Correlated equilibria in graphical games

We examine correlated equilibria in the recently introduced formalism of graphical games, a succinct representation for multiplayer games. We establish a natural and powerful relationship between the graphical structure of a multiplayer game and a certain Markov network representing distributions over joint actions. Our first main result establishes that this Markov network succinctly represents all correlated equilibria of the graphical game up to expected payoff equivalence. Our second main result provides a general algorithm for computing correlated equilibria in a graphical game based on its associated Markov network. For a special class of graphical games that includes trees, this algorithm runs in time polynomial in the graphical game representation (which is polynomial in the number of players and exponential in the graph degree).

[1]  R. Aumann Subjectivity and Correlation in Randomized Strategies , 1974 .

[2]  R. Aumann Correlated Equilibrium as an Expression of Bayesian Rationality Author ( s ) , 1987 .

[3]  Bayesian Rationality,et al.  CORRELATED EQUILIBRIUM AS AN EXPRESSION OF , 1987 .

[4]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[5]  Martin E. Dyer,et al.  A random polynomial-time algorithm for approximating the volume of convex bodies , 1991, JACM.

[6]  Martin E. Dyer,et al.  A Random Polynomial Time Algorithm for Approximating the Volume of Convex Bodies , 1989, STOC.

[7]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[8]  A. Dawid,et al.  Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models , 1993 .

[9]  Dean P. Foster,et al.  Calibrated Learning and Correlated Equilibrium , 1997 .

[10]  Adam L. Berger,et al.  A Maximum Entropy Approach to Natural Language Processing , 1996, CL.

[11]  Dean P. Foster,et al.  Regret in the On-Line Decision Problem , 1999 .

[12]  Eric van Damme,et al.  Non-Cooperative Games , 2000 .

[13]  Pierfrancesco La Mura Game Networks , 2000, UAI.

[14]  Michael L. Littman,et al.  Graphical Models for Game Theory , 2001, UAI.

[15]  Daphne Koller,et al.  Multi-Agent Influence Diagrams for Representing and Solving Games , 2001, IJCAI.

[16]  Luis E. Ortiz,et al.  Nash Propagation for Loopy Graphical Games , 2002, NIPS.

[17]  Satinder Singh,et al.  An Efficient Exact Algorithm for Singly Connected Graphical Games , 2002, NIPS 2002.

[18]  Daphne Koller,et al.  Multi-agent algorithms for solving graphical games , 2002, AAAI/IAAI.