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Possibilistic beliefs in strategic games

Author

Listed:
  • Jaeok Park

    (Yonsei University)

  • Doo Hyung Yun

    (Yonsei University)

Abstract

We introduce possibilistic beliefs into strategic games, describing a player’s belief about his opponents’ strategies as the set of their strategies he regards as possible. We formulate possibilistic strategic games where each player has preferences over his own strategies conditional on his possibilistic belief about his opponents’ strategies. We define several solution concepts for possibilistic strategic games such as (strict) equilibria, rationalizable sets, iterated elimination of never-best responses, and iterated elimination of strictly dominated strategies, and we study their properties and relationships. We develop a class of possibilistic strategic games called possibilistic supermodular games to relate supermodular games to possibilistic strategic games. Lastly, we discuss a direction of extending our possibilistic framework to games with incomplete information.

Suggested Citation

  • Jaeok Park & Doo Hyung Yun, 2023. "Possibilistic beliefs in strategic games," Theory and Decision, Springer, vol. 95(2), pages 205-228, August.
    • Handle: RePEc:kap:theord:v:95:y:2023:i:2:d:10.1007_s11238-022-09919-3
    DOI: 10.1007/s11238-022-09919-3
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    References listed on IDEAS

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    1. Jing Chen & Silvio Micali & Rafael Pass, 2015. "Tight Revenue Bounds With Possibilistic Beliefs and Level‐k Rationality," Econometrica, Econometric Society, vol. 83(4), pages 1619-1639, July.
    2. Apt Krzysztof R., 2007. "The Many Faces of Rationalizability," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-39, May.
    3. Sobel, Joel, 2019. "Iterated weak dominance and interval-dominance supermodular games," Theoretical Economics, Econometric Society, vol. 14(1), January.
    4. Olszewski, Wojciech, 2021. "On sequences of iterations of increasing and continuous mappings on complete lattices," Games and Economic Behavior, Elsevier, vol. 126(C), pages 453-459.
    5. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    6. Luo, Xiao, 2001. "General systems and [phiv]-stable sets -- a formal analysis of socioeconomic environments," Journal of Mathematical Economics, Elsevier, vol. 36(2), pages 95-109, November.
    7. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    8. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    9. Krzysztof R. Apt & Jonathan A. Zvesper, 2010. "The Role of Monotonicity in the Epistemic Analysis of Strategic Games," Games, MDPI, vol. 1(4), pages 1-14, October.
    10. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    11. Dow James & Werlang Sergio Ribeiro Da Costa, 1994. "Nash Equilibrium under Knightian Uncertainty: Breaking Down Backward Induction," Journal of Economic Theory, Elsevier, vol. 64(2), pages 305-324, December.
    12. Xiao Luo, 2016. "Rational beliefs in rationalizability," Theory and Decision, Springer, vol. 81(2), pages 189-198, August.
    13. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    14. Federico Echenique, 2005. "A short and constructive proof of Tarski’s fixed-point theorem," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 215-218, June.
    15. Chen, Yi-Chun & Long, Ngo Van & Luo, Xiao, 2007. "Iterated strict dominance in general games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 299-315, November.
    16. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
    17. Chen, Jing & Micali, Silvio, 2015. "Mechanism design with possibilistic beliefs," Journal of Economic Theory, Elsevier, vol. 156(C), pages 77-102.
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