University of California, Davis
Department of Agricultural and Resource Economics
Problem Set 5
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).
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
nant strategy, because A has a higher
payoff if 2 chooses B and B has a higher payoff if 2 chooses A.
The resulting equilibrium is a Nash equilibrium:
Firm 2 will choose strategy B, and 1 will choose
Neither firm has a do
For firm 1, B is better if 2 chooses A and A is better if 2
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
librium because neither firm has an incentive to
change its strategy
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.