Scenario 13.9
Consider the following game:
Two firms are situated next to a lake, and it costs each firm $1,500 per period to use filters that avoid polluting the lake. However, each firm must use the lake's water in production, so it is also costly to have a polluted lake. The cost to each firm of dealing with water from a polluted lake is $1,000 times the number of polluting firms.
-A "mixed strategy" equilibrium means that:
A) the strategies chosen by the players represent different behaviors.
B) one player has a dominant strategy, and one does not.
C) one player has a pure strategy, and one does not.
D) the equilibrium strategy is an assignment of probabilities to pure strategies.
E) the equilibrium strategy involves alternating between a dominant strategy and a Nash strategy.

Question

Scenario 13.9
Consider the following game:
Two firms are situated next to a lake, and it costs each firm $1,500 per period to use filters that avoid polluting the lake. However, each firm must use the lake's water in production, so it is also costly to have a polluted lake. The cost to each firm of dealing with water from a polluted lake is $1,000 times the number of polluting firms. 
-A "mixed strategy" equilibrium means that:
A) the strategies chosen by the players represent different behaviors. 
B) one player has a dominant strategy, and one does not. 
C) one player has a pure strategy, and one does not. 
D) the equilibrium strategy is an assignment of probabilities to pure strategies. 
E) the equilibrium strategy involves alternating between a dominant strategy and a Nash strategy.

Quizplus · Accepted Answer

In a mixed strategy equilibrium, the players assign probabilities to their pure strategies in order to make their opponent indifferent between their own pure strategies. This results in a situation where neither player has an incentive to deviate from their chosen strategy, and the outcome is a stable equilibrium. This type of equilibrium is particularly useful in games where there is no dominant strategy for either player, as it allows for the possibility of both players making random choices.

Scenario 13.9 Consider the Following Game