Consider the following public good provision game. There are 3 players with private infor-mation about their costs of contributing for the public good. Players have two actions: contribute ordon't contribute. If at least two players contribute for the public good, then they all get a payoff of1. If less than two players contribute, then all receive zero payoff. Only the players who contributefor the public good pays the cost. The costs are either a or 0.8 and each is equally likely.(a)Find the highest value of r in a Bayesian Nash equilibrium where all players withtype r contributes and all players with type 0.8 don't.(b)Now suppose that costs are either 0.2, 0.5 or 0.8 and all three are equally likely. Finda Bayesian Nash equilibrium in which players with type 0.2 always provide, players with type0.8 never provide and players with type 0.5 uses a mixed strategy in which they provide withprobability p > 0. Find the value of p.

There are three players who have private information about their contribution towards public good…

Consider the following public good provision game. There are 3 players with private infor- mation about their costs of contributing for the public good. Players have two actions: contribute or don't contribute. If at least two players contribute for the public good, then they all get a payoff of 1. If less than two players contribute, then all receive zero payoff. Only the players who contribute for the public good pays the cost. The costs are either az or 0.8 and each is equally likely. (a) Find the highest value of x in a Bayesian Nash equilibrium where all players with type x contributes and all players with type 0.8 don't. (b) Now suppose that costs are either 0.2, 0.5 or 0.8 and all three are equally likely. Find a Bayesian Nash equilibrium in which players with type 0.2 always provide, players with type 0.8 never provide and players with type 0.5 uses a mixed strategy in which they provide with probability p>0. Find the value of p.

Consider the following public good provision game. There are 3 players with private infor- mation about their costs of contributing for the public good. Players have two actions: contribute or don't contribute. If at least two players contribute for the public good, then they all get a payoff of 1. If less than two players contribute, then all receive zero payoff. Only the players who contribute for the public good pays the cost. The costs are either az or 0.8 and each is equally likely. (a) Find the highest value of x in a Bayesian Nash equilibrium where all players with type x contributes and all players with type 0.8 don't. (b) Now suppose that costs are either 0.2, 0.5 or 0.8 and all three are equally likely. Find a Bayesian Nash equilibrium in which players with type 0.2 always provide, players with type 0.8 never provide and players with type 0.5 uses a mixed strategy in which they provide with probability p>0. Find the value of p.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.11P

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