Question 1Which of these is a property of the Battle of the Sexes? 1 pointFor any given action of your opponent, the alternate action is the best choice. There are two non-random Nash equilibria, and one is better than the other for all players. There are two non-random Nash equilibria, and one is better for Man (player 1) and the other is better for Woman (player 2). Nash equilibrium does not exist.

If the Battle of the Sexes game were played sequentially:a. Only the mixed strategy equilibrium would exist.b. One of the two pure strategy equilibria would become the only equilibrium.c. The two pure strategy equilibria would alternate in being the equilibrium seen ineach round of the game.d. Only the dominant strategy equilibrium would exist.e. The two pure strategy equilibria would exist.

Consider the below payoff matrix for a two-player Battle of the Sexes game. Player 1 has a clear preference for soccer while Player 2 derives more satisfaction from going to watch ballet. The two versions of the game differ by how much one appreciates the presence of the other. Which of the following statement is TRUE? The Married Phase of this game has a mixed-strategy Nash equilibrium where Player 1 chooses Soccer 3/7 of the times and Player 2 chooses Soccer 4/7 of the times The Honeymoon Phase of this game has a mixed-strategy Nash equilibrium where Player 1 chooses Soccer 4/7 of the times and Player 2 chooses Soccer 3/7 of the times The Honeymoon Phase of this game has a mixed-strategy Nash equilibrium where both players choose Soccer 3/7 of the times This game does not have any mixed-strategy Nash equilibria

Question 6Which game has no mixed Nash equilibrium, i.e., no Nash equilibrium where at least one player chooses random behavior? Choose the correct game with a correct reason. 1 pointThe coordination game, because payoffs for each player are the same across two Nash equilibria. The battle of the Sexes, because players have made a promise where to visit during the next holiday. The matching pennies, because the result of a coin-toss trial can be perfectly predicted by today’s science. The prisoner’s dilemma, because defection is best for both players and they do not consider that mutual cooperation can be attained.

Question 6Which of the following games has the property that Nash equilibrium is played when players are rational (in the sense that each player tries to maximize her/his own payoff)? 1 pointBattle of the Sexes Traffic gameCoordination Game Prisoner’s Dilemma

In a simultaneous-choice, one-period game, a Nash equilibrium: (A) Will never exist. (B) Will always include dominant strategies. (C) Will always result in both players taking the same action. (D) May not maximize the sum of the players' p