Suppose two companies, Macrosoft and Apricot, are considering whether to develop a new product, a touch-screen t-shirt. The payoffs to each of developing a touch-screen t-shirt depend upon the actions of the other, as shown in the payoff matrix below (the payoffs are given in millions of dollars). If Macrosoft and Apricot make their decision at the same time, then which of the following statements is correct?
A)The only Nash equilibrium is that both develop a touch-screen t-shirt.
B)The only Nash equilibrium is that neither develops a touch-screen t-shirt.
C)The game does not have a Nash equilibrium.
D)The game has more than one Nash equilibrium.

Question

Suppose two companies, Macrosoft and Apricot, are considering whether to develop a new product, a touch-screen t-shirt. The payoffs to each of developing a touch-screen t-shirt depend upon the actions of the other, as shown in the payoff matrix below (the payoffs are given in millions of dollars).  If Macrosoft and Apricot make their decision at the same time, then which of the following statements is correct?
A)The only Nash equilibrium is that both develop a touch-screen t-shirt. 
B)The only Nash equilibrium is that neither develops a touch-screen t-shirt. 
C)The game does not have a Nash equilibrium. 
D)The game has more than one Nash equilibrium.

Quizplus · Accepted Answer

To find the Nash equilibrium, we need to look for the strategy of each player where neither player would want to deviate given the strategy of the other. One way to do it is to look at each player's best response to the other player's strategy. If both players' best response corresponds to their respective actions in the payoff matrix, then we have a Nash equilibrium.
In this case, if Apricot develops a touch-screen t-shirt, Macrosoft's best response is also to develop a touch-screen t-shirt. If Apricot does not develop a touch-screen t-shirt, then Macrosoft's best response is also not to develop a touch-screen t-shirt. Similarly, if Macrosoft develops a touch-screen t-shirt, Apricot's best response is also to develop a touch-screen t-shirt. If Macrosoft does not develop a touch-screen t-shirt, then Apricot's best response is also not to develop a touch-screen t-shirt.
Therefore, there are two Nash equilibria in this game: (Develop, Develop) and (Not Develop, Not Develop). Both choices are stable, meaning that neither player would want to deviate given the strategy of the other.

Suppose Two Companies, Macrosoft and Apricot, Are Considering Whether to Develop