Quality of equilibria in resource allocation games

Abstract

In situations where multiple parties are involved, local or selfish decisions result in outcomes that rarely align with what is best for society. In order to evaluate the quality of the resulting outcomes, we first need to predict which outcomes can occur. Game theory offers answers to this question, the Nash equilibrium being the most prominent example: it is an outcome where no party can improve by unilateral deviations. In that sense Nash equilibria are a good description of a stable outcome, but do not ask how that outcome was actually obtained. Implicitly, Nash equilibria make the assumption that parties choose their actions simultaneously. However, sequential decisions, where parties anticipate each other’s actions, are often more natural, and may lead to different equilibria. We consider multiple equilibrium concepts for a variety of games, including Nash and subgame perfect equilibria, and analyze the quality of these equilibria. The results include several lower and upper bounds on what is known as the price of anarchy, or variations thereof. The main class of games we consider is the class of congestion games. Congestion games model the allocation of scarce resources to a set of players. The model includes as special case the celebrated network routing games, a classical showcase problem in algorithmic game theory. Applications include the design of street networks in order to mitigate delays due to traffic jams, or the design of internet protocols that result in more efficient use of available bandwidth.