Location Games with Externalities

We propose a two step game of coalition or city formation. In a first step, each player chooses the location in which he wants to be. The payoff function, determined in the second step by a game between the different locations reflects two effects: a public effect such that payoffs decrease with the number of non-empty locations; a private effect such that payoffs to the inhabitants of a PartIcular location decrease with the size of the population at that location. We analyse the consequences for the set of stable profiles of an increase in the relative weight of the public effect in the payoff function. We show that the number of stable profiles increases with the public effect but that the newly added profiles are not always more concentrated.