Solving for dominant strategies and the Nash equilibrium Suppose Rashard and Alyssa 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 Rashard chooses Up and Alyssa chooses Down, Rashard will receive a payoff of 6 and Alyssa will receive a payoff of 3. In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Rashard chooses and Alyssa chooses