# PS5AW10 - ARE 100B Dr Larson University of California Davis...

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University of California, Davis Department of Agricultural and Resource Economics ARE 100B Winter 20 1 0 Dr. Larson Problem Set 5 Answers 1. For each of the following payoff matrices, determine (i) whether Firm 1 or Firm 2 (or both) has a dominant strategy; and (ii) the type of equilibrium that will result (dominant strategy equilibrium, Nash equilibrium, or none). (a) Firm 2 (b) Firm 2 A B A B Firm A 10,2 12,4 Firm A -2,-2 2,4 1 B 17,5 8,7 1 B 4,2 -2,-2 (c) Firm 2 (d) Firm 2 A B A B Firm A 1,1 2,2 Firm A 19,0 23,2 1 B 0,2 1,2 1 B 18,2 21,1 Game (a): (i) B is a dominant strategy for Firm 2, because its payoffs of 4 and 7 are higher than the pay offs for strategy A (2 and 5, respectively). Firm 1 does not have a do mi nant strategy, because A has a higher payoff if 2 chooses B and B has a higher payoff if 2 chooses A. (ii) The resulting equilibrium is a Nash equilibrium: Firm 2 will choose strategy B, and 1 will choose A. Game (b): (i) Neither firm has a do mi nant strategy. For firm 1, B is better if 2 chooses A and A is better if 2 chooses B. For firm 2, A is better if 1 chooses B and B is better if 1 chooses A. (ii) There are two Nash equilibria, (B,A) and (A,B). Strategy com bination (B,A) is a Nash equ i librium because neither firm has an incentive to change its strategy , taking the o ther ' s as given. For firm 1, changing strategy from B to A would decrease its pay off from 4 to -2, while for firm 2, changing strategy from A to B would decrease its payoff from 2 to -2. Strategy combination (A,B) is also a Nash equilibrium. If firm 1 changes strategy from A to B its payoff decreases from 2 to -2, and if firm 2 changes strategy from B to A its pay off decreases from 4 to -2.

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PS5AW10 - ARE 100B Dr Larson University of California Davis...

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