Chapter $18$ Homework

Atrempis $$ Average $/2$

$7.$ Solving for dominant strategies and the Nash equilibrium

Suppose Russell and Aaliyah are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the eamings of each person as a function of both of their choices. For example, the upper$-$right cell shows that if Russell chooses Up and Aaliyah chooses Down, Russell will receive a payoff of $8$ and Aaliyah will receive a payoff of $7.$

$\backslash$table$[[,,$Aaliyah$],[,,$Up$,$Down$],[,$Up$,8,5,8,7],[$Russell$,$Down,$3,6,9,8]]$

In this game, the only dominant strategy is for to choose

The outcome reflecting the unique Nash equilibrium in this game is as follows: Russell chooses and Aaliyah chooses

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