4. There is a project for which player 1 can exert effort e > 0 that costs her c(e) = 0.5e2. If player 1 andplayer 2 can come to an agreement, then a total value of v(e) = e is produced, which can be allocatedbetween the two players. Effort also produces a value y(e) = ke, where k = [0, 1], that player 1 canobtain for herself if player 1 and 2 fail to agree. The game has three stages: (I stage) Player 1 chooseseffort e > 0; (II Stage) Player 2 observes e and chooses and effort level a € [0, 1]; (III stage) Player 1observes a and either agrees (a) or rejects (r) the offer. If player 1 accepts the offer, then her payoff isae - 0.5e² and player 2's payoff (1-a)e. If she rejects the offer, then player 1's payoff is ke - 0.5e²and player 2's payoff is zero.What is the subgame perfect equilibrium effort choice?●

To find the subgame perfect equilibrium effort choice, we need to work backwards from stage III. In…

There is a project for which player 1 can exert effort e 20 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 2 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?

There is a project for which player 1 can exert effort e 20 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 2 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?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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