### Artificial IntelligenceAIMA Exercises

The following payoff matrix, from @Blinder:1983 by way of Bernstein:1996, shows a game between politicians and the Federal Reserve.
$$\begin{array} {|r|r|}\hline & Fed: contract & Fed: do nothing & Fed: expand \\ \hline Pol: contract & F=7, P=1 & F=9, P=4 & F=6, P=6 \\ Pol: do nothing & F=8, P=2 & F=5, P=5 & F=4, P=9 \\ Pol: expand & F=3, P=3 & F=2, P=7 & F=1, P=8\\ \hline \end{array}$$
Politicians can expand or contract fiscal policy, while the Fed can expand or contract monetary policy. (And of course either side can choose to do nothing.) Each side also has preferences for who should do what—neither side wants to look like the bad guys. The payoffs shown are simply the rank orderings: 9 for first choice through 1 for last choice. Find the Nash equilibrium of the game in pure strategies. Is this a Pareto-optimal solution? You might wish to analyze the policies of recent administrations in this light.

The following payoff matrix, from @Blinder:1983 by way of Bernstein:1996, shows a game between politicians and the Federal Reserve.
$$\begin{array} {|r|r|}\hline & Fed: contract & Fed: do nothing & Fed: expand \\ \hline Pol: contract & F=7, P=1 & F=9, P=4 & F=6, P=6 \\ Pol: do nothing & F=8, P=2 & F=5, P=5 & F=4, P=9 \\ Pol: expand & F=3, P=3 & F=2, P=7 & F=1, P=8\\ \hline \end{array}$$
Politicians can expand or contract fiscal policy, while the Fed can expand or contract monetary policy. (And of course either side can choose to do nothing.) Each side also has preferences for who should do what—neither side wants to look like the bad guys. The payoffs shown are simply the rank orderings: 9 for first choice through 1 for last choice. Find the Nash equilibrium of the game in pure strategies. Is this a Pareto-optimal solution? You might wish to analyze the policies of recent administrations in this light.

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