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 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.

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

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.

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.

Represent the following strategic interaction using a payoff matrix. A couple (a she and a he) is going out for an evening. They have two options: watching a football match or going to an opera. Unfortunately his mobile phone runs out of battery. Unable to reach each other, each of them needs to go to one of the possible venues without knowing where his/her partner has gone. Spending the evening alone (whether at the football or the opera) is the worst outcome for both of them. Conditional on going out together, she prefers football to opera while he prefers opera to football. Make “she” Player 1 when writing the payoff matrix.