Mediated Equilibria in Load-Balancing Games

• Authors: Joshua R. Davis;David Liben-Nowell;Alexa Sharp;Tom Wexler
• Venue: WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
• Year: 2009

Mediators are third parties to whom the players in a game can delegate the task of choosing a strategy; a mediator forms a mediated equilibrium if delegating is a best response for all players. Mediated equilibria have more power to achieve outcomes with high social welfare than Nash or correlated equilibria, but less power than a fully centralized authority. Here we begin the study of the power of mediation by using the mediation analogue of the price of stability--the ratio of the social cost of the best mediated equilibrium $\textsc{bme}$ to that of the socially optimal outcome $\textsc{opt}$. We focus on load-balancing games with social cost measured by weighted average latency. Even in this restricted class of games, $\textsc{bme}$ can range from as good as $\textsc{opt}$ to no better than the best correlated equilibrium. In unweighted games $\textsc{bme}$ achieves $\textsc{opt}$; the weighted case is more subtle. Our main results are (1) that the worst-case ratio $\textsc{bme}/\textsc{opt}$ is at least $(1+\sqrt{2})/2\approx 1.2071$ (and at most 1 + 驴 ≈ 2.618 [3]) for linear-latency weighted load-balancing games, and that the lower bound is tight when there are two players; and (2) tight bounds on the worst-case $\textsc{bme}/\textsc{opt}$ for general-latency weighted load-balancing games. We also give similarly detailed results for other natural social-cost functions.