There is a desirable good, the number of units of which is determined stochastically—either 1 or 2 units are available with probability 0.5 each. Individual 1 knows how many units are available but 2 does not. Individual 1 can propose to give individual 2 either 0 or 1 unit of the good. Then individual 2, after seeing 1’s proposal, either accepts or rejects the proposal. In the event of rejection, both individuals receive zero units. Each person cares only about the number of objects she obtains, i.e., her utility function is given by u(x) = x, where x denotes the number of units of the good received. Model this strategic environment as an extensive form game and answer the following questions. 1. Specify the normal form representation (using matrix) of this extensive form game. Explain what players’ strategy sets are and how you derive their payoffs. 2. Find the set of all pure strategy Nash equilibrium of this game.

There is a desirable good, the number of units of which is determined stochastically—either 1 or 2 units are available with probability 0.5 each. Individual 1 knows how many units are available but 2 does not. Individual 1 can propose to give individual 2 either 0 or 1 unit of the good. Then individual 2, after seeing 1’s proposal, either accepts or rejects the proposal. In the event of rejection, both individuals receive zero units. Each person cares only about the number of objects she obtains, i.e., her utility function is given by u(x) = x, where x denotes the number of units of the good received. Model this strategic environment as an extensive form game and answer the following questions. 1. Specify the normal form representation (using matrix) of this extensive form game. Explain what players’ strategy sets are and how you derive their payoffs. 2. Find the set of all pure strategy Nash equilibrium of this game.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.3P

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