Unit 10- Lesson 34- Games With PSNE and MSNE PDF

Preview

Summary

Spring 2016
Prof. Kathleen Brown...

Description

Unit 10: Mixed Strategies, Part 2 Lesson 34: Games with PSNE and MSNE Basic System for finding NE in mixed strategies. 1. Use variables to represent probabilities associated with each player pure strategies. 2. Write out the expected values of player A’s strategies as a function of player B’s (variable) probabilities. 3. Set A’s expected pay-offs equal and solve for B’s probability. 4. Repeat for the other player. Key is to find the probability that leaves opponent indifferent between two pure strategies. Some games can have NE in both pure and mixed strategies. Chicken A/B

Swerve

Don't

Swerve (0,0)

(-1,1)

Don’t

(-10,-10)

(1,-1)

In addition to Don’t Swerve/Swerve, and Swerve/Don’t there is a NE in mixed strategies. Let q = prob(A swerves) EU(B)(swerve) = q*0 + -1*(1-q) = q-1 EU(B)(Don’t Swerve) = q*1 + (-10)*(1-q) = q-10 + 10q = 11q - 10 11q - 10 = q -1 10q = 9 q = 9/10 A swerves with .9 prob, doesn’t with .1 prob. B is same. Expected outcomes are A swerve, B swerve .81 A swerve, B doesn’t .09 B swerve, A doesn’t .09 Nobody Swerve .01 EU(A) = .81*0 + 0.9*-1 + 0.9*1 + 0.01B*-10 = -0.1 Battle of the sexes, Assurance, Pure Coordination also have MSNE in additional to PSNE...