Question 1: Batman or Superman? Two friends, Rachel and Lois, are currently deciding whether to see the new Batman or Superman movie on Friday. Perhaps not surprisingly, Rachel wants to see Batman while Lois wants to see Superman. In particular, Rachel and Lois get gross payoffs of 85 and 45 if they go see Batman together, and gross payoffs of 35 and 105 if they go see Superman together. However, the two friends really want to go to the movies together as well; if they end up at different movies they both receive gross payoffs of 25. Rachel is a member of the World Batman Association, and as such has already been provided with two tickets to the Batman movie for free. They currently do not have tickets to the Superman movie however. On the Thursday prior to deciding which movie to go see, Lois must decide whether to purchase two Superman tickets that will cost Rachel and Lois 5 each. If Lois does not purchase the Superman tickets, then they cannot go to the Superman movie and will go see Batman with certainty. Assume that on Friday Rachel and Lois simultaneously decide on which movie to go to, having seen Lois's Thursday choice of whether to get the Superman tickets. 1.1 Write down the normal form of the Friday simultaneous movie choice subgame, given Lois previously purchased the Superman tickets. Find all NE in both pure and mixed strategies. 1.2 Draw the extensive form of the game and illustrate all pure-strategy SPNE. For each pure-strategy SPNE characterize the SPNE strategies, SPNE path, and SPNE payoffs. 1.3 Suppose that both players commit up front to playing the mixed strategy equilibrium on Friday if Lois gets Superman tickets on Thursday. Characterize the SPNE strategies, SPNE path, and SPNE payoffs under this scenario. 1.4 Can you find a positive) Superman ticket price such that Lois will be indifferent between purchasing and not-purchasing Superman tickets? If yes, find the ticket price that makes her indifferent. If no, explain why no such ticket price exists. 4+4+4+3=15 Marks 1 So, for example, the net payoffs for Rachel and Lois if Lois buys the Superman tickets on Thursday and they subse- quently go to the Batman movie would be 85-5=80 and 45-5=40 (and similarly for the other Friday outcomes if Lois buys the Superman tickets). Question 1: Batman or Superman? Two friends, Rachel and Lois, are currently deciding whether to see the new Batman or Superman movie on Friday. Perhaps not surprisingly, Rachel wants to see Batman while Lois wants to see Superman. In particular, Rachel and Lois get gross payoffs of 85 and 45 if they go see Batman together, and gross payoffs of 35 and 105 if they go see Superman together. However, the two friends really want to go to the movies together as well; if they end up at different movies they both receive gross payoffs of 25. Rachel is a member of the World Batman Association, and as such has already been provided with two tickets to the Batman movie for free. They currently do not have tickets to the Superman movie however. On the Thursday prior to deciding which movie to go see, Lois must decide whether to purchase two Superman tickets that will cost Rachel and Lois 5 each. If Lois does not purchase the Superman tickets, then they cannot go to the Superman movie and will go see Batman with certainty. Assume that on Friday Rachel and Lois simultaneously decide on which movie to go to, having seen Lois's Thursday choice of whether to get the Superman tickets. 1.1 Write down the normal form of the Friday simultaneous movie choice subgame, given Lois previously purchased the Superman tickets. Find all NE in both pure and mixed strategies. 1.2 Draw the extensive form of the game and illustrate all pure-strategy SPNE. For each pure-strategy SPNE characterize the SPNE strategies, SPNE path, and SPNE payoffs. 1.3 Suppose that both players commit up front to playing the mixed strategy equilibrium on Friday if Lois gets Superman tickets on Thursday. Characterize the SPNE strategies, SPNE path, and SPNE payoffs under this scenario. 1.4 Can you find a positive) Superman ticket price such that Lois will be indifferent between purchasing and not-purchasing Superman tickets? If yes, find the ticket price that makes her indifferent. If no, explain why no such ticket price exists. 4+4+4+3=15 Marks 1 So, for example, the net payoffs for Rachel and Lois if Lois buys the Superman tickets on Thursday and they subse- quently go to the Batman movie would be 85-5=80 and 45-5=40 (and similarly for the other Friday outcomes if Lois buys the Superman tickets)
