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22 November 2005. 29 August 2006. Eric Rasmusen, Erasmuse@indiana.edu.
http://www.rasmusen.org/.
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\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}
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\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. }
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If there is time, do the sequential Battle of the Sexes, and maybe do Cheap Talk.
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