Question

Consider the following pricing game between Staples and Dunder-Mifflin. The payoffs below are profits presented in $100,000’s, with the order [Dunder-Mifflin, Staples]

			Staples
		Low	Medium	High
	Low	1,0	1,2	0,1
Dunder-Mifflin	Medium	0,0	2,1	3,3
	High	1,2	1,1	0,1

1. Find all Nash equilibria.
2. Provide an argument for selecting among those equilibria.

Answer 1

Explanation:

Nash equilibria are the strategy of a player where the player gets maximum payoff given the strategy of another player. If the player deviates from this strategy he will lose.

To find the Nash equilibria of this game, the best response of both the players should be underlined given the response of another player. The strategy profile where both the payoffs are underlined is the Nash equilibria of the game.

The best responses of both Dunder-Mifflin and staple have been underlined.

If the price of the staple is low, then the price of Dunder-Mifflin should be either low or high because both give maximum and same payoff (1>0).

If the price of the staple is Medium, then the price of Dunder-Mifflin should be medium because it gives maximum payoff (2>1).

If the price of the staple is High, then the price of Dunder-Mifflin should be medium because it gives maximum payoff (3>0).

Similarly, for different price levels of Dunder-Mifflin, the best response of the staple is marked.

There are two Nash equilibria of this game (highlighted in yellow). Those are Nash equilibria because both the payoffs are underlined. And if the strategy for staple is changed given the strategy of Dunder-Mifflin, then the payoff will reduce. Similarly for Dunder-Mifflin, if the strategy of Dunder-Mifflin is changed given the strategy of staple then the payoff will reduce.

(1). Medium, High (3, 3)

For instance, Given the strategy High for staple, if the strategy for Dunder-Mifflin is changed from Medium to either high or low then the payoff will reduce (0<3).

(2). High, Low (1, 2)

The Nash equilibrium, (Medium, High) should be selected as it gives more payoff for both Dunder-Mifflin and staple (3>1, 3>2).