Aldi can choose to Stock or to Not Stock a product, Crunchy Biscuits. If it opts for Not Stock, the payoff to Aldi is 4 and the manufacturer of Crunchy Biscuits gets 3. If Aldi chooses to Stock, Crunchy Biscuits can set a Low price or a High price for the product. If it sets a Low price, following Aldi’s choice to Stock, the payoff is (10, 5) to Aldi and Crunchy Biscuits, respectively. If Aldi chooses Stock, then Crunch Biscuits opts for High, the payoffs are (5, 10). What are the Nash equilibria of the game?
Question
Aldi can choose to Stock or to Not Stock a product, Crunchy Biscuits. If it opts for Not Stock, the payoff to Aldi is 4 and the manufacturer of Crunchy Biscuits gets 3. If Aldi chooses to Stock, Crunchy Biscuits can set a Low price or a High price for the product. If it sets a Low price, following Aldi’s choice to Stock, the payoff is (10, 5) to Aldi and Crunchy Biscuits, respectively. If Aldi chooses Stock, then Crunch Biscuits opts for High, the payoffs are (5, 10). What are the Nash equilibria of the game?
Solution
The Nash equilibria of the game are the strategies where no player can unilaterally deviate and improve their payoff.
In this game, we have two players: Aldi and Crunchy Biscuits. They have two strategies each: Aldi can choose to Stock or Not Stock the product, and Crunchy Biscuits can choose to set a Low price or a High price.
Let's analyze the payoffs:
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If Aldi chooses Not Stock, the payoff is (4,3) regardless of Crunchy Biscuits' strategy. Aldi gets 4 and Crunchy Biscuits gets 3. This is a Nash equilibrium because neither player can improve their payoff by unilaterally changing their strategy.
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If Aldi chooses Stock and Crunchy Biscuits chooses Low, the payoff is (10,5). This is not a Nash equilibrium because Crunchy Biscuits can improve their payoff by unilaterally changing their strategy to High, which would give them a payoff of 10.
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If Aldi chooses Stock and Crunchy Biscuits chooses High, the payoff is (5,10). This is not a Nash equilibrium because Aldi can improve their payoff by unilaterally changing their strategy to Not Stock, which would give them a payoff of 4.
So, the only Nash equilibrium in this game is when Aldi chooses Not Stock and Crunchy Biscuits' strategy doesn't matter (it can be either Low or High).
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