Chapter $18$ Homework

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Attempts $0\mathrm{.}5$

Keep the Highest $\frac{1}{2}$

$6.$ Solving for dominant strategies and the Nash equilibrium

Suppose Gabriel and Nia are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper$-$right cell shows that if Gabriel chooses Up and Nia chooses Down, Gabriel will receive a payoff of $7$ and Nia will receive a payoff of $5.$

$q,$

Nia

Gabriel

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

The outcome reflecting the unique Nash equilibrium in this game is as follows: Gabriel chooses $$ and Nia chooses $.$

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