Problem 1:
Consider the following game between Sony, a manufacturer of video cassette players, and Columbia Pictures, a movie studio. Each firm must decide whether to use the VHS or Beta format — Sony to make video players, Columbia to release its movies for rental or purchase.
Columbia Pictures
Beta VHS
Sony Beta 20, 10 0, 0
VHS 0, 0 10, 20
A) Suppose this is a simultaneous-move, one-shot game. Restrict attention to pure strategies. Does either firm have a dominant strategy? Identify the Nash equilibrium or equilibria for this game [For extra practice, you can calculate the mixed-strategy NE, but you do not have to turn that part in ...
B) Now suppose this is a sequential-move game in which Sony moves first. Write down a complete list of Sony's possible strategies, and of Columbia's possible strategies.
C) Draw an extensive form for the sequential-move game described in part b). Make sure you identify which player is "moving" at each decision node, and indicate the payoffs to each possible outcome of the game
D) For the sequential-move game described in part b), identify a Nash equilibrium that is subgame perfect, and a Nash equilibrium that is not subgame perfect.
Problem 2: Consider the following modification of the game described in Problem: Suppose now that Dana (a stronger negotiator than Blair) decides to present Blair with a take-it-or-leave-it offer. Dana will offer Blair a particular share, XB, of the proceeds, and will keep the rest (XD = 200 —XB). Blair can choose to accept the offer, in which case Blair and Dana will split the $200 according to Dana's proposal, or to reject it — in which case Mordecaithe Mediator gets the entire $200.
A) Describe the Nash equilibrium (or equilibria) for this sequential-move game. Explain your reasoning.
B) Identify a subgame perfect Nash equilibrium for this game Explain your reasoning.
C) Do you think that the subgame perfect Nash equilibrium you identified in part b) is the most likely outcome of this game? Briefly explain.