Noncooperative Market Allocation and the Formation of Downtown

Can noncooperative behaviour of merchants lead to a market allocation that prima facie seems anticompetitive? We introduce a model in which service providers aim at optimizing the number of customers who use their services, while customers aim at choosing service providers with minimal customer load. Each service provider chooses between a variety of levels of service, and as long as it does not lose customers, aims at minimizing its level of service; the minimum level of service required to satisfy a customer varies across customers. We consider a two-stage competition, in the first stage of which the service providers select their levels of service, and in the second stage — customers choose between the service providers. (We show via a novel construction that for any choice of strategies for the service providers, a unique distribution of the customers’ mass between them emerges from all Nash equilibria among the customers, showing the incentives of service providers in the two-stage game to be well defined.) In the two-stage game, we show that the competition among the service providers possesses a unique Nash equilibrium, which is moreover super strong; we also show that all sequential better-response dynamics of service providers reach this equilibrium, with best-response dynamics doing so surprisingly fast. If service providers choose their levels of service according to this equilibrium, then the unique Nash equilibrium among customers in the second phase is essentially an allocation (i.e. split) of the market between the service providers, based on the customers’ minimum acceptable quality of service; moreover, each service provider’s chosen level of service is the lowest acceptable by the entirety of the market share allocated to it. Our results show that this seemingly-cooperative allocation of the market arises as the unique and highly-robust outcome of noncooperative (i.e. free from any form of collusion), even myopic, service-provider behaviour. The results of this paper are applicable to a variety of scenarios, such as the competition among ISPs, and shed a surprising light on aspects of location theory, such as the formation and structure of a city’s central business district.