Computationally efficient coordination in game trees

The solution concept of “correlated equilibrium” allows for coordination in games. For game trees with imperfect information, it gives rise to NP-hard problems, even for two-player games without chance moves. We introduce the “extensive form correlated equilibrium” (EFCE), which extends Aumann’s correlated equilibrium, where coordination is achieved by signals that are received “locally” at information sets. An EFCE is polynomial-time computable for two-player games without chance moves.

[1]  J. Nash,et al.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[2]  H. W. Kuhn,et al.  11. Extensive Games and the Problem of Information , 1953 .

[3]  Ray L. Birdwhistell,et al.  An Approach to Communication , 1962 .

[4]  C. E. Lemke,et al.  Equilibrium Points of Bimatrix Games , 1964 .

[5]  C. E. Lemke,et al.  Bimatrix Equilibrium Points and Mathematical Programming , 1965 .

[6]  William F. Lucas,et al.  An Overview of the Mathematical Theory of Games , 1972 .

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

[8]  L. Shapley.  A note on the Lemke-Howson algorithm , 1974 .

[9]  Andrew Chi-Chih Yao,et al.  Probabilistic computations: Toward a unified measure of complexity , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[10]  L. Lovász,et al.  Geometric Algorithms and Combinatorial Optimization , 1981 .

[11]  R. Myerson.  MULTISTAGE GAMES WITH COMMUNICATION , 1984 .

[12]  F. Forges,et al.  Correlated equilibria in repeated games with lack of information on one side: A model with verifiable types , 1986 .

[13]  F. Forges.  Published by: The , 2022 .

[14]  E. Vandamme.  Stability and perfection of nash equilibria , 1987 .

[15]  Eitan Zemel,et al.  Nash and correlated equilibria: Some complexity considerations , 1989 .

[16]  Larry Samuelson,et al.  Correlated And Mediated Equilibria In Game With Incompete Information , 1989 .

[17]  Kevin D. Cotter.  Correlated equilibrium in games with type-dependent strategies , 1991 .

[18]  Roger B. Myerson,et al.  Game theory - Analysis of Conflict , 1991 .

[19]  Imre Bárány,et al.  Fair Distribution Protocols or How the Players Replace Fortune , 1992, Math. Oper. Res..

[20]  D. Koller,et al.  The complexity of two-person zero-sum games in extensive form , 1992 .

[21]  F. Forges,et al.  Five legitimate definitions of correlated equilibrium in games with incomplete information , 1993 .

[22]  Christos H. Papadimitriou,et al.  On the Complexity of the Parity Argument and Other Inefficient Proofs of Existence , 1994, J. Comput. Syst. Sci..

[23]  Roger B. Myerson,et al.  Communication, correlated equilibria and incentive compatibility , 1994 .

[24]  Bernhard von Stengel,et al.  Fast algorithms for finding randomized strategies in game trees , 1994, STOC '94.

[25]  D. Koller,et al.  Efficient Computation of Equilibria for Extensive Two-Person Games , 1996 .

[26]  B. Stengel,et al.  Efficient Computation of Behavior Strategies , 1996 .

[27]  B. Stengel,et al.  COMPUTING EQUILIBRIA FOR TWO-PERSON GAMES , 1996 .

[28]  Bernhard von Stengel,et al.  Computing Normal Form Perfect Equilibria for Extensive Two-Person Games , 2002 .

[29]  S. Hart,et al.  A simple adaptive procedure leading to correlated equilibrium , 2000 .

[30]  Elchanan Ben-Porath,et al.  Correlation without Mediation: Expanding the Set of Equilibrium Outcomes by "Cheap" Pre-play Procedures , 1998 .

[31]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[32]  Shai Halevi,et al.  A Cryptographic Solution to a Game Theoretic Problem , 2000, CRYPTO.

[33]  Bernhard von Stengel,et al.  A new lower bound for the list update problem in the partial cost model , 2001, Theor. Comput. Sci..

[34]  Eilon Solan,et al.  Characterization of correlated equilibria in stochastic games , 2001, Int. J. Game Theory.

[35]  É. BernhardvonStengel,et al.  Computational complexity of correlated equilibria for extensive games , 2001 .

[36]  Joseph Y. Halpern,et al.  On the NP-completeness of finding an optimal strategy in games with common payoffs , 2001, Int. J. Game Theory.

[37]  Christos H. Papadimitriou,et al.  Algorithms, Games, and the Internet , 2001, ICALP.

[38]  Noam Nisan,et al.  Algorithmic Mechanism Design , 2001, Games Econ. Behav..

[39]  Bernhard von Stengel,et al.  Computational complexity of correlated equilibria for extensive games , 2001 .

[40]  José E. Vila,et al.  Computational complexity and communication: Coordination in two-player games , 2002 .

[41]  Joseph Y. Halpern.  A computer scientist looks at game theory , 2002, Games Econ. Behav..