Consider the expansion decision of two firms A and B operating in the same market. The payoff to each firm depends on its own expansion decision and its opponent’s expansion decision. If both firms choose to expand, the competition will be intense and both firm will get a low profit of 45. If none of the firms expand, both firm will get a profit of 80. However, if only Firm A expands and Firm B does not expand, Firm A will get a profit of 140 and Firm B will get 55. If only Firm B expands and Firm A does not expand, Firm B will get a profit of 140 and Firm A will get 40.
- Write the normal form (i.e., payoff matrix) of the game. Let Firm A to be the row player and Firm B to be the column player.
- Is there a dominant strategy for Firm A? Is there a dominant strategy for Firm B? List the dominant strategy if there is any.
- List the maximin strategies for Firm A and Firm B.
- What is the Nash equilibrium of the game if the two firms move simultaneously?
- Suppose Firm A moves first and Firm B moves after observing Firm A’s decision. Write the extensive form of the game.
- In the sequential game, what is the subgame perfect Nash equilibrium if Firm A moves first?