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Extensive-Form Correlated Equilibrium: Definition and Computational Complexity

Department of Mathematics, London School of Economics, London WC2A 2AE, United Kingdom
CEREMADE, University of Paris–Dauphine, 75775 Paris cedex 16, France
stengel{at}maths.lse.ac.uk, http://www.maths.lse.ac.uk/personal/stengel
francoise.forges{at}dauphine.fr, http://www.dauphine.fr/edocif/forges/francoise.forges.htm

This paper defines the extensive-form correlated equilibrium (EFCE) for extensive games with perfect recall. The EFCE concept extends Aumann's strategic-form correlated equilibrium (CE). Before the game starts, a correlation device generates a move for each information set. This move is recommended to the player only when the player reaches the information set. In two-player perfect-recall extensive games without chance moves, the set of EFCE can be described by a polynomial number of consistency and incentive constraints. Assuming P is not equal to NP, this is not possible for the set of CE, or if the game has chance moves.

Key Words: correlated equilibrium; extensive game; polynomial-time computable
History: Received: March 22, 2006; revision received: March 20, 2008;