Nash equilibria in discrete routing games with convex latency functions
Journal of Computer and System Sciences
On the Road to $\mathcal{PLS}$-Completeness: 8 Agents in a Singleton Congestion Game
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Malicious Bayesian Congestion Games
Approximation and Online Algorithms
A Multi-Agent Resource Negotiation for the Utilitarian Welfare
Engineering Societies in the Agents World IX
The Impact of Social Ignorance on Weighted Congestion Games
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Evolutionary equilibrium in Bayesian routing games: Specialization and niche formation
Theoretical Computer Science
Tradeoffs and Average-Case Equilibria in Selfish Routing
ACM Transactions on Computation Theory (TOCT)
Routing (un-) splittable flow in games with player-specific affine latency functions
ACM Transactions on Algorithms (TALG)
Social context congestion games
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Exact Price of Anarchy for Polynomial Congestion Games
SIAM Journal on Computing
Efficiency analysis of load balancing games with and without activation costs
Journal of Scheduling
Social context congestion games
Theoretical Computer Science
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In his seminal work, Harsanyi (Manag. Sci. 14, 159–182, 320–332, 468–502, 1967) introduced an elegant approach to study non-cooperative games with incomplete information. In our work, we use this approach to define a new selfish routing game with incomplete information that we call Bayesian routing game. Here, each of n selfish users wishes to assign its traffic to one of m parallel links. However, users do not know each other’s traffic. Following Harsanyi’s approach, we introduce, for each user, a set of possible types. In our model, each type of a user corresponds to some traffic and the players’ uncertainty about each other’s traffic is described by a probability distribution over all possible type profiles. We present a comprehensive collection of results about our Bayesian routing game. Our main findings are as follows: Using a potential function, we prove that every Bayesian routing game has a pure Bayesian Nash equilibrium. More precisely, we show this existence for a more general class of games that we call weighted Bayesian congestion games. For Bayesian routing games with identical links and independent type distribution, we give a polynomial time algorithm to compute a pure Bayesian Nash equilibrium. We study structural properties of fully mixed Bayesian Nash equilibria for the case of identical links and show that they maximize Individual Cost. In general, there is more than one fully mixed Bayesian Nash equilibrium. We characterize fully mixed Bayesian Nash equilibria for the case of independent type distribution. We conclude with bounds on Coordination Ratio for the case of identical links and for three different Social Cost measures: Expected Maximum Latency, Sum of Individual Costs and Maximum Individual Cost. For the latter two, we are able to give (asymptotically) tight bounds using the properties of fully mixed Bayesian Nash equilibria we proved.