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Consider a market in which Aldi must choose whether to Enter (E) or Not Enter (NE). If Aldi chooses to Not Enter, its payoff is 10 and its rival Coles’ payoff is 20. If Aldi Enters this is observed by Coles, and Coles must choose either to Punish (P) or Accommodate (A). If following Entry by Aldi Coles Punishes the payoffs are 5 to Aldi and 10 to Coles. If following Entry by Aldi Coles Accommodates the payoffs are 12 to Aldi and 15 to Coles. What are the Nash equilibria of the game?Group of answer choices(NE, A)(E, P)(NE, P) and (E, A)(NE, P)(E, A)

Question

Consider a market in which Aldi must choose whether to Enter (E) or Not Enter (NE). If Aldi chooses to Not Enter, its payoff is 10 and its rival Coles’ payoff is 20. If Aldi Enters this is observed by Coles, and Coles must choose either to Punish (P) or Accommodate (A). If following Entry by Aldi Coles Punishes the payoffs are 5 to Aldi and 10 to Coles. If following Entry by Aldi Coles Accommodates the payoffs are 12 to Aldi and 15 to Coles. What are the Nash equilibria of the game?Group of answer choices(NE, A)(E, P)(NE, P) and (E, A)(NE, P)(E, A)

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Solution

The Nash equilibria of the game are (NE, P) and (E, A).

Here's why:

A Nash equilibrium is a set of strategies, one for each player, such that no player has incentive to unilaterally change her action given the other player’s action.

  1. If Aldi chooses to Not Enter (NE), its payoff is 10 and Coles’ payoff is 20. Coles cannot change its strategy because it doesn't have a decision to make in this case. So, (NE, P) is a Nash equilibrium.

  2. If Aldi chooses to Enter (E), Coles has to decide whether to Punish (P) or Accommodate (A). If Coles chooses to Punish, the payoffs are 5 to Aldi and 10 to Coles. If Coles chooses to Accommodate, the payoffs are 12 to Aldi and 15 to Coles. Given that Aldi has entered, Coles would prefer to Accommodate because it gets a higher payoff (15 > 10). Knowing this, Aldi would choose to Enter because it gets a higher payoff by entering and being accommodated (12 > 10). So, (E, A) is also a Nash equilibrium.

Therefore, the Nash equilibria of the game are (NE, P) and (E, A).

This problem has been solved

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Consider a market in which Aldi must choose whether to Enter (E) or Not Enter (NE). If Aldi chooses to Not Enter, its payoff is 10 and its rival Coles’ payoff is 20. If Aldi Enters this is observed by Coles, and Coles must choose either to Punish (P) or Accommodate (A). If following Entry by Aldi Coles Punishes the payoffs are 5 to Aldi and 10 to Coles. If following Entry by Aldi Coles Accommodates the payoffs are 12 to Aldi and 15 to Coles. What are the credible equilibria (SPE) of the game?

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