There is a project for which player 1 can exert effort e ≥ 0 that costs her c(e) = 0.5e². If player 1 and player 2 can come to an agreement, then a total value of v(e) = e is produced, which can be allocated between the two players. Effort also produces a value y(e) = ke, where k = [0, 1], that player 1 can obtain for herself if player 1 and 2 fail to agree. The game has three stages: (I stage) Player 1 chooses effort e ≥ 0; (II Stage) Player 2 observes e and chooses and effort level a = [0, 1]; (III stage) Player 1 observes a and either agrees (a) or rejects (r) the offer. If player 1 accepts the offer, then her payoff is ae - 0.5e² and player 2's payoff (1-a)e. If she rejects the offer, then player 1's payoff is ke - 0.5e² and player 2's payoff is zero. • What is the subgame perfect equilibrium effort choice? • Suppose that player 2 can choose k € [0, 1] before the above game is played. What would he choose? What would be the equilibrium effort? • Suppose now that the government, rather than player 2, can choose k before the above game is played. Assuming that the government aims to maximize total welfare e - 0.5e², what value of k would it choose? What would be the equilibrium effort?

There is a project for which player 1 can exert effort e ≥ 0 that costs her c(e) = 0.5e². If player 1 and player 2 can come to an agreement, then a total value of v(e) = e is produced, which can be allocated between the two players. Effort also produces a value y(e) = ke, where k = [0, 1], that player 1 can obtain for herself if player 1 and 2 fail to agree. The game has three stages: (I stage) Player 1 chooses effort e ≥ 0; (II Stage) Player 2 observes e and chooses and effort level a = [0, 1]; (III stage) Player 1 observes a and either agrees (a) or rejects (r) the offer. If player 1 accepts the offer, then her payoff is ae - 0.5e² and player 2's payoff (1-a)e. If she rejects the offer, then player 1's payoff is ke - 0.5e² and player 2's payoff is zero. • What is the subgame perfect equilibrium effort choice? • Suppose that player 2 can choose k € [0, 1] before the above game is played. What would he choose? What would be the equilibrium effort? • Suppose now that the government, rather than player 2, can choose k before the above game is played. Assuming that the government aims to maximize total welfare e - 0.5e², what value of k would it choose? What would be the equilibrium effort?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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