Problem_set_11_solut - Kaushik Basu Spring 2007 Econ 367 Game-Theoretic Methods Problem Set 11 Consider the symmetric normal-form game described

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Kaushik Basu Spring 2007 Econ 367: Game-Theoretic Methods Problem Set 11 1. Consider the symmetric normal-form game described below. H D H 1, 1 3, 0 D 0, 3 4, 4 (a) Locate all the Nash equilibria (pure and mixed-strategy) in this game. (b) Focusing on pure strategies alone, locate all the Evolutionarily Stable Strategies in this game. Answer: (a) Pure Strategy Nash Equilibria: (H, H) and (D, D) Mixed Strategy Nash equilibria: (H, H), (D, D), and (H with probability ½; D with probability ½) (b) H is an ESS D is an ESS 2. Consider a two-period game between a landlord and a laborer in which the landlord offers the worker a wage of w dollars (for a day’s work) and the worker can accept (A) or reject (R) the offer. A day’s work has a leisure cost of $4 for the worker. If the worker accepts the deal, the landlord gets an output of $10. If the worker rejects it, the landlord gets 0. (a) In the subgame perfect equilibrium of this two-period game what wage does the landlord offer? What payoffs do the two players receive in the equilibrium? Suppose the players meet in period 3 (after the above two-period interaction) to play the following simultaneous-move game. T B T 4, 4 0, 0 B 0, 0 2, 2 (b) In this 3-period game, what is the lowest wage offer that the laborer will accept in a subgame perfect equilibrium? Explain why such a wage is accepted.
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Answer: (a) 10-w 0 w-4 0 Landlord offers wage = 4 to make the laborer indifferent between accepting or rejecting the offer and thus the landlord can maximize his own pay-off. Landlord’s payoff is 10 (output) – 4 (labor cost) = 6; worker’s payoff is 4 (wage) – 4 (leisure cost) = 0. The landlord wants to maximize his payoff by offering a wage that is just
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This note was uploaded on 05/31/2008 for the course ECON 3670 taught by Professor Basu during the Spring '08 term at Cornell University (Engineering School).

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Problem_set_11_solut - Kaushik Basu Spring 2007 Econ 367 Game-Theoretic Methods Problem Set 11 Consider the symmetric normal-form game described

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