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\noindent
22 March 2005.  Eric Rasmusen, Erasmuse@indiana.edu.
Http://www.rasmusen.org.   Comments    welcomed.
 
  
\begin{LARGE}
\begin{center}
 {\bf   Adverse Selection in Stock Sales:  A Classroom Game for
Chapter 9}
\end{center}
\end{LARGE}

\begin{Large}

This is a game modelling a financial market in which sellers of stock know the value of the stock better than buyers do, but buyers  get more utility  from  a given stock  than sellers do.

There are two kinds of people: buyers and sellers. Each buyer   starts with a checking account with  \$200.  Each seller  starts with  4 stock certificates from 4 different companies. Stock par  values are  \$90,  \$70,
\$30,  and  \$10 in
equal proportions.

Buyers  value stocks more than cash, because they wish to save. Each buyer has  the following payoff function, where payoff is measured in utils. 
 

$$ 
\pi (buyer) = cash + 1.5  * (stock \; value)  
$$

  The initial payoff of a buyer is 200 utils from his \$200 in cash, but it
would rise to 300 utils if the buyer could convert his \$200 in cash  to
\$200 in stocks.

Sellers  value cash more than stocks, because they wish to  consume
now. Each seller has payoff function
 $$
\pi (seller) = 1.5*cash +   (stock\; value)
$$
 
  In the game, buyers and sellers buy and sell stock. The buyers pay
with checks registered on the  blackboard.  If   buyer Smith buys a
stock certificate for \$40 from Smith, he writes ``Smith'' on the
board, and under it writes ``Owes \$40 to Jones''. If Smith then buy a
certificate for \$90 from Lee, he writes  ``Owes \$90 to Lee'' under
the first entry.

\newpage

The game is repeated with different features. Each time, sellers start with 4 new shares, and buyers start with \$200. Players do {\it  not} keep their earnings from previous rounds. Think of the movie {\it Groundhog Day}(http://www.imdb.com/title/tt0107048/, viewed 22 March 2005). 

 1. Symmetric Information.  The instructor writes the value of each company on
the board.

2.  Asymmetric Information--decentralized.   The instructor tells the sellers, but
not the buyers, the value of each company.

3. Asymmetric Information--centralized.    The instructor tells the sellers, but
not the buyers, the value of each company.

 
 4. Asymmetric Information--centralized.    Partial regulation: Sellers  must
disclose if their stock is worth less than 50. The instructor tells
the sellers, but not the buyers, the value of each company.

 5. Asymmetric Information--centralized.      Truth  regulation: Sellers  {\it may}
guarantee their stock value.  The instructor tells the sellers, but
not the buyers, the value of each company.

  
 

 \bigskip

 
 
\noindent
{\bf  Mechanics} 

 Each buyer and each seller is a team of students. This is a good idea
even in a small class, so students can consult with each other and
thus learn more.

Each buyer and seller should be identified by the last name of one
member of the team.

  
   Sellers sit on one side of the room. The instructor shows them a
page with codes showing the value of each company.

  At the end of each round, five minutes must be allowed for players to add up their scores. 

  To implement guarantees in round 6,  write on the card: ``Worth 30--
Rasmusen''.  At the end of the game,the instructor could  cross the
guarantees out-- or let them say there till he teaches the class
again.

 
 \end{Large}


\newpage

 \begin{LARGE}

 \vspace*{-24pt}

\noindent
  \hspace*{-72pt}Your Names:   \\
\hspace*{-72pt}  Your Firm's Name:\\
 \hspace*{-72pt} Buyer, or Seller?:\\
 
 \vspace{32pt}

 \hspace*{-72pt}
\begin{tabular} {| l ||  l | l | l || l | l|| l|  }
\hline
   &  &    &   &  &  &  \\
Round &  Initial \hspace*{24pt}   & Initial\hspace*{24pt}  &  Initial
\hspace*{24pt}   &  Final&
Final \hspace*{24pt} & Final\hspace*{24pt} \\
 & Cash &  Stocks  & Payoff  &    Cash & Stocks   & Payoff \\
 & &    &   &  &    & \\
\hline
 1  &  &    &   &  &    & \\
   &  &    &   &  &  &  \\
\hline
2  &  &    &   &  &    & \\
   &  &    &   &  &  &  \\
\hline
 3  &  &    &   &  &    & \\
   &  &    &   &  &  &  \\
\hline
4   &  &    &   &  &    & \\
   &  &    &   &  &  &  \\
\hline
5   &  &    &   &  &    & \\
   &  &    &   &  &  &  \\
\hline
\hline
Average  &  &    &   &  &    & \\
   &  &    &   &  &  &  \\
\hline
\end{tabular} 

 


\begin{center}
 {\bf  TABLE 1:   SCORESHEET }
\end{center}

 
 
 \end{LARGE}
  
\newpage

 \bigskip
\noindent
{\bf Instructor's Notes   }


Equipment:  A deck of cards without the aces. Pieces of paper showing
the values of stocks in different rounds.

 Ideally, you would fix the number of sellers equal to the number of buyers in advance and set the  par value of all stock to be exactly \$200  times the number of sellers (though divided up unequally).  

 Printout of the company values.

 Refer to the game of PIT.

Winners: Easy for buyers, round by round.

 For seller, luck matters. So take an overall average.


  FORCE a centralized market for a while. 

 For the first couple of rounds, I asked players to tell me their initial and ending payoffs, and I wrote those on the blackboard (without the names of the players). 

 One  realization: 


 Sellers: 173, 221,   235, 248,  255,  263,  398


Buyers: 231, 241, 285, 287,  339, 355, 

 One of the buyers got 355 because he engaged in selling on margin, quite imaginatively. Another probably added numbers up wrong. 


\newpage

\begin{LARGE}

\noindent
 {\bf Lessons: }

\noindent
  
 (1)  Asymmetric info can bog down a market and stop gains from trade
from being realized.

(2) Discloure regulation can help.

(3) Just requiring honesty  in voluntary disclosure can do as well. 

 Private markets are good when reputaion matters. Centralized excahgnes break down. 

 Otherwise, public markets are handy. 
 
\end{LARGE}





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