Suppose there are two large hospitals A and B in a market ea

Suppose there are two large hospitals, A and B, in a market, each facing the decision of whether to add an expensive heart transplant unit without knowing what its rival will do. The payoff matrix shows the total profit for each hospital (with values for A\'s profit shown first) resulting from the four combinations of strategies. What is a dominant strategy in game theory? Does A have a dominant strategy? Does B? What is the solution (i.e., Nash equilibrium) to this game?

Solution

A dominant strategy of the player is a strategy which is better for him that any other strategy. He chooses this strategy always irrespective of what the other player is doing.

Yes Player A has a dominat strategy, Adopt he plays this strategy no matter what B is playing.

B Does not have any dominant strategy.

The nash equilibrium of this game is (Adopt, Adopt). This is because when A chooses Adopt, B also chooses to adopt. It is the equilibrium and no player has an incentive to move from this equilibriu.