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The Complexity of Computing Best-Response Automata in Repeated Games

Author

Listed:
  • Itzhak Gilboa

    (TAU - Tel Aviv University)

Abstract

The following problem is examined: given a game and the opponents' finite automata, find a best-response automaton for a certain player in the repeated game. It is shown that the problem is relatively "easy" (i.e., of polynomial time complexity) if the number of players is fixed, but "difficult" otherwise.

Suggested Citation

  • Itzhak Gilboa, 1988. "The Complexity of Computing Best-Response Automata in Repeated Games," Post-Print hal-00756286, HAL.
    • Handle: RePEc:hal:journl:hal-00756286
    DOI: 10.1016/0022-0531(88)90274-8
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    Citations

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    Cited by:

    1. Ehud Kalai, 1987. "Bounded Rationality and Strategic Complexity in Repeated Games," Discussion Papers 783, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Itzhak Gilboa & Ehud Kalai & Eitan Zemel, 1989. "The Complexity of Eliminating Dominated Strategies," Discussion Papers 853, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Oliver Compte & Andrew Postlewaite, 2010. "Plausible Cooperation, Fourth Version," PIER Working Paper Archive 15-006, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 23 Jan 2015.
    4. Sung, Shao-Chin & Dimitrov, Dinko, 2010. "Computational complexity in additive hedonic games," European Journal of Operational Research, Elsevier, vol. 203(3), pages 635-639, June.
    5. Gilboa Itzhak & Schmeidler David, 1994. "Infinite Histories and Steady Orbits in Repeated Games," Games and Economic Behavior, Elsevier, vol. 6(3), pages 370-399, May.
    6. Jakub Dargaj & Jakob Grue Simonsen, 2020. "A Complete Characterization of Infinitely Repeated Two-Player Games having Computable Strategies with no Computable Best Response under Limit-of-Means Payoff," Papers 2005.13921, arXiv.org, revised Jun 2020.
    7. Holm, Hakan J., 1995. "Computational cost of verifying enforceable contracts," International Review of Law and Economics, Elsevier, vol. 15(2), pages 127-140, June.
    8. Olivier Compte & Andrew Postlewaite, 2007. "Effecting Cooperation," PIER Working Paper Archive 09-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 29 May 2009.
    9. Sgroi, Daniel & Zizzo, Daniel John, 2009. "Learning to play 3×3 games: Neural networks as bounded-rational players," Journal of Economic Behavior & Organization, Elsevier, vol. 69(1), pages 27-38, January.
    10. Compte, Olivier & Postlewaite, Andrew, 2015. "Plausible cooperation," Games and Economic Behavior, Elsevier, vol. 91(C), pages 45-59.
    11. Westhoff, Frank H. & Yarbrough, Beth V. & Yarbrough, Robert M., 1996. "Complexity, organization, and Stuart Kauffman's The Origins of Order," Journal of Economic Behavior & Organization, Elsevier, vol. 29(1), pages 1-25, January.
    12. Scott E. Page, 2008. "Uncertainty, Difficulty, and Complexity," Journal of Theoretical Politics, , vol. 20(2), pages 115-149, April.
    13. Lu Hong & Scott E. Page, 1998. "Diversity and Optimality," Research in Economics 98-08-077e, Santa Fe Institute.
    14. Fernando Oliveira, 2010. "Modeling Emotions and Reason in Agent-Based Systems," Computational Economics, Springer;Society for Computational Economics, vol. 35(2), pages 155-164, February.
    15. Stephan Schosser & Bodo Vogt, 2015. "What automaton model captures decision making? A call for finding a behavioral taxonomy of complexity," FEMM Working Papers 150010, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    16. D. Sgroi & D. J. Zizzo, 2002. "Strategy Learning in 3x3 Games by Neural Networks," Cambridge Working Papers in Economics 0207, Faculty of Economics, University of Cambridge.
    17. Daijiro Okada & Abraham Neyman, 2004. "Growing Strategy Sets in Repeated Games," Econometric Society 2004 North American Summer Meetings 625, Econometric Society.
    18. Ho, Teck-Hua, 1996. "Finite automata play repeated prisoner's dilemma with information processing costs," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 173-207.
    19. Nachbar, John H & Zame, William R, 1996. "Non-computable Strategies and Discounted Repeated Games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 103-122, June.
    20. Oliveira, Fernando S., 2010. "Limitations of learning in automata-based systems," European Journal of Operational Research, Elsevier, vol. 203(3), pages 684-691, June.
    21. Hubie Chen, 2013. "Bounded rationality, strategy simplification, and equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 593-611, August.
    22. Roy, Jaideep, 2000. "Learning with bounded memory," UC3M Working papers. Economics 7224, Universidad Carlos III de Madrid. Departamento de Economía.
    23. João E. Gata, 2019. "Controlling Algorithmic Collusion: short review of the literature, undecidability, and alternative approaches," Working Papers REM 2019/77, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    24. Ehud Kalai, 1995. "Games," Discussion Papers 1141, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    25. Tim Roughgarden, 2010. "Computing equilibria: a computational complexity perspective," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 193-236, January.

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