  Can noncooperative behaviour of merchants lead to a market split that prima
facie seems anticompetitive? We introduce a model in which service providers,
with ISPs being the main example, aim at optimizing the number of customers
using their services, while customers aim at choosing service providers with
low customer load (high bandwidth per subscriber, for ISPs). Each service
provider chooses between a variety of levels of service (latencies, for ISPs),
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,
service providers select their levels of service; in the second stage,
customers choose between service providers. In the two-stage game, we show that
the competition among service providers possesses a unique Nash equilibrium,
which is moreover super-strong; we also show that 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 a 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 its market slice, seemingly making no
attempt to attract other customers. Our results show that this prima facie
market allocation (collusive split of the market) arises as the unique and
highly robust outcome of noncooperative, even myopic, service-provider
behaviour. These results are applicable to a wide variety of scenarios, from
explaining phenomena observable in food markets, to shedding a surprising light
on aspects of location theory.
