4. [12 marks] Person A is dating person B. Unfortunately, they are not very good at coordinating their dates: when they are still dating, they play the mixed-strategy equilibrium of a battle-of-the-sexes game (where they can choose either seeing the Jets or going to the movies). Instead of dating, each person can dump' the other one, with A having the first option to dump B. The game is in Figure 2 (payoffs are: (A,B)). a. [8 marks) Calculate the mixed-strategy equilibrium in the BOS game, and find each person's expected payoff from this equilibrium. b. [4 marks] Given the payoffs in (a.), what is the equilibrium of the overall sequential game? Explain your answer. Fig. 2 2 ( 21.5) Dump B Dump (2.5, 1.5) M A J pate B (3,2)/(1,1) Date A M60.0|(2,4) 4. [12 marks] Person A is dating person B. Unfortunately, they are not very good at coordinating their dates: when they are still dating, they play the mixed-strategy equilibrium of a battle-of-the-sexes game (where they can choose either seeing the Jets or going to the movies). Instead of dating, each person can dump' the other one, with A having the first option to dump B. The game is in Figure 2 (payoffs are: (A,B)). a. [8 marks) Calculate the mixed-strategy equilibrium in the BOS game, and find each person's expected payoff from this equilibrium. b. [4 marks] Given the payoffs in (a.), what is the equilibrium of the overall sequential game? Explain your answer. Fig. 2 2 ( 21.5) Dump B Dump (2.5, 1.5) M A J pate B (3,2)/(1,1) Date A M60.0|(2,4)