[Cheap Talk] Two players must decide whether to implement a project, which has gross value v E {0,100, 200} to each player. Both players think each value is equally likely. Player 1 (the sender) learns the true value of the project. Then, he reports a value {high,medium,low} to player 2 (the decider), and player 2 decides whether or not to implement the project. If the project is not implemented, both players get zero. If a project with value v is implemented, payoffs are P1 : v – 75 P2 : v – 125 (a) Show that there is no Perfect Bayesian Equilibrium (PBE) in which player 1 always reveals the true value to player 2. (b) Find a PBE in which player 1 reports “high" if the project is worth $200, "low" if the project is worth $0 (and either "low" or "high" when the project is worth $100, figure out which one works). (c) Find another PBE (or, if you believe there are no others, explain).

[Cheap Talk] Two players must decide whether to implement a project, which has gross value v E {0,100, 200} to each player. Both players think each value is equally likely. Player 1 (the sender) learns the true value of the project. Then, he reports a value {high,medium,low} to player 2 (the decider), and player 2 decides whether or not to implement the project. If the project is not implemented, both players get zero. If a project with value v is implemented, payoffs are P1 : v – 75 P2 : v – 125 (a) Show that there is no Perfect Bayesian Equilibrium (PBE) in which player 1 always reveals the true value to player 2. (b) Find a PBE in which player 1 reports “high" if the project is worth $200, "low" if the project is worth $0 (and either "low" or "high" when the project is worth $100, figure out which one works). (c) Find another PBE (or, if you believe there are no others, explain).

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter18: Auctions

Section: Chapter Questions

Problem 18.1IP

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