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Attempts $$ Do No Harm $/2$

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

Suppose Ethan and Cadence 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 Ethan chooses Up and Cadence chooses Down, Ethan will receive a payoff of $6$ and Cadence will receive a payoff of $4.$

$\backslash$table$[[$Ethan$,,$Cadence$],[,$Up$,$Down$],[$Up$,4,3,6,4],[$Down$,6,7,7,6]]$

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

The outcome reflecting the unique Nash equilibrium in this game is as follows: Ethan chooses $q,$ and Cadence chooses $$