Question 1 A crime is witnessed by 3 citizens. Every citizen would like the police to be informed about the crime, but prefers that someone else reports it (filing a report is a hassle). Each of the three citizens chooses simultaneously (and independently) whether to call the police or not. When no one makes a call, every citizen receives payoff 0. If at least one citizen calls the police, citizens who call get payoff 5, and those who don't call get payoff 9. (a) Find all Nash equilibria in pure strategies. (b) Compute a symmetric Nash equilibrium in mixed strategies (i.e., an equilibrium in which every citizen calls with the same probability p E (0, 1)). (c) Does the game have a Nash equilibrium in pure or mixed strategies different from those you identified in (a) and (b)? If yes, construct one. If not, argue why not.

Question 1 A crime is witnessed by 3 citizens. Every citizen would like the police to be informed about the crime, but prefers that someone else reports it (filing a report is a hassle). Each of the three citizens chooses simultaneously (and independently) whether to call the police or not. When no one makes a call, every citizen receives payoff 0. If at least one citizen calls the police, citizens who call get payoff 5, and those who don't call get payoff 9. (a) Find all Nash equilibria in pure strategies. (b) Compute a symmetric Nash equilibrium in mixed strategies (i.e., an equilibrium in which every citizen calls with the same probability p E (0, 1)). (c) Does the game have a Nash equilibrium in pure or mixed strategies different from those you identified in (a) and (b)? If yes, construct one. If not, argue why not.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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