Entry in Markets and Contests and Some Related Problems

We consider a model in which agents choose a single niche to act. These niches could be different markets around the world or different contests. We look for the existence of a free entry equilibrium in which no agent wishes to switch to a different niche. When agents form a continuum, continuity suffices to show existence. We apply this result to the existence of a Walrasian equilibrium without Walras'law. With a discrete number of agents, equilibrium, in general, does not exist. It does when there are two niches only or when payoffs in each niche depend only on the number of agents in this niche. The latter set up generalizes hedonic games