Games with Congestion-Averse and Congestion-Seeking Players

Igal Milchtaich and Anna Zalkind

Abstract

The paper studies a class of resource-symmetric singleton congestion games with two types of players having diametrically opposite preferences. Congestion-averse players wish to avoid congestion while congestion-seeking players favor it. We show that a pure-strategy Nash equilibrium may or may not exist, depending on the number of players of each type and the number of resources in the game. The same numbers also determine whether the game is acyclic with respect to unilateral best-improvement moves, that is, whether such moves always lead to an equilibrium. We also study the sequential-move versions of the game, in which the players choose resources one by one after observing the choices of all preceding players, and cannot later change them. The players’ choices in a subgame perfect equilibrium in this game do not necessary constitute an equilibrium in the original, simultaneous-move game. However, the converse does hold: every equilibrium in the simultaneous-move game is a sequential-move equilibrium, in the sense that it is obtained as the equilibrium path in some subgame perfect equilibrium for some entrance order.

JEL classification

C72

Keywords

Congestion Games; Congestion-Seeking Players; Weak Acyclicity; Weak Potential; Sequential-Move Equilibrium; Pure-Strategy Equilibrium