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\begin{center}
{\bf Errata for Eric Rasmusen's Games and Information,
Third
Edition, arranged by page number. Updated July 18, 2003. 123 October 2008.
}
\end{center}
I apologize for the errors in this book, but I have tried to keep
this errata current as partial compensation. I extend my gratitude to
those readers who have pointed errors out to me. Specifically, I thank
Kyung Baik, David Collie (Cardiff Business School), Ralf Elsas (Goethe
U.), Diego Garcia (Dartmouth),
Bettina Kromen (U. Koeln), Eva Labro (London School of Economics),
Frank P. Maier-Rigaud, Ron Mallon (U. of Utah), Alexandra Minicozzi
(U. Texas), Luis Pacheco (U. Portucalense), Pedro Sousa (U.
Portucalense), and Charles Tharp. Martin Caley of the Isle of Man
Treasury was particularly helpful, and I thank him for his very
careful reading.
If you find any new errors, please let me know, so future readers can
be warned. Do not be shy-- if you think it might be an error, do not
feel you have to check it out thoroughly before letting me know. It's
my duty to make sure and to be clear, not yours.
I can be reached at Eric Rasmusen, Indiana University, Kelley
School of Business, Rm. 438, 1309 E 10th Street, Bloomington, Indiana,
47405-1701. Office: (812) 855-9219. Fax: 812-855-3354.
Erasmuse@Indiana.edu. The webpage for
{\it Games and Information} is at
\url{http://rasmusen.org/GI/}.
To view Acrobat (.pdf) files, you will need to download the Adobe
Acrobat Reader from http://www.adobe.com/acrobat/readstep.html.
If you don't use the web, just let me know and I'll send you
hardcopy.
There was a reprint in October 2001, so you may find some of these
errors corrected in your printing of
the book.
Besides the errata below, I
have digitized photos of a few of the pages with corrections. These
photo files are each around 300K in size.
Errata not fixed in the October 2001 reprint:
Preface, page xxiv: ``Michael Mesterton-Gibbons
(Pennsylvania)'' is wrong. It should be ``Mike Mesterton-Gibbons
(Florida State)''.
The computer addresses changed at IU, and I don't have the pdf files below up on the web any more. If you want them, email me and I'll see if I can find them.
*Chapter 1, page 24 and its \url{http://pacioli.bus.indiana.edu/erasmuse/GI/pages/p024.pdf} replacement text (important mistake)
Chapter 5, Reputation and Repeated Games with Symmetric Information, \url{http://pacioli.bus.indiana.edu/erasmuse/GI/pages/p118.jpg} page 118 (arrow pointed the wrong way)
Chapter 6, Dynamic Games with Incomplete Information, page 149: \url{http://php.indiana.edu/~erasmuse/GI/ed5.txt} extra explanation
Chapter 7, Moral Hazard: Hidden Actions \url{http://pacioli.bus.indiana.edu/erasmuse/GI/pages/p168.jpg} page 168 (e* computation mistake, differentiation mistake)
Chapter 8, Further Topics in Moral Hazard \url{http://pacioli.bus.indiana.edu/erasmuse/GI/pages/fig08.2.jpg} page 200 (Figure 8.2 drawn more to scale)
Chapter 15, Entry, \url{http://pacioli.bus.indiana.edu/erasmuse/GI/pages/p391.jpg} page 391 and \url{http://pacioli.bus.indiana.edu/erasmuse/GI/pages/p392.jpg} page 392
\url{http://pacioli.bus.indiana.edu/erasmuse/GI/pages/p396.jpg} Mathematical Appendix, page 396
\newpage
\noindent
{\bf Chapter 1 The Rules of the Game }
p. 16. second paragraph, line 3 (fixed in
October 2001 reprint). OldCleaner's expected profit is 32, not 38,
with a Low price. This does not affect the suboptimality of that
strategy, though.
p. 24. Near Table 1.4. Drop
Table 1.4 and the discussion of the Swiss Cheese Game,since this does
not fit the definition of ``weakly dominated'' that I defined
earlier. So drop:
``The easiest example is table 1.4's Swiss Cheese Game.
Every strategy is weakly dominated for every player.
Thus, one iterated dominance equilibrium is {\it (Up,
Left)}, found by first eliminating Smith's {\it Down}
and then Jones's {\it Right}, but {\it (Down, Right)} is
also an iterated dominance equilibrium. And, in fact,
every strategy combination is also a weak dominant
strategy equilibrium as well as an iterated dominance
equilibrium.
\begin{center}
{\bf Table 1.4 The Swiss Cheese Game }
\begin{tabular}{lllccc}
& & &\multicolumn{3}{c}{\bf Jones}\\
& & & {\it Left} & & $ Right$
\\
& & $ Up$ & {\bf 0,0} & $\leftrightarrow$ &
{\bf 0,0} \\
& {\bf Smith:} &&$\updownarrow$& & $\updownarrow$ \\
& & {\it Down } & {\bf 0,0} &
$\leftrightarrow$ & {\bf
0,0} \\
\multicolumn{6}{l}{\it Payoffs to: (Smith, Jones) }
\end{tabular}
\end{center}
The Swiss Cheese Game is pathological, but it is not hard to come
up with less obvious examples, such as...''
\bigskip
Then start the next paragraph:
``Consider the Iteration Path Game...''
p. 32. In the book:
Suppose the pareto-superior equilibrium ({\it Small},
{\it Small}) were chosen as a focal point in { Ranked Coordination},
but
the game was repeated over a long interval of time. The numbers in
the payoff matrix might slowly change until ({\it Small, Small}) and
({\it Large, Large}) both had payoffs of 1.6, and ({\it Large, Large})
started to dominate.
Should be:
Suppose the pareto-superior equilibrium ({\it Large},
{\it Large}) were chosen as a focal point in { Ranked Coordination},
but
the game was repeated over a long interval of time. The numbers in
the payoff matrix might slowly change until ({\it Small, Small}) and
({\it Large, Large}) both had payoffs of 1.6, and shortly thereafter
({\it Small, Small})
might start to dominate.
p. 52, Figure 2.6 (fixed in October 2001
reprint) Should be payoffs to ``(Smith, Jones)'', not ``(Smith,
Brown)'' .
p. 52, Figure 2.6 (fixed
in October 2001 reprint) Jones's nodes should be labelled $J_1$ and
$J_2$, not $B_1$ and $B_2$.
p. 55. (fixed in October 2001
reprint). ``Jones uses the likelihood and his priors.'' INSTEAD OF
``Jones uses the the likelihood and his priors.''
p. 57, Figure 2.8. Line (4)
is missing its heading, which should be $(B)|Large$.
p. 76. Paragraph starting ``First, it is
possible...'' Replace $Up$ with $Down$ and (3.14) with
(3.12). Also change ``$\theta^*>1$'' to ``$\theta^*>1$, or $\theta^*
\leq 0$''.
p. 77. (fixed in
October 2001 reprint) The second
paragraph, third line, should have $zy$, to fit the
picture in Table 3.5.
\bigskip
\noindent
{\bf Chapter 4: Dynamic Games with Symmetric Information }
p. 93, Figure 4.2.
$Exit$ should read $Out$ and $Remain$ should read $In$. Also
'Payoffs to (Smith,Jones)' needs to be added.
p. 107. Problem 4.2d, first line. Should be ``Union after Lenin
died'' (missing word).
\bigskip
\noindent
{\bf Chapter 5: Reputation and Repeated Games }
p. 109 (fixed in October 2001 reprint). Line
12: ``known'', not ``knowns''.
p. 113 (fixed in October 2001 reprint).
Line 2: ``always '', not ``alwyas ''.
p. 116, paragraph starting ``It is important to remember that...''
(Nov.2001). Replace ``Fuderberg'' with
``Fudenberg''.
p. 118, Table 5.2b. The arrow on
the line {\it High Quality} should be pointed left towards 5,5 and not
to the right.
\bigskip
\noindent
{\bf Chapter 6: Dynamic Games with Incomplete Information}
p. 148, Figure 6.3. ``Strong'' entrant, not ``Stong'', fixed in
October 2001 reprint.
p. 149, line 4. Delete ``$+0.05[40]$''.
My explanation here is bad, so I will elaborate on it. Figure
6.3 is abbreviated, and contains within it the game in Figure 6.1. The
(-10,300) and (- 10, 0) payoffs indicate what happens if the
incumbent chooses FIGHT depending on whether the entrant is weak
(300) or strong (0). In either case, the entrant gets -10 when the
incumbent chooses FIGHT.
If, however, the incumbent chooses COLLUDE, then the entrant gets a
payoff of 40, from Figure 6.1.
Suppose the entrant is strong and Nature told the incumbent that. But
suppose the entrant does not know whether Nature told the incumbent.
Nature did tell the incumbent with probability 0.1, and if the
entrant then enters, the incumbent will collude and the entrant's
payoff will be 40. Nature was silent with probability 0.9, and if the
entrant then enters, the incumbent will fight and the entrant's payoff
will be -10. The expected payoff is thus $-5 (= 0.1[40] + 0.9 [-10])$.
p. 157.
The error is that in the form it takes in the book, there is no
equilibrium with limit pricing, and the answer I had posted on the web
made a mistake in its Low-price pooling equilibrium. For the question
to make sense, the low-cost incumbent (C=20) must suffer some loss if
entry occurs. In the original question, the low-cost incumbent is
indifferent about whether entry occurs, so a High price is a weakly
dominant strategy for it. To fix the problem, I have below added a
competition cost of 50. I've also clarified the wording a bit.
\bigskip
\noindent \textbf{Problem 6.2: Limit Pricing.}\footnote{ See Milgrom
and Roberts (1982a).} An incumbent firm operates in the local computer
market, which is a natural monopoly in which only one firm can
survive. In the first period, the incumbent can price $Low$, losing 40
in profits, or $High$, losing nothing. It knows its own operating cost
$C$, which is 20 with probability 0.75 and 30 with probability 0.25. A
potential entrant knows those probabilities, but not the incumbent's
exact cost. In the second period, the entrant can enter at a cost of
100, and its operating cost of 25 is common knowledge. If there are
two firms in the market, each incurs a loss of 50, but one then drops
out and the survivor earns the monopoly revenue of 200. There is no
discounting; $r=0$.
\bigskip
\noindent
{\bf Chapter 7: Moral Hazard: Hidden Actions }
p. 163. Screening should be Figure 7.1e, not 7.1d.
p. 167. In the paragraph
starting ``Let's now fit out...'' replace ``then'' with ``let'' in two
places. This is more a clarification than a correction; this paragraph
is laying out specific functional forms for the problem, which
includes a payoff linear in output and wages for the principal.
p. 168. I made some mistake
in Mathematica, and the computation of $e^*$ is slightly off (and so
all the resulting numbers are off too). Thus, replace the paragraph,
``but this cannot be solved analytically. Using the computer
program Mathematica, I found that $e^* \approx 0.84934$, from
which, using the formulas above, we get $q^* \approx
100*log(1+.84934) \approx 61.48$ and $w^* \approx 41.32$.''
with
``but this cannot be solved analytically. Using the computer
program Mathematica, I found that $e^* \approx 0.77$, from which,
using the formulas above, we get $q^* \approx 100*log(1+ 0.77)
\approx 57.26$ and $w^* \approx 36.50$.''
The $e^*$ miscalculation continues in the discussion of the three
contracts at the bottom of the page. Change that section to read:
1 The {\bf forcing contract} sets $w(e^*) = w^*$ and $w(e \neq 0.77)
=0$. Here, $w(0.77) = 37$ (rounding up) and $w(e \neq e^*) =0$.
2 The {\bf threshold contract} sets $w(e \geq e^*) = w^*$ and $w(e