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Question: an incumbent firm operates a store in a local market...

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An incumbent firm operates a store in a local market and faces the potential entry of a single rival. The entrant’s choices are to enter or to stay out of the market. If the entrant stays out, it earns 1 (the return from the best alternative investment); the incumbent earns 5. If the entrant comes in, then the incumbent must decide whether to cooperate with the entrant (in which case both earn a return of 2) or to fight entry (in which case both earn a zero return). What is the subgame perfect equilibrium of this game? Would your answer change if the incumbent operated 20 stores in 20 separate markets, and faced 20 potential entrants, one in each market, who must make their entry decisions sequentially? Provide a brief discussion of your results in the context of empirical evidence on entry deterrence.

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