A Polynomial-time Nash Equilibrium Algorithm for Repeated Stochastic Games

By Enrique Munoz de Cote, Michael L. Littman. 2008

36 citations recorded by the source corpus.

We present a polynomial-time algorithm that always finds an (approximate) Nash equilibrium for repeated two-player stochastic games. The algorithm exploits the folk theorem to derive a strategy profile that forms an equilibrium by buttressing mutually beneficial behavior with threats, where possible. One component of our algorithm efficiently searches for an approximation of the egalitarian point, the fairest pareto-efficient solution. The paper concludes by applying the algorithm to a set of grid games to illustrate typical solutions the algorithm finds. These solutions compare very favorably to those found by competing algorithms, resulting in strategies with higher social welfare, as well as guaranteed computational efficiency.

Subfields: Economics and Econometrics, Management Science and Operations Research

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Citations in the corpus

Learning with Opponent-Learning Awareness (2017, positive): “Similar in spirit to this work, Munoz de Cote and Littman (2008) propose a Nash equilibrium algorithm for repeated stochastic games that explicitly attempts to find the egalitarian point by switching between competitive and zero-sum strategies.”
A Survey of Learning in Multiagent Environments: Dealing with Non-Stationarity (2017, background): “Other interesting games are stochastic versions of well-known games such as PD, coordination, and chicken (Munoz de Cote and Littman, 2008; Elidrisi et al., 2014).”
Coordinate to cooperate or compete: Abstract goals and joint intentions in social interaction (2016, methodology): “These dynamics were chosen to be identical to those in (De Cote & Littman, 2008) so that our data can also be compared to the models of that work.”