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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?

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 credible equilibria (SPE) of the game?

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Solution

This seems to be a mistake as there is no text provided to respond to in a specific language. However, I can provide the answer to the original question about the credible equilibria (SPE) of the game.

The Subgame Perfect Equilibrium (SPE) is a concept used in game theory to analyze the strategic behavior of players in a sequential game. It is a refinement of the Nash Equilibrium that takes into account not only the strategies that are optimal in the final stage of the game, but also those that are optimal in every subgame.

In this case, we have a sequential game with two players: Aldi and Coles. The game has two stages: in the first stage, Aldi decides whether to Enter (E) or Not Enter (NE); in the second stage, if Aldi has chosen to Enter, Coles decides whether to Punish (P) or Accommodate (A).

To find the SPE, we use backward induction, starting from the second stage of the game:

  1. If Aldi Enters, Coles has to decide between Punishing or Accommodating. The payoff for Coles is higher if it Accommodates (15) than if it Punishes (10). Therefore, Coles' optimal strategy in this subgame is to Accommodate if Aldi Enters.

  2. Knowing Coles' strategy, Aldi has to decide between Entering or Not Entering. If Aldi Enters, its payoff will be 12 (since we know that Coles will Accommodate), and if it does not Enter, its payoff will be 10. Therefore, Aldi's optimal strategy in this game is to Enter.

So, the Subgame Perfect Equilibrium of this game is for Aldi to Enter and Coles to Accommodate (E, A), with payoffs of 12 for Aldi and 15 for Coles.

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