STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Selfish traffic allocation for server farms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Computing equilibria for congestion games with (im)perfect information
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Computing Nash equilibria for scheduling on restricted parallel links
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Computing Nash equilibria of action-graph games
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
The price of anarchy of finite congestion games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Computing equilibria in multi-player games
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Networks preserving evolutionary equilibria and the power of randomization
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Utilitarian resource assignment
Journal of Discrete Algorithms
Selfish Routing with Incomplete Information
Theory of Computing Systems
Nashification and the coordination ratio for a selfish routing game
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Evolutionary equilibrium in Bayesian routing games: specialization and niche formation
ESA'07 Proceedings of the 15th annual European conference on Algorithms
The contribution of game theory to complex systems
PCI'05 Proceedings of the 10th Panhellenic conference on Advances in Informatics
Congestion games with player-specific constants
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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In this paper we consider Nash equilibria for the selfish task allocation game proposed in Koutsoupias, Papadimitriou (1999) [26], where a set of n users with unsplittable tasks of different size try to access m parallel links with different speeds. In this game, a player can use a mixed strategy (where he uses different links with a positive probability); then he is indifferent between the different link choices. This means that the player may well deviate to a different strategy over time. We propose the concept of evolutionary stable strategies (ESS) as a criterion for stable Nash equilibria, i.e. equilibria where no player is likely to deviate from his strategy. An ESS is a steady state that can be reached by a user community via evolutionary processes in which more successful strategies spread over time. The concept has been used widely in biology and economics to analyze the dynamics of strategic interactions. We first define a symmetric version of a Bayesian parallel links game where every player is not assigned a task of a fixed size but instead is assigned a task drawn from a distribution, which is the same for all players. We establish that the ESS is uniquely determined for a given symmetric Bayesian parallel links game (when it exists). Thus evolutionary stability places strong constraints on the assignment of tasks to links. We characterize ESS for the Bayesian parallel links game, and investigate the structure of evolutionarily stable equilibria: In an ESS, links acquire niches, meaning that there is minimal overlap in the tasks served by different links. Furthermore, all links with the same speed are interchangeable for every task with weight w: Every player must place a task with weight w on links having the same speed with the same probability. Also, bigger tasks must be assigned to faster links and faster links must have a bigger load. Finally, we introduce a clustering condition-roughly, distinct links must serve distinct tasks-that is sufficient for evolutionary stability, and can be used to find an ESS in many models.