316 r 1) and a potential rival d. For whichv (player 2), are running for the local mayoralty. The incumbeo broad base of support (B) or a small base of support (S). cach probability . The incumbent knows his level of support bunecurring w a rival does not. The incumbent thirst chooses how much soft mon campaign financing: a low quantity (Z) or a high quantity Bayesian equilibria? has either a quantity (H), a decision that campaign financing L thet noto Campaigning: Two politicians, an incumbent (player 1) and 15.4 is observed by the potential rival. The rival can then deci run (N). If the incumbent chooses a level of the support base and the reaction of the potential the following payoff matrix (these are from winning, campaigning. rival, the payoffs are given payoffs that represent the expectatio by Player 2's response 10.0 Bİ 6,4 Support base s 4,4 6,0 The cost in payoffs that an incumbent incurs for choosing H instead of 2 if he has a broad base of support and 4 if he has a small base of support that is, these are costs that are deducted from the payoffs in the payoff matrix that are conditional on the type). A rival who runs against an incumbent with a broad base of support who chose H will obtain a payoff of-10, while a rival who runs against an incumbent with a small base of support who chose H will obtain a payoff of -4. If the rival chooses not to run then he obtains 0, as in the payoff matrix. a. Draw the extensive form of this game and identify the proper sub- games. Draw the matrix that represents the normal form of the exten- sive form. b. If the rival could commit in advance to a certain pure strategy that he would follow regardless of the incumbent's choice of financing. anticipating that the incumbent would then choose his best response, what would that strategy be? What would be the incumbent's best response to this strategy? Is the pair of strategies you found a Bayesian Nash equilibrium? equilibrium? equilibrium c. Can the pair of strategies you found in (b) be part of a perfect Bayesian d. Are there other pairs of strategies that can be part of a perfect Bayesian 316 r 1) and a potential rival d. For whichv (player 2), are running for the local mayoralty. The incumbeo broad base of support (B) or a small base of support (S). cach probability . The incumbent knows his level of support bunecurring w a rival does not. The incumbent thirst chooses how much soft mon campaign financing: a low quantity (Z) or a high quantity Bayesian equilibria? has either a quantity (H), a decision that campaign financing L thet noto Campaigning: Two politicians, an incumbent (player 1) and 15.4 is observed by the potential rival. The rival can then deci run (N). If the incumbent chooses a level of the support base and the reaction of the potential the following payoff matrix (these are from winning, campaigning. rival, the payoffs are given payoffs that represent the expectatio by Player 2's response 10.0 Bİ 6,4 Support base s 4,4 6,0 The cost in payoffs that an incumbent incurs for choosing H instead of 2 if he has a broad base of support and 4 if he has a small base of support that is, these are costs that are deducted from the payoffs in the payoff matrix that are conditional on the type). A rival who runs against an incumbent with a broad base of support who chose H will obtain a payoff of-10, while a rival who runs against an incumbent with a small base of support who chose H will obtain a payoff of -4. If the rival chooses not to run then he obtains 0, as in the payoff matrix. a. Draw the extensive form of this game and identify the proper sub- games. Draw the matrix that represents the normal form of the exten- sive form. b. If the rival could commit in advance to a certain pure strategy that he would follow regardless of the incumbent's choice of financing. anticipating that the incumbent would then choose his best response, what would that strategy be? What would be the incumbent's best response to this strategy? Is the pair of strategies you found a Bayesian Nash equilibrium? equilibrium? equilibrium c. Can the pair of strategies you found in (b) be part of a perfect Bayesian d. Are there other pairs of strategies that can be part of a perfect Bayesian