# Consider the following game: there are two players, an incumbent (denoted I) and a potential entrant...

###### Question:

Consider the following game: there are two players, an incumbent (denoted

I) and a potential entrant (denoted E) to the market. The entrant has two actions: it can either enter the market in which the incumbent operates, or not enter. The incumbent has two actions: it can either fight the entrant, or accommodate. The payoffs are as follows: if E enters and I fights, E gets -1 and I gets 2. If E does not enter, I gets 10 for any of its two actions, and E gets 0. If E enters and I accommodates, then both get the payoff 5.

1. Suppose that both players act simultaneously. Depict the game with the help of a game matrix. Find the Nash equilibria (in pure strategies).

2. Now suppose that E moves first, and then the I follows. Depict this sequential game with the help of a game tree. What is the equilibrium of the game? (remember from the lecture that we have to apply ”backward reasoning” - start from the end and move to the start of the game).

3. Suppose that before the game starts, I announces: ”If E enters, than I always fight”. Does it convince E in a simultaneous move game? Does it convince E in the sequential game? Why?

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