Attempts Average $/2$

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

Suppose Antonio and Trinity 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 Antonio chooses Up and Trinity chooses Down, Antonio will receive a payoff of $4$ and Trinity will receive a payoff of $5.$

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

The outcome reflecting the unique Nash equilibrium in this game is as follows: Antonio chooses Down and Trinity chooses Down $.$