The two largest auto manufacturers, Toyota and GM, have experimented with hydrogen powered cars in the past, and they are currently considering the decision to introduce a hydrogen powered car into the commercial automobile market. The payoffs from the possible actions are measured in millions of dollars per year, and the possible outcomes are summarized in the following game matrix:

If both firms enter the market simultaneously, what is the Nash equilibrium?
A) Toyota produces and GM does not produce.
B) GM produces and Toyota does not produce.
C) There are two Nash equilibria - GM produces and Toyota does not produce, or Toyota produces and GM does not produce.
D) There is no Nash equilibrium in this game.

Question

The two largest auto manufacturers, Toyota and GM, have experimented with hydrogen powered cars in the past, and they are currently considering the decision to introduce a hydrogen powered car into the commercial automobile market. The payoffs from the possible actions are measured in millions of dollars per year, and the possible outcomes are summarized in the following game matrix:

If both firms enter the market simultaneously, what is the Nash equilibrium?

If both firms enter the market simultaneously, what is the Nash equilibrium?
A) Toyota produces and GM does not produce. 
B) GM produces and Toyota does not produce. 
C) There are two Nash equilibria - GM produces and Toyota does not produce, or Toyota produces and GM does not produce. 
D) There is no Nash equilibrium in this game.

Quizplus · Accepted Answer

Both firms have a dominant strategy to not enter the market, as this results in a payoff of $0, which is better than any other possible outcome. However, if one firm enters the market, the other firm will have an incentive to also enter the market, as the payoff from entering ($10 million) is greater than the payoff from not entering ($0). Therefore, there are two Nash equilibria in which only one firm enters the market, resulting in a payoff of $10 million for the entering firm and $0 for the non-entering firm. The two equilibria are: GM produces and Toyota does not produce, or Toyota produces and GM does not produce.

The Two Largest Auto Manufacturers, Toyota and GM, Have Experimented