Entry across markets and contests and some related problems

Abstract We consider a model where the agents choose a single niche in which to act such as different markets, contests or groups. We look for the existence of a free entry equilibrium in which no agent wishes to switch to a different niche. When the integer problem is neglected, continuity suffices to show existence of equilibrium. We apply this result to the existence of a Walrasian equilibrium without Walras’ law. When the number of agents in each niche is an integer, an equilibrium may not exist. Nonetheless, it does exist when there are two niches only or when payoffs in each niche depend only on the number of agents in this niche. We provide an algorithm to find the equilibrium number of agents. Equilibrium payoffs may be Pareto dominated. Our model encompasses a number of set ups showing that, mathematically, share the same structure.