Question

two players, gabriel and evangeline simultaneously decide whether to go to a party or stay at home. if evangeline will not be at the party, then gabriel would rather stay at home. similarly, if gabriel will not be at the party, then evangeline would rather stay at home. the best outcome for both gabriel and evangeline is to be at the party together. the payoff matrix is summarized as below. gabriel go to party stay at home evangeline go to party 1,000, 1,000 0, 0 stay at home 0, 0 500, 500 1 (a) find the pure strategy nash equilibria of this game. (b) find the mixed strategy nash equilibrium of this game.

Answer 1

The pure strategy Nash Equilibria is for both Gabriel and Evangeline to go to the party together. The mixed strategy Nash Equilibrium is for both players to choose to go to the party with a probability of 2/3 and stay at home with a probability of 1/3.

Step-by-step explanation:

The pure strategy Nash Equilibria for this game can be found by looking for any cell in the payoff matrix where no player has an incentive to change their strategy. In this case, the best outcome for both Gabriel and Evangeline is to go to the party together, as they both receive a payoff of 1,000 units. This is a pure strategy Nash Equilibrium.

For the mixed strategy Nash Equilibrium, we need to find the probabilities of each player choosing a certain strategy that would make the other player indifferent between their two choices. In this case, both players have a mixed strategy Nash Equilibrium if they each choose to go to the party with a probability of 2/3, and stay at home with a probability of 1/3. With these probabilities, both players are indifferent between their two choices, and there is no incentive to deviate from this strategy.