Filtered Fictitious Play for Perturbed Observation Potential Games and Decentralised POMDPs

Archie C. Chapman, Simon A. Williamson, Nicholas R. Jennings
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:105-113, 2011.

Abstract

Potential games and decentralised partially observable MDPs (Dec-POMDPs) are two commonly used models of multi-agent interaction, for static optimisation and sequential decisionmaking settings, respectively. In this paper we introduce filtered fictitious play for solving repeated potential games in which each player’s observations of others’ actions are perturbed by random noise, and use this algorithm to construct an online learning method for solving Dec-POMDPs. Specifically, we prove that noise in observations prevents standard fictitious play from converging to Nash equilibrium in potential games, which also makes fictitious play impractical for solving Dec-POMDPs. To combat this, we derive filtered fictitious play, and provide conditions under which it converges to a Nash equilibrium in potential games with noisy observations. We then use filtered fictitious play to construct a solver for Dec-POMDPs, and demonstrate our new algorithm’s performance in a box pushing problem. Our results show that we consistently outperform the state-of-the-art Dec-POMDP solver by an average of 100% across the range of noise in the observation function.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-chapman11a, title = {Filtered Fictitious Play for Perturbed Observation Potential Games and Decentralised POMDPs}, author = {Chapman, Archie C. and Williamson, Simon A. and Jennings, Nicholas R.}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {105--113}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/chapman11a/chapman11a.pdf}, url = {https://proceedings.mlr.press/r9/chapman11a.html}, abstract = {Potential games and decentralised partially observable MDPs (Dec-POMDPs) are two commonly used models of multi-agent interaction, for static optimisation and sequential decisionmaking settings, respectively. In this paper we introduce filtered fictitious play for solving repeated potential games in which each player’s observations of others’ actions are perturbed by random noise, and use this algorithm to construct an online learning method for solving Dec-POMDPs. Specifically, we prove that noise in observations prevents standard fictitious play from converging to Nash equilibrium in potential games, which also makes fictitious play impractical for solving Dec-POMDPs. To combat this, we derive filtered fictitious play, and provide conditions under which it converges to a Nash equilibrium in potential games with noisy observations. We then use filtered fictitious play to construct a solver for Dec-POMDPs, and demonstrate our new algorithm’s performance in a box pushing problem. Our results show that we consistently outperform the state-of-the-art Dec-POMDP solver by an average of 100% across the range of noise in the observation function.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Filtered Fictitious Play for Perturbed Observation Potential Games and Decentralised POMDPs %A Archie C. Chapman %A Simon A. Williamson %A Nicholas R. Jennings %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-chapman11a %I PMLR %P 105--113 %U https://proceedings.mlr.press/r9/chapman11a.html %V R9 %X Potential games and decentralised partially observable MDPs (Dec-POMDPs) are two commonly used models of multi-agent interaction, for static optimisation and sequential decisionmaking settings, respectively. In this paper we introduce filtered fictitious play for solving repeated potential games in which each player’s observations of others’ actions are perturbed by random noise, and use this algorithm to construct an online learning method for solving Dec-POMDPs. Specifically, we prove that noise in observations prevents standard fictitious play from converging to Nash equilibrium in potential games, which also makes fictitious play impractical for solving Dec-POMDPs. To combat this, we derive filtered fictitious play, and provide conditions under which it converges to a Nash equilibrium in potential games with noisy observations. We then use filtered fictitious play to construct a solver for Dec-POMDPs, and demonstrate our new algorithm’s performance in a box pushing problem. Our results show that we consistently outperform the state-of-the-art Dec-POMDP solver by an average of 100% across the range of noise in the observation function. %Z Reissued by PMLR on 04 October 2026.
APA
Chapman, A.C., Williamson, S.A. & Jennings, N.R.. (2011). Filtered Fictitious Play for Perturbed Observation Potential Games and Decentralised POMDPs. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:105-113 Available from https://proceedings.mlr.press/r9/chapman11a.html. Reissued by PMLR on 04 October 2026.

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