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22 November 2005.  29 August 2006.    Eric Rasmusen, Erasmuse@indiana.edu.
http://www.rasmusen.org/.
 
 

 \begin{center}
\begin{large}
 {\bf 1 The Rules of the Game }

\end{large}
 \end{center}

\begin{Huge}


 
{\bf Table  2:  The Prisoner's Dilemma}

 \begin{tabular}{lllccc} &       &             &\multicolumn{3}{c}{\bf Column}\\
&       &             &   {\it Deny}  &   & {\it Confess}     \\ 
&   &  {\it Deny}      &     -1,-1 &    & -10, 0 \\
 & {\bf Row} &&  & &  \\
  &  &       {\it   Confess}     &      0,-10  &    & {\bf - 8,-8} \\
\multicolumn{6}{l}{\it Payoffs to: (Row,Column) }
  \end{tabular}
 

\newpage





{\it{\bf Players} are the individuals who make decisions. Each
player's goal is to maximize his utility by choice of actions.}


\noindent {\it An {\bf action} or {\bf move} by player $i$, denoted $a_{i},$ is
a choice he can make.}


\noindent {\it Player $i$'s {\bf strategy} $s_i$ is a rule that tells him which
action to choose at each instant of the game, given his information set.}

 \noindent {\it Player $i$'s {\bf strategy set} or {\bf strategy space} $S_i =
\{ s_i\}$ is the set of strategies available to him. }

 \noindent {\it A {\bf strategy profile} $s=(s_1,\ldots,s_n)$ is a list
consisting of one strategy for each of the {\rm n} players in the game.}



\newpage

\begin{center}

 
{\bf Table  2:  The Prisoner's Dilemma}

 \begin{tabular}{lllccc} &       &             &\multicolumn{3}{c}{\bf Column}\\
&       &             &   {\it Deny}  &   & {\it Confess}     \\ 
&   &  {\it Deny}      &     -1,-1 &    & -10, 0 \\
 & {\bf Row} &&  & &  \\
  &  &       {\it   Confess}     &      0,-10  &    & {\bf - 8,-8} \\
\multicolumn{6}{l}{\it Payoffs to: (Row,Column) }
  \end{tabular}
\end{center}

For (1) Simultaneous game,  and (2) Sequential game in which Row moves first: what are the 

Players

Actions

Strategies

Strategy Sets

Strategy Profiles

  

\newpage


\noindent {\it By player $i$'s {\bf payoff} $\pi_i(s_1,\ldots,s_n)$, we mean
either:\\ 
 (1) The utility player $i$ receives after all players and Nature have
picked their strategies and the game has been played out; or\\
  (2) The expected
utility he receives as a function of the strategies chosen by himself and the
other players.}


 \noindent {\it A {\bf strategy profile} $s=(s_1,\ldots,s_n)$ is a list
consisting of one strategy for each of the {\rm n} players in the game.}

\noindent {\it An {\bf equilibrium} $s^* = (s_1^*,\ldots,s_n^*)$ is a strategy
profile consisting of a best strategy for each of the {\rm n} players in the
game.}


\noindent {\it The {\bf outcome} of the game is a set of interesting elements
that the modeller picks from the values of actions, payoffs, and other variables
after the game is played out.}


\newpage

\begin{center}

 
{\bf Table  2:  The Prisoner's Dilemma}

 \begin{tabular}{lllccc} &       &             &\multicolumn{3}{c}{\bf Column}\\
&       &             &   {\it Deny}  &   & {\it Confess}     \\ 
&   &  {\it Deny}      &     -1,-1 &    & -10, 0 \\
 & {\bf Row} &&  & &  \\
  &  &       {\it   Confess}     &      0,-10  &    & {\bf - 8,-8} \\
\multicolumn{6}{l}{\it Payoffs to: (Row,Column) }
  \end{tabular}
\end{center}

For (1) Simultaneous game,  and (2) Sequential game in which Row moves first: what are  

Payoffs 

Equilibria
 
Outcomes

 



\newpage

\begin{center} {\bf Table  8:     Ranked Coordination    }

 \begin{tabular}{lllccc}
 &       &             &\multicolumn{3}{c}{\bf Jones}\\
&       &             &    $Large$  & & $Small$  \\
 &   &  $Large$   &     {\bf 2,2} & $\leftarrow$  & $-1,-1$ \\
 & {\bf Smith} &     & $\uparrow$  & & $\downarrow$ \\
 &  &       $Small$     &      $-1,-1$ & $\rightarrow$  & {\bf 1,1} \\ & & & &\\
 \end{tabular}
 \end{center}
 \vspace{-24pt}
 {\it Payoffs  to:  (Smith, Jones). Arrows show how a player can increase his
payoff.   }

 

\begin{center} {\bf Table  9:   Dangerous  Coordination   }

 \begin{tabular}{lllccc} &       &             &\multicolumn{3}{c}{\bf Jones}\\
&       &             &    $Large$  & & $Small$  \\ &   &  $Large$   &     {\bf
2,2} & $\leftarrow$  & $-1000, -1$ \\
  & {\bf Smith} &     & $\uparrow$  & & $\downarrow$ \\ &  &       $Small$     &
$-1, -1$ & $\rightarrow$  & {\bf 1,1} \\ & & & &\\
 \end{tabular} \end{center}
 \vspace{-24pt}
 {\it Payoffs  to:  (Smith, Jones). Arrows show how a player can increase his
payoff.    }


\newpage


 You win by matching your response
to those of as many of the other players as possible.

\noindent 1  Circle one of the following numbers:  100, 14, 15, 16, 17, 18.

\noindent 2 Circle one of the following numbers 7, 100, 13, 261, 99, 666.

\noindent 3  Name Heads or Tails.

\noindent 4  Name Tails or Heads.

\noindent 5 You are to split a pie, and get nothing if your proportions add to
more than 100 percent.

\noindent 6  You are to meet somebody in New York City.  When?  Where?


\newpage

 \begin{center} {\bf The Battle of the Sexes    }

 \begin{tabular}{lllccc}
 &       &             &\multicolumn{3}{c}{\bf Woman}\\ &       &             &
$Prize \; Fight$  & & $Ballet$  \\ &   &  $Prize \; Fight$   &  {\bf 2,1} &
$\leftarrow$  & $0$, 0 \\ & {\bf Man} &     & $\uparrow$  & & $\downarrow$ \\
 &  &       $Ballet$     &      $0$, $0$ & $\rightarrow$  & {\bf 1,2} \\ & & &
&\\
 \end{tabular}
 
 {\it Payoffs  to: (Man, Woman). Arrows show how a player can increase his
payoff.    }
\end{center}


If there is time, do the sequential Battle of the Sexes, and maybe do Cheap Talk. 




 


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