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Equilibrium Selection in Potential Games with Noisy Rewards

Abstract : Game theoretical learning in potential games is a highly active research area stemming from the connection between potential games and distributed optimisation. In many settings an optimisation problem can be represented by a potential game where the optimal solution corresponds to the potential function maximizer. Accordingly, significant research attention has focused on the design of distributed learning algorithms that guarantee convergence to the potential maximizer in potential games. However, there are currently no existing algorithms that provide convergence to the potential function maximiser when utility functions are corrupted by noise. In this paper we rectify this issue by demonstrating that a version of payoff-based loglinear learning guarantees that the only stochastically stable states are potential function maximisers even in noisy settings.
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https://hal.inria.fr/hal-00644411
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Submitted on : Thursday, November 24, 2011 - 2:02:10 PM
Last modification on : Friday, July 26, 2019 - 1:44:05 PM
Long-term archiving on: : Friday, November 16, 2012 - 11:56:29 AM

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David Leslie, Jason Marden. Equilibrium Selection in Potential Games with Noisy Rewards. NetGCOOP 2011 : International conference on NETwork Games, COntrol and OPtimization, Telecom SudParis et Université Paris Descartes, Oct 2011, Paris, France. ⟨hal-00644411⟩

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