Abstract
We study the computational complexity of deciding the existence of a Pure Nash Equilibrium or a subgame perfect Nash equilibrium with a given payoff and other related problems in finite multi-player extensive games with perfect information. We propose three ways of representing a game with different degrees of succinctness for the components of the game. We show that when the number of moves of each player is large and the player function and the utilities are represented succinctly the considered problems are PSPACE-complete. In contraposition, when the game is described extensively by means of its associated tree all the problems are decidable in polynomial time.
Work partially supported by IST program of the EU under contract IST-2004-015964 (AEOLUS) and by Spanish CICYT under grant TIC2002-04498-C05-03 (Tracer).
Due to lack of space proofs are omitted, we refer the interested reader to the extended version of the paper report LSI-05-39-R available at http://www.lsi.upc.edu.
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Àlvarez, C., Gabarró, J., Serna, M. (2005). Polynomial Space Suffices for Deciding Nash Equilibria Properties for Extensive Games with Large Trees,. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_64
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DOI: https://doi.org/10.1007/11602613_64
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