4. Consider the following normal form game in which player I chooses a row and player 2 chooses a column. (This exercise is based on an example from Kreps, 1990). LL M R 200, 4 -200, 2 10, 0 -200, -200 -200, -200 200, -9 2, 0 200, 4 Kreps, D. M. (1990). Game Theory and Economic Modelling, Oxford: Oxford University Press. . If you were player 2 in this game and you were playing it once without the ability to engage in pre-play communication with player 1, what strategy would you choose? b. What are all the pure-strategy Nash equilibria of this game? c. Is your strategy choice in (a) a component of any pure-strategy Nash equilibrium strategy profile? d. Suppose now that pre-play communication were possible. Would you expect to play something different from your choice in (a)? An Application: Antitrust Investigation Game ANTITRUST LAW Consider the following simultaneous-move antitrust investigation game between two players: Firm A (a single potential antitrust violator) and the Antitrust Authority. Suppose Firm A gains $50 from engaging in anticompetitive activities. Compliance generates a reputational benefit for the Antitrust Authority with monetary value equal to $75. Firm A must choose between comply with the antitrust regulations "Comply" and engage in anticompetitive activities ("Don't Comply"). The Antitrust Authority must decide whether to conduct an investigation that will cost $25. If Firm A is investigated and is found to have not complied, then it will owe a $125 fine, and hence it will get a net payoff equal to -$75 ($50 gains minus the fine). The Antitrust Authority in this case receives a net payoff equal to $100: The $125 payment from Firm A minus the $25 cost of conducting the investigation. If Firm A is investigated and is found to have complied, then it will owe a $0 fine, and hence it will get a payoff equal to $0. The Antitrust Authority in this case will receive a net payoff equal to $50: The $75 reputational benefit minus the $25 cost of conducting the investigation Assume all amounts are expressed in thousands. Antitrust Authority Investigate Don't Investigate $100 Don't Comply -$75 1350 Firm A $50 $75 Comply a. Does either party have a dominant strategy? What is the Nash equilibrium of the game? Suppose now that the game is played sequentially. First, the Antitrust Authority decides whether or not to conduct an investigation. Next, after observing the Antitrust Authority's decision, Firm A must decide whether to comply or not comply. b. Construct the game tree and evaluate the equilibrium of this sequential game. Finally, suppose that the Antitrust Authority moves first and credibly commits to a fixed probability of an investigation, "p." Firm A moves second after observing "p," and chooses between comply or engage in anticompetitive activities. Next, the Antitrust Authority "flips the coin" and investigates with the probability "p" that it previously committed to. C. What probability "p" would maximize the Antitrust Authority's payoff