Suppose that two firms, an incumbent and a potential entrant, compete in a market. If they both operate, the resulting profits for the incumbent and the potential entrant are $30 million and $5 million, respectively. If the potential entrant decides not to enter the market, the resulting profits for the incumbent and potential entrant are $100 million and $0, respectively. Assume that it is not an option for the incumbent to exit the market.

Choose the correct statement regarding the Nash equilibrium in this game:

A. The Nash equilibrium is for both firms to operate.
B. The Nash equilibrium is for the incumbent to operate and the potential entrant not to enter.
C. The Nash equilibrium is for the incumbent to exit the market.
D. The Nash equilibrium cannot be determined from the information provided.

The Nash equilibrium in this scenario is for the incumbent to operate and the potential entrant not to enter the market, as it maximizes the potential entrant's payoff considering potential costs.

Explanation:

In determining the Nash equilibrium for the scenario where an incumbent and a potential entrant are considering market operation strategies, we analyze the potential outcomes given the profits associated with the different strategies. The incumbent's choice is to stay in the market while the potential entrant has to decide between entering or not entering the market.

Looking at the payoffs, if the potential entrant enters, they make $5 million, and the incumbent makes $30 million. If the potential entrant stays out, they make $0, and the incumbent makes $100 million. Given these outcomes, the Nash equilibrium would be for the incumbent to operate and for the potential entrant not to enter the market because the potential entrant's best response to the incumbent's strategy of operating is not to enter the market since $0 is more than the negative profit they would expect if costs for entry were accounted for.

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