Equilibria in bottleneck games

Abstract

This paper introduces a bottleneck game with finite sets of commuters and departing time slots as an extension of congestion games by Milchtaich (1996). After characterizing Nash equilibrium of the game, we provide sufficient conditions for which the equivalence between Nash and strong equilibria holds. Somewhat surprisingly, unlike in congestion games, a Nash equilibrium in pure strategies may often fail to exist, even when players are homogeneous. In contrast, when there is a continuum of atomless players, the existence of a Nash equilibrium and the equivalence between the set of Nash and strong equilibria hold as in congestion games (Konishi, Le Breton, and Weber, 1997a).