the reputation would be the acceptor's reputation for reading contracts
carefully.
If the acceptor can persuade offerors that he does read contracts carefully, he can
maintain
such a reputation, but such persuasion may be difficult. Since only sincere clauses
are offered
in equilibrium,   neither a diligent contract reader   nor a deviant non-reader
would ever find
a misleading contract. How, then, could outsiders tell whether the acceptor was
really reading
them? Verifying that the acceptor is following   equilibrium
behavior becomes
especially difficult when that behavior is to read with probability $\alpha$ less
than
one, since
in each negotiation round, the acceptor could fail to read  and claim that his
failure was  a
matter of chance.

 If the acceptor can somehow commit to read every offer, however, the social
surplus is almost
as high as  when the offeror can commit to offering sincere clauses. The only
difference is the
cost of reading.
  
\bigskip

 \begin{center}
 5.    EQUILIBRIA WITHOUT PRECOMMITMENT 
     \end{center}

     Let us now assume that neither player can precommit to any
action. The offeror might offer either kind of clause and the acceptor
might or might not read  the fine print of each clause offered.

\noindent
   Any equilibrium must have the following properties:
 \begin{enumerate}
 \item[(a)] The offeror does not offer a misleading clause with
probability one. If it were known he did this,  the
acceptor would always reject outright, and so the offeror would incur the contract-
writing
cost $c_{wm}$ for no benefit.
   \item[(b)]
 The offeror does not offer a sincere clause with probability one. If he did, the
acceptor would never read the clause, and so the offeror would  deviate to
offering a misleading clause to obtain $x_m-c_{wm}$ instead of $x_s-c_{ws}$.
  \item[(c)]
 The acceptor does not have probability one of  accepting without
reading.    If he did, the offeror would only offer misleading
clauses.
 \item[(d)]
 The acceptor does not read with probability one.  If he did, the
offeror would never offer misleading clauses, making the reading
pointless.
 \item[(e)]
 The acceptor does not mix   between accepting and rejecting.  The offeror
would respond by always choosing misleading clauses, which point (a)
says     cannot happen.
 \item[(f)]
The acceptor does not mix   between reading and rejecting. Then no
misleading offer would  have any hope of being accepted. The   offeror
would respond by always choosing sincere clauses, which point (b) says
cannot happen.
     \end{enumerate}


\noindent
 Points (a) through (f)  leave two possible equilibria. In the first, both players
use mixed
strategies.
    
   
\begin{center}
 {\it THE MIXING EQUILIBRIUM }   (if $c_r  \leq \frac{y_s y_m}{y_s+y_m}$)
\end{center}

\vspace{-.6in} 
\begin{quotation}
\noindent
 \begin{enumerate}
 \item[\underline{Offeror:}  ] Offer  the sincere clause  with
probability  $ p_s^*   =1-\frac{c_r} {y_m}$ and the  misleading clause
otherwise.
\item[\underline{Acceptor:} ]  Accept   without reading with probability $ p_a^* =
\frac{x_s -
c_{ws} + c_{wm}}{x_m}$. Otherwise read the clause, and accept it  only if the offer
is sincere.
 \end{enumerate}
  \end{quotation}

  Let the probability that the offeror offers the sincere clause
be $p_s$ and the probability that the acceptor accepts  without
reading be $p_a$.  The offeror's pure-strategy payoffs   are
 \begin{equation} \label{e1}
 \pi_{offeror}(sincere) = -c_{ws} + p_a x_s + (1-p_a)x_s
 \end{equation}
 and 
\begin{equation} \label{e2}
  \pi_{offeror}(misleading) = -c_{wm} +p_a x_m + (1-p_a )\cdot 0,
 \end{equation}
    since the misleading clause will be rejected if the acceptor
chooses to read. If there is to be  a mixed strategy equilibrium, the
two pure-strategy payoffs must be equal,  so
\begin{equation} \label{e2a}
   -c_{ws} + p_a x_s + (1-p_a)x_s = -c_{wm} +p_a x_m 
 \end{equation}
 and 
 \begin{equation} \label{e3}
 p_a^* =\frac{x_s -c_{ws} + c_{wm}}{x_m}.
 \end{equation}
      

 \noindent
The acceptor's pure-strategy  payoffs   are
 \begin{equation} \label{e5}
 \pi_{acceptor}(accept) =  p_s y_s -(1-p_s )y_m
 \end{equation}
 and 
\begin{equation} \label{e6}
  \pi_{acceptor}(read ) = -c_r + p_s y_s -(1-p_s )\cdot 0
  \end{equation}
 since the misleading clause will be rejected if the acceptor reads it. If there is
to be a mixed strategy equilibrium, the two pure-strategy payoffs must be equal, so
 \begin{equation} \label{e5a}
    p_s y_s -(1-p_s )y_m
  = -c_r + p_s y_s,   
  \end{equation}
 and 
  \begin{equation} \label{e7}
 p_s^* =1-\frac{c_r}{y_m}.
 \end{equation}
   For the probabilities in  (\ref{e3}) and (\ref{e7}) to remain between zero and
one requires that
 \begin{equation} \label{e9d}
    x_s   -c_{ws} + c_{wm}  \geq 0,
 \end{equation}
  which is guaranteed by assumption  (\ref{e00}), and 
  \begin{equation} \label{e9e}
   c_r \leq y_m. 
 \end{equation}
 If   assumption (\ref{e9e}) is false, the Mixing Equilibrium does not exist;
  the acceptor would never wish to  read the clause  even as part of
a mixed
strategy.
 
We must also check for another possible deviation from equilibrium:  the acceptor
has the option to reject  the clause without reading
it, for a payoff of 0. Comparing the payoff of 0 to the payoff in (\ref{e6}) from
the pure strategy of reading the clause (which is $-c_r + p_s
y_s$), it is apparent that for  him  to  refrain from outright
rejection requires that
  \begin{equation} \label{e8}
   c_r  \leq p_s y_s.  
 \end{equation}
Substituting  in (\ref{e8}) for the equilibrium level of $p_s$ from (\ref{e7}) and
solving for
$c_r$ yields
 \begin{equation} \label{e9}
     c_r  \leq \frac{y_s y_m}{y_s+y_m}
 \end{equation}
 If condition (\ref{e9}) is false, then the Mixing Equilibrium   does
not exist. Note that condition (\ref{e9}) implies   that $c_r <
y_s$. Reading must be cheap enough relative to the value of a
sincere clause that the acceptor is willing to undertake the amount of
reading needed to give the offeror incentive to sometimes offer the
sincere clause. Condition (\ref{e9}) also implies  condition (\ref{e9e}),   that
$c_r <
y_m$, which it therefore subsumes.  

Using the equilibrium mixing probabilities we can compute the equilibrium payoffs.
From
equation   (\ref{e1}),
 \begin{equation} \label{e9a}
 \pi_{offeror}^*     =     x_s -c_{ws}, 
 \end{equation}
  which is non-negative by assumption (\ref{e00}). From (\ref{e6}) and (\ref{e7}),
 \begin{equation} \label{e9b}
 \pi_{acceptor}^*   =   y_s -c_r  \left(1 + \frac{  y_s}{y_m} 
\right),
 \end{equation}
  which is non-negative  if condition (\ref{e9})  is true and the equilibrium
exists. The total social surplus  is thus
\begin{equation} \label{e9c}
  \pi_{offeror}^*  + \pi_{acceptor}^*   =  x_s  + y_s -
c_{ws} -c_r -\frac{c_ry_s}{y_m} \geq 0,
 \end{equation}
which is less than the surplus when the acceptor can
precommit to reading every offer.


\bigskip

\noindent
There also exists a second equilibrium, which is  in pure  strategies. 

 
 
\begin{center}
{\it THE NO-OFFER EQUILIBRIUM  } 
\end{center}
\vspace{-.6in}
 \begin{quotation}
\noindent
  \begin{enumerate}
 \item[ \underline{Offeror:}  ]    Do not offer either clause.
  \item[ \underline{Acceptor:} ] Reject any clause that is offered.
 \item[ \underline{Out-of-equilibrium belief:}] If the offeror
deviates and offers a clause,  the acceptor believes it   is   sincere
with a probability $\beta$ of  no more than  $ Max \{\frac{y_m}{y_s +
y_m}, \frac{c_r} {y_s} \} $.
  \end{enumerate}
 \end{quotation}

 Neither player has incentive to deviate from the    No-Offer
Equilibrium. The offeror has no incentive to offer clauses if the
acceptor always rejects, and the acceptor has no incentive to read or
accept the clause given his beliefs. The dilemma is similar to the
situation in some signalling and coordination games, but here unlike
in those games (e.g.,  In-Koo Cho \& David Kreps (1987),   Eric Van
Damme (1989)), the intuitive criterion and forward induction have no
bite.\footnote{  If   a small
number of honest offerors will never make misleading offers (i.e.,
$c_{wm}=\infty$ for them), then the No-Offer Equilibrium   breaks
down, because an offer observed out-of-equilibrium would have to be a
sincere clause offered by one of these honest offerors. This, however, brings in
other
complications; if we also added
a number of dishonest offerors for whom $c_{wm}=0$, then the out-of-equilibrium
offer might
come from one of them, and the No-Offer
Equilibrium   is revived. See Section 6 for a model of pure adverse selection.  }

 The out-of-equilibrium beliefs needed to sustain the No-Offer
Equilibrium are obtained as follows. If $\beta$ is the  acceptor's
subjective probability that the offeror's out-of-equilibrium offer is
sincere, then the acceptor's   subgame payoff is
   \begin{equation} \label{e10}
    \pi_{acceptor} (accept) = \beta  y_s  -(1-\beta) y_m,      
 \end{equation}
 which  yields   $\beta = \frac{y_m}{y_s + y_m}$ for the value of $\beta$ which
makes the  acceptor prefer to reject and receive the payoff of 0.

It must also be true that the acceptor does not think it worthwhile to read the
clause. The payoff from reading, given the belief $\beta$, is
 \begin{equation} \label{e11}
    \pi_{acceptor} (read ) = \beta  y_s  -(1-\beta)(0) -c_r,       
 \end{equation}
 which yields $\beta =\frac{c_r}{y_s} $ for the value of $\beta$ which
makes the acceptor prefer to reject and receive the payoff of 0.

 The equilibrium payoffs are zero   in  the No-Offer Equilibrium.
Its existence, unlike existence of  the Mixing
Equilibrium, requires no special assumptions.

\bigskip 

We can now summarize the possible outcomes of the complete-information model of
negotiation.  As Table 1 shows, the social
surplus---and thus the payoffs for each player, since they split the
social surplus---can be Pareto-ranked.     The best outcome is when
the offeror can be trusted to always offer only sincere clauses, and
the next best is when the acceptor can be trusted to always read the
clauses offered to him. These are placed above the line in Table 1
because they are really separate games. Of
the two equilibria that can exist when precommitment is impossible,
the best is the Mixing Equilibrium.   Worst of all is the No-Offer
Equilibrium, in which  an atmosphere of mistrust prevents the
acceptor from bothering to even read any clauses that might be offered
to him, which results in none being offered.


 
 \begin{center}
{ TABLE 1:     THE SOCIAL SURPLUS  } 
 

 \begin{tabular}{ll}
\hline
\hline
 & \\
 EQUILIBRIUM  & TOTAL SURPLUS \\
 & \\
  Honest offeror & $ x_s  + y_s -c_{ws}  $  \\
 Careful acceptor & $ x_s  + y_s -c_{ws} -\alpha c_r $   \\
 & \\ 
 \hline
& \\
  Mixing  & $   x_s  + y_s -c_{ws} -c_r -\frac{c_ry_s}{y_m} $\\
   No Offers & 0 \\
  & \\
 \hline
\end{tabular}
\end{center}


  In the abstract, we cannot pick any one of these four outcomes as
being ``the equilibrium'' of the game. Which outcome should be
predicted depends on the particular circumstances. Sometimes
reputation on the part of the offeror or of the acceptor will make one
of the commitment equilibria the best prediction. In other situations,
commitment will not be plausible and we should expect to see one of
the last two equilibria,  the exact equilibrium depending on
expectations.  The expectations might in turn depend on history, or on
focal points special to the situation being analyzed.


 

\bigskip


\begin{center}
   6. AN ADVERSE SELETION MODEL OF  CONTRACT-READING COSTS  
     \end{center}

 The model described above  is one of moral hazard. The problem is
that the offeror could always choose the efficient, sincere, clause,
but it is not in his interest to do so. Contract-reading costs   have
important effects in an even simpler model, however, in which a given
offeror's contract is either good or bad for the accepter, but not
even the offeror knows which. The entire model of Section 2 can be
used, with just one change: the offeror does not have a choice between
  a sincere clause and a misleading clause.  Rather, with
probability $\gamma$ his only choice is between a sincere clause and
no offer at all; and with probability $(1-\gamma)$ his only choice is
between a misleading clause and no offer at all.

  Most of this section will be spent establishing the equilibria of
this model. The reader uninterested in these details may skip to the
summary at the end of the section.

\noindent
 As in Section 5, it will be useful to start by considering what cannot be
true in equilibrium before we go on to  describe the actual
equilibria.
 
 

 \begin{enumerate}
 \item[(a)]  The acceptor  has positive probability of accepting
without reading in any equilibrium in which offers are made.
Otherwise, the misleading offeror would never offer a clause, which
would make the acceptor want to  deviate to accepting.
 \item[(b)] There cannot be a    separating   equilibrium in pure
strategies. It cannot be an equilibrium for the sincere offeror to
offer and the misleading offeror not to offer, because then the
acceptor would accept without reading, giving the misleading offeror
an incentive to offer. It cannot be an equilibrium for the sincere
offeror not  to offer and the misleading offeror to offer, because
then the acceptor would  reject without reading and the misleading offeror
would deviate to not offering.
\item[(c)] 
 If the acceptor mixes between reading and accepting
outright, the sincere offeror  will offer with probability one.  That
is because his offer will be accepted either outright or after being
read.
 \item[(d)]
   The acceptor will not mix between reading and rejecting. Then the
misleading offeror would never offer, leading to case (b).
  
     \end{enumerate}




 \noindent
  This leaves us with four    equilibria. Two varieties are
pooling
equilibria, in which either both types of offeror     offer clauses or
both do not offer them. The other two are   partially separating
equilibria,   in which  the two types of offerors choose different
mixing probabilities and the acceptor mixes either between reading and
accepting or between rejecting and accepting.

\bigskip


\begin{center}
   {   \it THE GOOD  POOLING EQUILIBRIUM }  (if $\gamma  \geq
Max(\frac{y_m}
{y_m+y_s}, 1-\frac{c_r}{y_m}) $ )
\end{center}
\vspace{-.6in}
 \begin{quotation}
\noindent
  \begin{enumerate}
 \item[\underline{Offerors:}]Both types of offeror  make offers.  
\item[\underline{Acceptor:}]The acceptor   accepts without reading.
\end{enumerate}
\end{quotation}


Either type of offeror gets a positive payoff if he offers a clause
and it is accepted, so to check the equilibrium we only need to
determine whether the acceptor will   accept rather than reject or
read. The acceptor's payoff from accepting without reading is
\begin{equation} \label{e80}
  \pi_{acceptor}(accept) = \gamma y_s -(1-\gamma) y_m.
\end{equation} 
 Equilibrium payoff   (\ref{e80})  is  bigger\footnote{In the
description of the equilibrium, the equivalent of strong inequality
(\ref{e81}) is
changed to a
weak inequality because even an equality  supports the
equilibrium. To avoid awkward phrasing such  as ``is no less than'' or
``is greater than or equal to'' here and elsewhere I have used strong
inequalities in the proofs. }  than  the payoff of zero from
rejecting
if
\begin{equation} \label{e81}
\gamma  > \frac{y_m}{y_m+y_s}. 
\end{equation} 
 
\noindent
  The acceptor's
payoff from   reading is 
\begin{equation} \label{e81a}
  \pi_{acceptor}(read) =  -c_r + \gamma y_s -(1-\gamma)  (0). 
\end{equation} 
Deviation payoff (\ref{e81a})  is less than     equilibrium
payoff   (\ref{e80})   if
\begin{equation} \label{e81b} 
\gamma > 1-\frac{c_r}{y_m }. 
\end{equation} 

\newpage

\bigskip
 \begin{center}
{\it THE BAD  POOLING EQUILIBRIUM  } 
\end{center}
\vspace{-.6in}
 \begin{quotation}
\noindent
  \begin{enumerate}
 \item[\underline{Offerors:}]Neither type makes an offer. 
\item[\underline{Acceptor:}]The acceptor would reject anything
offered.
\item[\underline{Out-of-Equilibrium Belief:}]  The
acceptor believes the probability that the clause is misleading
conditional on it being offered is $\hat{\gamma} \leq  Min(\frac{y_m}
{y_m+y_s}, 1-\frac{c_r}{y_m })$.
 \end{enumerate}
\end{quotation}
      

 Since there is a cost to making an offer,  neither type of offeror
will want to make an offer  the acceptor is sure to reject, so the
offerors will not deviate. 

 The acceptor's subjective expected payoff from deviating to  accept  an out-of-
equilibrium offer is
  \begin{equation} \label{e82}
 \pi_{acceptor}(accept) = \hat{\gamma} y_s -(1-\hat{\gamma}) y_m
\end{equation} 
 Payoff (\ref{e82}) is  bigger than the payoff  of 0 from rejecting 
the out-of-equilibrium offer if
\begin{equation} \label{e83}
\hat{\gamma} < \frac{y_m}{y_m+y_s}. 
\end{equation} 

\noindent
 The expected payoff from deviating to  read an 
 out-of-equilibrium offer is  
 \begin{equation} \label{e83a}
 \pi_{acceptor}(read) = -c_r+ \hat{\gamma} y_s -(1-\hat{\gamma})  (0), 
\end{equation}
which is less than the equilibrium payoff (\ref{e82}) from
rejecting if
\begin{equation} \label{e83b}
\hat{\gamma} < 1-\frac{c_r}{y_m }. 
\end{equation} 


 There is no pooling equilibrium in which the offeror refrains from
making  an offer  and the acceptor would read an   out-of-equilibrium offer. The
prospect of having an offer read would deter the
misleading offeror but not the sincere offeror, and so break up the pooling
behavior.

 \newpage
\bigskip
\begin{center}
{\it THE  READING-ACCEPTING   EQUILIBRIUM}  (if $c_r  \leq
Min(   (1-\gamma)y_m,\frac{y_m y_s}{y_m+y_s})$)  
\end{center}
\vspace{-.6in}
 \begin{quotation}
\noindent
  \begin{enumerate}
 \item[\underline{Sincere Offeror:}]The sincere offeror  makes an
 offer.
 \item[\underline{Misleading Offeror:}] The misleading offeror
 makes
an offer with probability $\theta_m = \frac{\gamma c_r}{(1-\gamma)
(y_m-c_r)}$.
 \item[\underline{Acceptor:}] The acceptor  accepts with
probability $\theta_a= \frac{c_{wm}}{x_m}$ and otherwise  reads the
clause and accepts only if it is sincere.
\end{enumerate}
\end{quotation}


 


The sincere offeror makes an offer  because he knows the acceptor will
accept it, with or without reading the clause.

 For   the misleading offeror  to use a mixed strategy, he must be
indifferent between making an  offer and not making one. This requires
that
 \begin{equation} \label{e84}
\pi_{misleading\; offeror} (offer) = -c_{wm} + \theta_a x_m + (1-
\theta_a)(0)  = \pi_{misleading\; offeror} (no\; offer )=0,
\end{equation} 
 which tells us that 
\begin{equation} \label{e85}
\theta_a =\frac{c_{wm}}{x_m}.
\end{equation} 
 Assumption ({\ref{e00}) tells us that expression (\ref{e85}) is less
than one, and so can be a probability.

	 For the acceptor to be willing to mix between  reading and
accepting requires that he be indifferent between them. With
probability $ \gamma + \theta_m (1-\gamma)$ the offeror makes an
offer.  Fraction $  \frac{\gamma} {\gamma + \theta_m (1-\gamma)}$ of
those offers are sincere and fraction $ \frac{\theta_m (1-\gamma) } {
\gamma + \theta_m (1-\gamma)}$ are misleading. Hence,
\begin{equation} \label{e86}
\pi_{acceptor} (accept ) = \frac{\gamma}  { \gamma + \theta_m (1-
\gamma)} (y_s) + \frac{\theta_m (1-\gamma) }{ \gamma + \theta_m (1-
\gamma)}(-y_m)
\end{equation} 
 and 
\begin{equation} \label{e87}
\pi_{acceptor} (read) = -c_r+ \frac{\gamma} {\gamma + \theta_m (1-
\gamma)} (y_s) + \frac{\theta_m (1-\gamma) } { \gamma + \theta_m (1-
\gamma)}(0).
\end{equation} 
 Equating these two payoffs yields
\begin{equation} \label{e88}
\theta_m = \frac{\gamma c_r}{(1-\gamma)(y_m-c_r)}.
\end{equation} 
   This  is always positive, and it will be less than one if $c_r<(1-
\gamma)y_m$.

 We must also check that the acceptor would not prefer to deviate to
rejecting outright. This has a payoff of zero, which must be compared
with the equilibrium payoff. The equilibrium payoff can be written
from equation (\ref{e87}}) and the equilibrium value of $\theta_m$ as
\begin{equation} \label{e89}
\pi_{acceptor} (read) = -c_r+ \frac{\gamma} {\gamma + \theta_m (1-
\gamma)} (y_s) = -c_r+ \frac{\gamma} {\gamma +  [\frac{\gamma c_r}{(1-
\gamma) (y_m-c_r)}] (1-\gamma)} (y_s).
\end{equation} 
 It turns out that equation (\ref{e89}) is positive if $c_r <
\frac{y_m y_s}{y_m +y_s}$.

 \bigskip





\bigskip
\begin{center}
{\it THE   ACCEPTING-REJECTING   EQUILIBRIUM } (if $c_r  \geq
\frac{y_m y_s}
{y_m+y_s}$ )
\end{center}
\vspace{-.6in}
 \begin{quotation}
\noindent
  \begin{enumerate}
 \item[\underline{Sincere Offeror:}]The sincere offeror  makes an
 offer with probability  $\theta_s$ 
 \item[\underline{Misleading Offeror:}] The misleading offeror
 makes
an offer with probability $\theta_m$.
 \item[\underline{Acceptor:}] The acceptor  accepts  the clause
with probability $\frac{c_{ws}}{x_s}$ and otherwise  rejects it.

 If $\gamma \leq  \frac{y_m  }{y_m+y_s}    $   then $\theta_s = 1$ and
$\theta_m =
\frac{\gamma y_s}{(1-
\gamma)  y_m}$. 

If $\gamma \geq  \frac{y_m  }{y_m+y_s}    $ then $\theta_s = \frac{
(1-\gamma)y_m}
{\gamma y_s}$ and $\theta_m = 1$.



\end{enumerate}
\end{quotation}

 
 

 For   the sincere offeror  to use a mixed strategy, he must be
indifferent between making an  offer and not making one. This requires
that
 \begin{equation} \label{e89a}
\pi_{sincere\; offeror} (offer) = -c_{ws} + \theta_s x_s + (1-
\theta_a)(0)  = \pi_{sincere\; offeror} (no\; offer )=0,
\end{equation} 
 which tells us that 
\begin{equation} \label{e90}
\theta_a =\frac{c_{ws}}{x_s}.
\end{equation} 
Assumption ({\ref{e00}) tells us that expression (\ref{e85}) is less than one, and
so can be a
probability.

 For   the misleading offeror  to use a mixed strategy, he must be indifferent
between making
an  offer and not making one. This requires,   as in the Reading-Accepting
Equilibrium, that
 \begin{equation} \label{e91}
\pi_{misleading\; offeror} (offer) = -c_{wm} + \theta_a x_m + (1-
\theta_a)(0)  = \pi_{misleading\; offeror} (no\; offer )=0,
\end{equation} 
 which tells us that 
\begin{equation} \label{e92}
\theta_a =\frac{c_{wm}}{x_m}.
\end{equation} 
 Assumption ({\ref{e00}) tells us that expression (\ref{e85}) is less
than one, and so can be a probability.

  Equations (\ref{e90}) and  (\ref{e92}) contradict each other unless the
parameters take very
special values. This
tells us that it is almost never true that both types of offerors use mixed
strategies in the same equilibrium. So we must look at two cases:

\noindent
	{\it Case 1.} Suppose that $\theta_s=1$, so the sincere offeror
does not mix. For the acceptor to be willing to mix between rejecting
and accepting requires that he be indifferent between them.  With
probability $ \gamma + \theta_m (1-\gamma)$ the offeror makes an
offer.  Fraction $  \frac{\gamma} {\gamma + \theta_m (1-\gamma)}$ of
those offers are sincere and fraction $ \frac{\theta_m (1-\gamma) } {
\gamma + \theta_m (1-\gamma)}$ are misleading. Hence, just as in the
Reading-Accepting   Equilibrium,
\begin{equation} \label{e93}
\pi_{acceptor} (accept ) = \frac{\gamma}  { \gamma + \theta_m (1-
\gamma)} (y_s) + \frac{\theta_m (1-\gamma) }{ \gamma + \theta_m (1-
\gamma)}(-y_m).
\end{equation} 
  Since $ \pi_{acceptor} (read)=0$, equating the
  two equilibrium  pure-strategy payoffs yields
\begin{equation} \label{e94}
\theta_m = \frac{\gamma y_s}{(1-\gamma)(y_m  )}.
\end{equation} 
   This  is always positive. It  will be less than one if $\gamma 
<\frac{y_m}{ y_s+y_m}$.

 We must also check that the acceptor would not prefer to deviate to
reading the clause. This has an expected payoff of 
 \begin{equation} \label{e95}
\pi_{acceptor} (read) = -c_r+ \frac{\gamma} {\gamma + \theta_m (1-
\gamma)} (y_s) + \frac{\theta_m (1-\gamma) } { \gamma + \theta_m (1-
\gamma)}(0) =   -c_r+ \frac{\gamma} {\gamma + [\frac{\gamma y_s}{(1-
\gamma)(y_m  )}] (1-
\gamma)} (y_s).  
\end{equation} 
 After simplifying, the acceptor's payoff from reading the clause is
less than his equilibrium payoff of zero if
 \begin{equation} \label{e96}
c_r >\frac{y_m y_s} {y_m + y_s } .
\end{equation} 


\noindent
	{\it  Case 2.}  Suppose that $\theta_m=1$, so the misleading offeror
does not mix.   For the acceptor to be willing to mix between
rejecting and accepting requires that he be indifferent between them.
With probability $ \gamma \theta_s +  (1-\gamma)$ the offeror makes
an offer.  Fraction $  \frac{\gamma \theta_s} {\gamma \theta_s+   (1-
\gamma)}$ of those offers are sincere and fraction $ \frac{ (1-
\gamma) } { \theta_s\gamma +  (1-\gamma)}$ are misleading. Hence,
\begin{equation} \label{e97}
\pi_{acceptor} (accept ) = \frac{\gamma \theta_s} {\gamma \theta_s+
(1-\gamma)} (y_s) +  \frac{ (1-\gamma) } { \theta_s\gamma +  (1-
\gamma)}(-y_m).
\end{equation} 
  Since $ \pi_{acceptor} (read)=0$, equating the two equilibrium
pure-strategy payoffs yields
\begin{equation} \label{e98}
\theta_s = \frac{ (1-\gamma) y_m}{\gamma y_s}.
\end{equation} 
   This  is always positive. It  will be less than one if $\gamma >
\frac{y_m  }
{y_m+y_s}.$

 We must also check that the acceptor would not prefer to deviate to
reading the clause. This has an expected payoff of 
 \begin{equation} \label{e99}
\begin{array}{ll}
\pi_{acceptor} (read) &= -c_r+\left( \frac{\gamma \theta_s} {\gamma \theta_s+
(1-\gamma)}\right)  \left(y_s \right) +  \left(\frac{ (1-\gamma) } { \theta_s\gamma
+  (1-
\gamma)}\right) \left(0 \right)\\
 & \\
   &  =  -c_r+  \left(\frac{\gamma  \left(\frac{ (1-\gamma) y_m}{\gamma y_s}
\right) } {\gamma
\left( \frac{ (1-\gamma) y_m}{\gamma y_s}  \right)+   (1-\gamma)}  \right)\left(y_s
\right).
\end{array}
\end{equation} 
 After simplifying, the acceptor's payoff from deviating to reading the clause is
less than his
equilibrium payoff of zero if
 \begin{equation} \label{e100}
c_r > \frac{y_m y_s}{y_m+y_s},
\end{equation} 
 a condition identical to that for Case 1. 



 \bigskip

\noindent
 {\it Summary of the  Adverse Selection Model}

  There are four possible equilibria. Under any
parameters, the Bad Pooling Equilibrium exists, in which no offers are
made because any that were offered would be rejected. If the
proportion of sincere offerors is high enough, the Good Pooling
Equilibrium exists, in which the offeror always offers and the
acceptor accepts without reading. If the reading cost is low enough,
the Reading-Accepting Equilibrium exists, in which both types of
offers are made to some extent (but some misleading offerors make no
offer) and the acceptor mixes between reading and accepting outright.
If the reading cost is too high for the Reading-Accepting Equilibrium,
the Rejecting-Accepting Equilibrium exists: the acceptor mixes
between reading and accepting, but never reads. Both types of offers
are made, with one type   of offeror or the other mixing between
offering and not offering.

 
 The Bad Pooling Equilibrium is the equivalent of the No-Offer
Equilibrium in the moral hazard model, and the Reading-Accepting
Equilibrium is the equivalent
of the Mixed-Strategy Equilibrium. The Good Pooling   and Rejecting-Accepting
Equilibria do not have such close
  equivalents in the moral hazard
model, since in that model if the acceptor never reads, the offeror
will always choose the misleading clause.

 The usefulness of the adverse selection model is to  show  that   contract-
reading costs  are not important just because of moral hazard, the possibility that
one party to a contract deliberately chooses to be opportunistic. Contract-reading
costs affect the situation in roughly the same way whether a model is based on 
  moral hazard   or o 
adverse selection. It is not the offeror's choice
between sincere and misleading clauses, but   two other things which  drive the
outcome in either kind of model:   (a)  the offeror  must
decide  between
offering and not offering a new clause, and (b)   the
acceptor must decide to read or not read, knowing that both sincere
and misleading clauses are possible.

  The correspondence between the two model is not exact because behavior in the
adverse selection model is more constrained by the assumptions: there is no
possibility of either all clauses being sincere or none being sincere.   Since not
every offer can be sincere,    the first-best surplus is less than in the moral
hazard model. For this reason, commitment to reading clauses  is not so useful
under adverse selection. It can, to be sure, avoid the Bad Pooling Equilibrium, but
the benefit depends on the proportion of sincere offerors  in the population (the
$\gamma$ parameter).  If that proportion is low enough, the cost of reading, $c_r$,
can even be greater than the benefit of escaping the Bad Pooling Equilibrium,
$\gamma y_s$, yielding a negative payoff, so the acceptor would not want to commit
to reading offered clauses.  The other effect of ruling out extreme proportions of
misleading or sincere clauses is that since not every offer can be misleading,  the
acceptor is less vulnerable than under moral hazard.  That is why in the  adverse
selection model the acceptor is willing to follow the  equilibrium behavior of the
Good Pooling   and Rejecting-Accepting Equilibria; if  the acceptor never reads
clauses but does accept them sometimes, some of the accepted clauses will still be
sincere, unlike in the moral hazard model.

  Both models have as equilibria the extreme result that no offeror offers a clause
because the acceptor would reject any clause offered without reading it. The
resulting inefficiency   is less in the adverse selection model.  In the moral
hazard model, the offeror could always offer a sincere clause, so when he offers a
misleading clause there is an opportunity cost. In the adverse selection model, the
offeror  who offers a  misleading clause  could not have offered a sincere one, so
the inefficiency is less--- contractual incompleteness is sometimes efficient in
the adverse selection model.  In both models, however, the pessimistic equilibrium
results in the loss of all the possible gains from adding extra clauses to
contracts and thus explains inefficient incomplete contracts.


\bigskip

\begin{center}
   7.  INTERPRETATION 
     \end{center}

 
     The Introduction asked the question of why contracts are incomplete, and the
model above has shown  that contract-reading costs can give the answer. The model
has other things to teach, however.    Most
fundamentally, even if the parties to a contract cannot trust each other,
negotiation still increases welfare.   Lengthy dealmaking sessions are not
necessarily
inefficient: to the extent  that they add mutually beneficial details
to the deal, they are efficient.  Dealmakers are productive members of
society, and quick agreement is not necessarily a sign of efficiency.    In the No-
Offer Equilibrium, quick and simple agreement is a sign of extreme inefficiency.
Since   negotiation, as opposed to simple bargaining over shares of a surplus,
enhances efficiency, it is worth considering what  encourage negotiation.  Below I
will lay out ten lessons of the model for law and business.

\bigskip

\noindent
{\it 1. Contract-reading costs matter as much as contract-writing
costs. } Although the contract-writing costs, $c_{ws}$ and $c_{wm}$,
have an influence in this model, not much would change if they were
set to zero.  As Table 1 shows, these costs are simply subtracted from
the social surplus like any simple transactions cost.  The contract-reading cost,
$c_r$, is
much more important. It has an
indirect effect, via the subtraction of $\frac{c_r y_s} {y_m}$, as
well as a direct effect. This effect is still continuous in $c_r$, so
if contract-reading costs are small, it might seem that their effect
on welfare is also low. The contract-reading cost    has a second
impact, however:  it  generates multiple equilibria. The
contract-reading cost, in combination with pessimistic expectations,
can lead to  the No-Offer Equilibrium, in which  the benefit from  the
sincere clause is entirely lost.  The ultimate effect
of a contract-reading cost of $c_r$ can  then be much greater than the
magnitude of $c_r$ itself. Lumping all 
``transaction costs'' together--- contract-reading and contract-writing costs
both--- is inappropriate.     A small contract-reading cost can destroy
the entire gains from trade.

  Contract-reading costs are  both  realistic and hard to eliminate. It is
relatively easy to write  fifty new pages for a
contract to provide for  extra contingencies  but it is quite
difficult for the reader to be sure what those fifty pages contain.
Standard ``boilerplate'' contracts, written for no
particular transaction and pulled out once a contract must be
executed,  are a good solution for the problem of  contract-writing costs,   but
not for
contract-reading costs.\footnote{The Web now has many sites offering
boilerplate. Some offer them for free, e.g.,  Legal-Forms-Kit.com,
http://www.legal-forms-kit.com/freelegalforms.html (August 15, 2001),
and some at a price, e.g.,    Legal-Forms.ca, http://www.contracts-on-demand.com/
(August 15, 2001).    } The accepting side of the contract
still does not know what the boilerplate contains and must worry about
whether it is pure boilerplate or boilerplate with some non-standard
clauses cleverly hidden inside.

\noindent 
 {\it 2.  Legal default rules, or even mandatory rules are important
to overcome contract-reading costs. } One view of contract law is that its
importance is limited by the possibility that parties can always replace the legal
defaults with their own contract terms, limiting the loss from inefficient laws to
the contract-writing cost incurred when everyone replaces them with customized
terms.  The model shows, howver, that  legal  default
rules are important for more than just to save contract-writing costs. If an
efficient default rules is in place, the two parties    often will not  need the
sincere
clause of the
model--- it will be automatically added by a neutral third party, the law, unless
they took steps to remove it.    The default rule
is important for much more than just saving the costs $c_r$ and
$c_{ws}$. Even if the contract-reading and contract-writing costs are
small, the default rule is important, because it replaces the negotiation game.
This is
similar to the
conclusions of  various  models of strategic contracting  under
incomplete information---see  Ayres \& Gertner (1989, 1992), Hermalin
\& Katz (1993),  and Jason Johnston (1990), but  here   the strategic behavior does
not arise from incomplete information but from the contract clause itself.

 One might go further and use this model to argue for mandatory contract
rules, which override  whatever may be written in the contract. If it
is practical for a court to determine that a clause is misleading, the
best solution is for courts to refuse to enforce such clauses.   
Courts do this to some extent, refusing to enforce suspicious fine print,
which is the subject of the  1990 Katz article discussed in the
Introduction.

The disadvantage of  legal default and mandatory rules is, of course,
that they reduce  the flexibility of the contract.  If different
``sincere clauses'' are appropriate for  different contracts,  it is
difficult for courts to choose which clause should be used, as  Alan
Schwartz (1993) emphasizes.   Often, the  parties will not  find the  legal default
rule efficient and the courts will not be able to  tell whether a clause was exante
fair to the acceptor or not.

\noindent
 	{\it 3.  A reputation for honesty in negotiation  is a valuable asset.} The
contracting
parties do best  if the offeror is intrinsically honest, the case of precommitment
to offering
sincere clauses analyzed in Section 3.  His honesty does not eliminate the
contract-writing
cost, but it does eliminate the need to read the contract and it  allows efficient
clauses to be
added. Any player who has established a reputation for honesty will  be an
attractive business partner and   be offered  more attractive
contracts.

\noindent
	{\it 4.  Good fences make good neighbors. It is better to deal with someone
who is on
guard against you. }    Even if the offeror  cannot be trusted to be honest  in the
absence of
external influences, if the acceptor can commit to always reading the offers,
welfare is almost
as high, as Section 4 showed. The offeror actually
prefers to
deal with an acceptor who always reads    clauses, because he   need not worry
about
pessimistic expectations which would cause the acceptor to dismiss his offers
without serious
consideration.

  \noindent
  {\it 5.   Corporate lawyers are worth their salary even if
they never discover flaws in contracts.} Point (4) implies that reading is valuable
even if
it never reveals anything untoward.  The
purpose of a company's legal staff is to deter the other side from
trying to be sly or dishonest, and if the staff's lawyers are well
enough respected, they will never   discover any dishonesty. The corporate
counsel's veto of a
contract term is like the atomic bomb, most useful when not used. This
supplements the  list of reasons---which in the context of this paper
amount to finding Pareto-improving clauses--  that Ronald Gilson (1984) lays out
for why     corporate lawyers are socially useful.

\noindent {\it 6.   A mistrustful attitude in negotiations can be
self-enforcing.} If a model has multiple equilibria, that means that
expectations are important to the outcome. If the acceptor expects the
offeror to offer only misleading clauses, he will not bother to read
any clauses that are offered, and so the offeror will offer none. This
is the worst case from the point of view of both parties, and changing
the expectations---however that might be done---is  an important
prerequisite to negotiations.

\noindent
	{\it 7.   Inefficient work rules can persist indefinitely in union labor
contracts,
even when both union and management recognize that Pareto improvements are
possible.   } Some
socially inefficient union work rules can be explained in terms of redistribution
within the
union, e.g., ``no show'' featherbedding jobs which can be used by a union to reward
certain
members.  Others, however, such as trains being required to carry double the needed
crew,
truck drivers
being forbidden to help unload trucks, and painters not being allowed to use spray
guns of
certain widths are harder to explain.\footnote{These and other examples can be
found in
Reynolds (1987) starting at page 107.} A corollary of result  (6) is that   when
labor and
management mistrust each other, they may continue to renew a contract known to be
inefficient
rather than trying to propose improvements which the other side might  believe were
really
attempts  to sneak an advantage.

\noindent 
 {\it 8. Forcing the parties to come to the bargaining table can help them.} A
common feature
of labor laws is a requirement that  labor and management come to the bargaining
table and
negotiate ``in good faith''.\footnote{Section 8(d), 29 U.S.C. @ 158(d) (1988)
defines
the duty to
bargain as ``the mutual obligation of the employer and the representative of the
employees to
meet at reasonable times and confer in good faith with respect to wages, hours, and
other terms
and conditions of employment . . . but such obligation does not compel either party
to agree to
a proposal or require the making of a concession.'' A representative lawsuit
is {\it NLRB v. Billion Motors, Inc.}, 700 F.2d 454, 456 (8th Cir. 1983), in which
a union
complained that the company's negotiator was unprepared, failed to show up to
meetings, made
sham proposals, and announced impasse prematurely. For a legal discussion by an
economist that
discusses the usefulness of the duty to bargain in generating information, see
Keith Hylton
(1994). } This does not mean that they must make offers acceptable to each other,
only that
they must talk, so it seems a peculiar and useless requirement. The negotiation
model suggests
  it is not, because it may serve as a requirement that the parties read  each
other's
offers, which   can raise welfare by overcoming pessimistic out-of-equilibrium
beliefs.

\noindent  
 {\it 9.  Warranties cannot entirely solve the problem of
product
quality.  }   Product quality   is   not so serious a problem as contract
terms, because
if the quality were the only problem, warranties could be provided. The quality of
the
warranty itself, however, is also    in question. The warranty's  fine print may
take back what
opening   sentences seem to provide. One cannot have a warranty of the warranty; at
best, the
law must fall back on canons of construction such as that vague contracts are
construed against
the writer.

   The negotiation model could   be adapted to a situation in which product
quality is
uncertain but the   buyer can inspect the product at low cost. This inspection
might  simply
take the form of reading promotional materials provided by the seller, if the law
provided
penalties for sellers who lie.    The model suggests that expectations will
determine the
outcome, and that the equilibrium may be in mixed strategies. It may also result in
no
information being provided because the buyer, being pessimistic, would not go to
the effort of
inspecting it anyway. In such a case, the seller would have to provide incentives
for the buyer
to incur the costs of inspecting or reading.\footnote{We are beginning to see
advertisers
paying consumers to read advertisements on the Internet. See ``Are Advertisers
Ready to Pay
Their Viewers?'' {\it Wall Street Journal}, Bart Ziegler, November 14, 1996,
reprinted as pages
218-220 of  {\it Readings in Games and Information}, Eric Rasmusen, editor, Oxford:
Blackwell
Publishers, 2001. }

 	

\noindent
    {\it 10. Offers and mechanisms that are theoretically attractive
will be rejected by rational agents if they are too complicated.  }
  Two  standard puzzles for economists are why more complex contracts
are not used  in practice and why experimental subjects reject complex
offers that  yield   high  expected utility.  Mechanisms of the
kind discussed in Tirole (1999) can achieve the first-best under
surprisingly poor informational conditions, but the mechanisms are
often complicated, involving a menu of contracts  and coordination of
Nash expectations when there are multiple equilibria. Real-world
contracts may involve many contingencies, but they are rarely as
difficult to design or understand as these mechanisms. 
Also, numerous puzzles in the psychology of decision making  
contradict expected utility theory because experimental subjects choose simple
offers that yield them lower utility.  The two best known are perhaps the
Allais Paradox and the Ellsberg Paradox. Both of these involve  the
typical subject    preferring    simple  offers to more complicated
offers that would yield them higher expected utility,where it is the
clever design of the offers that allows us to make that claim about their
utility function.\footnote{For descriptions of the paradoxes
see pages 163-167 of Dawes (1988). Dawes notes that decision theorists have tried
to introduce new axioms of decision that essentially add pessimism, but ``the
assumption of pessimism implies the belief that one's choice somehow affects the
probabilities of the  consequences'' (p. 167). That, of course, is what mistrust of
the offeror is all about. } 



  Contract-reading costs help explain both phenomenon. In this article's model, a
complex contract   is    a
  contract with one extra clause added.  Complex
mechanisms may be theoretically ideal, but only in a world where the
parties to the mechanism can understand them costlessly. Otherwise,
the acceptor of such a mechanism  rationally fears that the complexity
hides something  that is to his disadvantage and to the offeror's
advantage. The puzzles of decisionmaking are similar. When someone
makes an intricate   offer---probabilities of probabilities, for
example, as in the Ellsberg Paradox---the acceptor rationally is
apprehensive. This is true even in an experimental setting, in which
the offeror seems unlikely to be trying to maximize profits, since
experimenters are notorious for trying to  trick  subjects into making
wrong decisions. The simple choice may be the wrong choice, but at
least its degree of wrongness is limited  since it is understandable. 
 







\bigskip

 
\begin{center}
 8.  CONCLUDING REMARKS
 \end{center}

	 After the long list of lessons in Section 7, it may be helpful for me to
summarize the basics of  this article.  Much  real-world contracting involves
finding  new clauses to add to a basic agreement, clauses which may or may not
increase the welfare of both parties. The parties must decide which complications
to propose, how closely to  examine the other side's proposals, and whether to
accept them.   In this article,  negotiation has been modelled as  an auditing game
in which one player offers a clause that the other player may or may  not examine
carefully.     The model suggests a reason   why contracts are incomplete:
contract-reading  costs  matter  as much as contract-writing  costs. Fine print
that is  cheap to write can be expensive to read carefully enough to detect the
absence of trap clauses artfully written to benefit the writer. As a result,
complicated clauses that purport to benefit both parties may be rejected outright
even if they really do benefit both parties, and  contract is left incomplete.

\bigskip

\noindent
  {\bf Contact Information and Acknowledgements}\\
  Eric B. Rasmusen is
  Professor of Business Economics and Public Policy and
Sanjay Subhedar Faculty Fellow, Indiana University, Kelley School of
Business, BU 456, 1309 E. 10th Street, Bloomington, Indiana, 47405-
1701. Office: (812) 855-9219. Fax: 812-855-3354. Erasmuse@indiana.edu.
Php.indiana.edu/$\sim$erasmuse.

\bigskip

\noindent 
 Professor Rasmusen thanks Maria Arbatskaya, William Bright,  Lutz
Busch,   Peter Cramton, Kenneth Elzinga,  T. Lynn Fisher, Benjamin
Hermalin, Michihiro Kandori, Felice Martinello, Wolfgang Pesendorfer,
J. Mark Ramseyer, David Waterman, two anonymous referees   and
participants in seminars at Brock University, CIRANO (Montreal),
Indiana University,  the  U. S. Department of Justice, Kyushu
University, the University of Manitoba, Otaru University of Commerce,
the Central Bank of Turkey, Virginia Polytechnic Institute,  the
University of Virginia, and the   American Law and Economics
Association for helpful comments. I thank  Harvard Law School's Olin
Center   and the University of Tokyo's Center for International
Research on the Japanese Economy for their hospitality.   Not  all of
those I thank have seen this draft, and they bear no responsibility
for errors.}

 \newpage

\begin{center} {REFERENCES} \end{center}

Avenhaus, Rudolf, Bernhard von Stengel \& Shmuel Zamir (2002),
``Inspection Games, '' from Volume III of    {\it The Handbook of Game
Theory}, edited by Robert Aumann and Sergiu Hart, forthcoming.

Ayres, Ian  \& Robert Gertner (1989) ``Filling Gaps in Incomplete
Contracts: An Economic Theory of Default Rules,''   {\it Yale Law
Journal}, 99: 87-130 (October 1989).

-----\& -----(1992) ``Strategic Contractual Inefficiency and the
Optimal Choice of Legal Rules,''   {\it Yale Law Journal},    101:
729-773 (January 1992).


 Baiman, Stan and Joel Demski (1980) ``Economically Optimal
Performance Evaluation and Control Systems,'' {\it Journal of
Accounting Research}, 18: 184-220 (Supplement 1980).

  Bernheim,B.-Douglas \& Michael D.  Whinston (1998) ``Incomplete
Contracts and Strategic Ambiguity,'' {\it  American Economic Review},
88:   902-32 (September 1998).

 

Cho, In-Koo \& David Kreps (1987) ``Signaling Games and Stable
Equilibria,'' {\it Quarterly Journal of Economics,}   102: 179-221
(May 1987).

Chung, Tai-Yeong  (1991) ``Incomplete Contracts, Specific Investments,
and Risk Sharing,'' {\it  Review of Economic Studies},   58: 1031-1042 (October
1991).

Dawes, Robyn (1988) {\it    Rational Choice in an Uncertain World}, San Diego:
Harcourt, Brace, Jovanovich Publishers, 1988.

Dresher, Melvin (1962) ``A Sampling Inspection Problem in Arms Control
Agreements: A Game-Theoretic Analysis,'' Memorandum No. RM-2972-ARPA,
RAND Corporation, Santa Monica, California.

Gilson, Ronald (1984) ``Value Creation by Business Lawyers: Legal
Skills and Asset Pricing,'' {\it Yale Law Journal} 94: 244-313
(December 1984).

  Hart, Oliver \& John Moore   (1988)  ``Incomplete Contracts and
Renegotiation,'' {\it Econometrica}, 56: 755-786 (July 1988).


Hermalin, Benjamin E.  \& Michael L. Katz,  ``Judicial Modification of
Contracts between Sophisticated Parties: A More Complete View of
Incomplete Contracts and Their Breach,'' {\it Journal of Law,
Economics, \&
Organization,}  9: 230-255 (October 1993).



Holmstrom, Bengt \&   Paul R.  Milgrom (1991) ``Multi-Task Principal
Agent Problems: Incentive Contracts, Asset Ownership and Job Design,''
{\it Journal of Law, Economics, and Organization}, 7: 24-52 (Special
issue, 1991).

 Hylton, Keith (1994) ``An Economic Theory of the Duty to Bargain,''
{\it Georgetown Law Journal}, 83: 19-76 (November 1994).

 Johnston, Jason (1990) ``Strategic Bargaining and the Economic Theory
of Contract Default Rules,''   {\it Yale Law Journal},   100: 615-657
(December 1990).

 Katz, Avery (1990) ``Your Terms or Mine?  The Duty to Read the Fine
Print in Contracts,'' {\it RAND Journal of Economics},   21: 518-537
(Winter 1990).

Kennan, John \& Robert Wilson (1993) ``Bargaining with Private
Information,'' {\it Journal of Economic Literature},  31: 45-104
(March 1993).

 

Lulfesmann, Christoph (2001) ``Incomplete Contracts, Non-Contractible
Quality, and Renegotiation,''{\it  Contributions to Theoretical
Economics},    1: 2.
  http://www.bepress.com/bejte/contributions/vol1/iss1/art2.

  Macaulay, Stewart (1963) ``Non-Contractual Relations in Business: A
Preliminary Study,''
{\it 
American Sociological Review},    28: 55-67 (February 1963).

 
Myerson, Roger \& Mark Satterthwaite (1983)  ``Efficient Mechanisms
for Bilateral Trading,'' {\it Journal of Economic Theory}, 29:1-21
(April 1983).


 Rasmusen, Eric (1993) ``Lobbying When the Decisionmaker Can Acquire
Independent Information,'' {\it  Public Choice }  77: 899-913.

-----(2001) {\it Games and Information: An Introduction to Game
Theory}, Third edition (first edition 1989). Oxford: Blackwell
Publishing, 2001.


  Reynolds,  Morgan (1987) {\it Making America Poorer: The Cost of
Labor Law}, Washington: Cato Institute, 1987.


Schwartz, Alan (1993) ``The Default Rule Paradigm and the Limits of
Contract Law,'' {\it Southern California Interdisciplinary Law
Journal}, 3: 390-419   (Fall 1993).

Sebenius,  James (1992)   ``Negotiation Analysis: A Characterization
and Review,'' {\it Management Science},  38: 18-38  (January 1992).

 Spier, Kathryn (1992) ``Incomplete Contracts and Signalling,'' {\it
RAND Journal of Economics},   23: 432-43 (Autumn 1992).

Stigler, George (1980) ``An Introduction to Privacy in Economics and
Politics,'' {\it Journal of Legal Studies}, 9: 623-644 (December 1980)
.

Tirole, Jean (1999) ``Incomplete Contracts: Where Do We Stand?'' {\it
Econometrica} 67: 741-781 (July 1999).


 Townsend, Robert (1979) ``Optimal Contracts and Competitive Markets
with Costly State Verification,'' {\it Journal of Economic Theory},
21: 265-293 (October 1979).

Van Damme, Eric (1989) ``Stable Equilibria and Forward Induction,''
{\it Journal of Economic Theory},  48: 476-496  (August 1989).

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