Answered: Nash equilibria

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

Chapter15: Strategic Games

Section: Chapter Questions

Problem 3MC

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PART C D

Transcribed Image Text:(d) Now, consider the dynamic setup once again where player 1 moves before player 2, and the payoffs remain unchanged (a = 0). i Draw the game tree for this dynamic game. What are the possible strategies for each player? Recall that a strategy profile for a player not at the initial node of the game tree must specify an action for the player at every node. ii. Find the backward-induction solution(s) to this game. Calculate the equilibrium payoffs for each player. Com- pared to the simultaneous game, is there a first-mover advantage or a second-mover advantage? How is this different to the result in the ii. previous dynamic game when a= 2?

Transcribed Image Text:1. Static and Dynamic Game. Consider the following 2-by-2 game: C D 1A (1,10) (1,1) B (2, a) (0,1) (a) erwise, find the pure-strategy Nash equilibria, if any of this game. (There is no need to look for equilibria in mixed strategies) Assume for now that a = 2. Using dominant strategies or oth- (b) Now, consider the dynamic game in which player 1 moves before player 2, and the payoffs remain unchanged. i.: possible strategies for each player? Recall that a strategy profile for a player not at the initial node of the game tree must specify an action for the player at every node. Draw the game tree for this dynamic game. What are the ii "Find the backward-induction solution(s) to this game. Calculate the equilibrium payoffs for each player. Com- pared to the simultaneous game, is there a first-mover advantage or a ii. second-mover advantage? (c) Now, assume that a = 0 in the original static game. i. Find all the Nash equilibria in pure and mixed strategies. Denoting p the probability player 1 plays A and q the prob- ability that player 2 plays C, compute and graph the best-response functions of each player. Show that where the two best response func- tions intersect represent the Nash equilibrium or equilibria of the game. Calculate the equilibrium payoff of each player. ii. iii.

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