Regret based dynamics: convergence in weakly acyclic games
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Adaptive Learning in Systems of Interacting Agents
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Cooperative control and potential games
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IEEE Transactions on Image Processing
On the structure of weakly acyclic games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Sampled fictitious play for approximate dynamic programming
Computers and Operations Research
Convergence to equilibrium of logit dynamics for strategic games
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Multiagent learning in large anonymous games
Journal of Artificial Intelligence Research
Weakly-acyclic (internet) routing games
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Distributed selfish load balancing on networks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Automatica (Journal of IFAC)
Hedonic coalition formation for optimal deployment
Automatica (Journal of IFAC)
Weakly-Acyclic (Internet) Routing Games
Theory of Computing Systems
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We consider repeated multiplayer games in which players repeatedly and simultaneously choose strategies from a finite set of available strategies according to some strategy adjustment process. We focus on the specific class of weakly acyclic games, which is particularly relevant for multiagent cooperative control problems. A strategy adjustment process determines how players select their strategies at any stage as a function of the information gathered over previous stages. Of particular interest are “payoff-based” processes in which, at any stage, players know only their own actions and (noise corrupted) payoffs from previous stages. In particular, players do not know the actions taken by other players and do not know the structural form of payoff functions. We introduce three different payoff-based processes for increasingly general scenarios and prove that, after a sufficiently large number of stages, player actions constitute a Nash equilibrium at any stage with arbitrarily high probability. We also show how to modify player utility functions through tolls and incentives in so-called congestion games, a special class of weakly acyclic games, to guarantee that a centralized objective can be realized as a Nash equilibrium. We illustrate the methods with a simulation of distributed routing over a network.