Question

1. Let W represent a team's win total. Suppose that Major League Baseball instituted a subsidy, S, which is given by S = 0 when W < 90, and is determined by the formula S = 10, 000W when W ≥ 90. Before the subsidy was introduced, the prot-maximizing Detroit Tigers aimed to win 85 games, and the win-maximizing Seattle Mariners aimed to win 95 games. (a) Assuming that the two teams have identical marginal revenue curves, draw a graph that shows MC, MR, and both teams' win totals before the subsidy was introduced. (b) Draw a graph showing the changes that occur due to the introduction of the subsidy. Assume that the subsidy aects MR. (c) How do the win totals change after the subsidy is introduced?

Answer 1

7 Consider a one-shot game with two equilibria and suppose this game is

repeated twice. Explain in words why there may be equilibria in the two-period

game which are di®erent from the equilibria of the one-shot game.

Solution: When the game is repeated twice the strategy space for each player becomes

more complex. Each player's strategy speci¯es the action to be taken in period 1 as well as

the action to be taken in period 2 as a function of the outcome in period 1. The possibility of

linking period 2's actions to past actions allows for equilibrium outcomes that would not be

attainable in the corresponding one-shot game (for example, the use of a 'punishment' action

in period 2 if one of the players deviates from the designated period 1 payo®-maximizing

action).

4.8¤¤ Consider the game in Figure 4.12 Show, by backward induction, that

rational players choose d at every node of the game, yielding a payo® of 2 for Player

1 and zero for Player 2. Is this equilibrium reasonable? What are the rationality

assumptions implicit in it?

Solution: [IMPORTANT NOTE: there is a typo in the game tree: the payo®s in the

second and third to last nodes should be increased by 2.]

12This game was ¯rst proposed by

Rosenthal, Robert (1981), \Games of Perfect Information, Predatory Pricing and the Chain-Store Par