Value of reputation in the chain-store game with multiple incumbents

We extend the basic chain-store game to the two-incumbent case. A highly stylized model is developed to analyze incentives of incumbent firms to maintain reputation for toughness. Entry deterrence has a public good property. Since maintaining reputation is costly, each incumbent has an incentive to free ride on the entry deterring activities of its counterpart. As a result of these incentives, both incumbents accommodate when they both have a relatively high initial reputation for toughness. This extreme form of underinvestment in entry deterrence becomes less likely as the number of markets with potential entry increases. We also demonstrate that an incumbent's payoff is a decreasing function of its reputation over a large range of parameters. This result stands in sharp contrast to the existing versions of the chain-store game where high reputation for toughness always benefits a weak incumbent.