The table given below represents the payoff matrix of firms A and B,when they choose to produce either high output or low output.In each cell,the figure on the left indicates Firm B's payoffs and the figure on the right indicates Firm A's payoffs.
-If X = 10 and Y = 15,then from the information in Table 14-3 we can say that:
A)the payoff matrix represents a prisoner's dilemma game.
B)the game has a dominant-strategy equilibrium.
C)the game has a Nash equilibrium.
D)the payoff matrix represents a Cournot oligopoly.

Question

The table given below represents the payoff matrix of firms A and B,when they choose to produce either high output or low output.In each cell,the figure on the left indicates Firm B's payoffs and the figure on the right indicates Firm A's payoffs. 
-If X = 10 and Y = 15,then from the information in Table 14-3 we can say that:
A)the payoff matrix represents a prisoner's dilemma game. 
B)the game has a dominant-strategy equilibrium. 
C)the game has a Nash equilibrium. 
D)the payoff matrix represents a Cournot oligopoly.

Quizplus · Accepted Answer

To find the Nash equilibrium, we need to look for a situation where neither firm has an incentive to deviate from their current strategy, given the other firm's strategy. 
In this case, if Firm A produces high output, given that Firm B is producing low output, A's payoff would be 50 (the second number in the top row). If A produces low output, given that B is producing low output, A's payoff would be 40 (the second number in the bottom row). So, A would prefer to produce high output. 
Similarly, if Firm B produces high output, given that Firm A is producing low output, B's payoff would be 50 (the first number in the left column). If B produces low output, given that A is producing low output, B's payoff would be 40 (the first number in the right column). So, B would prefer to produce high output. 
Therefore, the Nash equilibrium is for both firms to produce high output.

The Table Given Below Represents the Payoff Matrix of Firms