5. Find all the Bayesian-Nash equilibria in pure strategies. Consider the following normal form game 1 A B 2 A B -1,-1 1,0 0,1 0,0 Now introduce a bit of incomplete information in the following way. In the incomplete information version player i gets (1+t) when it plays A and its rival plays B. Here t, is private information for player i. Each player j believes that t; (ij) is uniformly distributed over [- +e]. Everything else is the same as in the original game. Show that when e converges to zero the pure strategy Bayesian- Nash equilibrium converges to the mixed strategy Nash equilibrium of the complete information game.

5. Find all the Bayesian-Nash equilibria in pure strategies. Consider the following normal form game 1 A B 2 A B -1,-1 1,0 0,1 0,0 Now introduce a bit of incomplete information in the following way. In the incomplete information version player i gets (1+t) when it plays A and its rival plays B. Here t, is private information for player i. Each player j believes that t; (ij) is uniformly distributed over [- +e]. Everything else is the same as in the original game. Show that when e converges to zero the pure strategy Bayesian- Nash equilibrium converges to the mixed strategy Nash equilibrium of the complete information game.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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2
Information Is complete
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