The following figure shows a market entry game. A Challenger decides whether or

Question

The following figure shows a market entry game. A Challenger decides whether or not to enter a market (In" or "Out"). The Incumbent observes the decision and then chooses whether to-Fight" or to 'Acquiesce". As in class, at each point the first payoff is the one of the first-mover, in this case the Challenger, and the second payoff is the one of the second-mover, in this case the Incumbent. Find the Subgame Perfect Nash Equilibrium. Challenger In Out Incumbent 100 Fight Acquiesce 500 200 200 0 a The Subgame Perfect Nash Equilibrium is when the Challenger chooses "In and the Incumbent chooses "Acquiesce, leading to a payoff of 200 for each player. b. The Subgame Perfect Nash Equilibrium is when the Challenger chooses-In, and the Incum bent chooses "Fight," leading to a payoff of 0 for each player. c. The Subgame Perfect Nash Equilibrium is when the Challenger chooses Out and the Incumbent chooses Acquiesce," leading to a payoff of 100 for the Challenger and 500 for the Incumbent. The Subgame Perfect Nash Equilibrium is when the Challenger chooses "Out" and the Incumbent chooses "Fight," leading to a payoff of 100 for the Challenger and 500 for the Incumbent.

Explanation / Answer

The correct answer to the question is "A". We will choose backward induction to know the subgame perfect Nash equilibrium.

Nash equilibrium means a strategy from which neither player can deviate unilaterally or they will face loss.

In the first case, we will see what the incumbent will do in case the challenger decided to enter the market. if he gives a fight they both lose and get 0,0. But if the incumbent acquiesces both get 200,200. Getting 200 is more than getting nothing knowing that the incumbent will chose to give up.

The challenger knowing that the incumbent will give up or acquiesce and he will get 200 from that decision he will enter the market. As 200 is more than staying out and getting and getting only 100. So, getting in and acquiesce is a subgame perfect Nash equilibrium in this game. from this point if any of the players try to deviate they will face loss, if the incumbent decided to fight he looses of the challenger didn't enter the market he looses too.   

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