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Essential stability of the alpha cores of finite games with incomplete information

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  • Noguchi, Mitsunori

Abstract

We introduce a variant of Milgrom and Weber’s (1985) model of n-person games with incomplete information (games for short) and define a correspondence that maps each game to its α-core (the α-core correspondences). Our main objective is to prove such a correspondence to be generically lower semicontinuous. For a multi-valued solution correspondence, the lower semicontinuity is relevant as a theoretical base for predicting outcomes using game-theoretic models. We introduce a family of games parametrized by both payoff functions and information structures (common priors), which allows simultaneous perturbations in those two parameters. We then appeal to Fort’s (1951) theorem to conclude that generic games are essential relative to the parameter space.

Suggested Citation

  • Noguchi, Mitsunori, 2021. "Essential stability of the alpha cores of finite games with incomplete information," Mathematical Social Sciences, Elsevier, vol. 110(C), pages 34-43.
    • Handle: RePEc:eee:matsoc:v:110:y:2021:i:c:p:34-43
    DOI: 10.1016/j.mathsocsci.2021.01.003
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    References listed on IDEAS

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    1. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
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    5. Askoura, Y. & Sbihi, M. & Tikobaini, H., 2013. "The ex ante α-core for normal form games with uncertainty," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 157-162.
    6. Noguchi, Mitsunori, 2018. "Alpha cores of games with nonatomic asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 1-12.
    7. Yu, Jian, 1999. "Essential equilibria of n-person noncooperative games," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 361-372, April.
    8. Erik J. Balder, 1988. "Generalized Equilibrium Results for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 265-276, May.
    9. Noguchi, Mitsunori, 2014. "Cooperative equilibria of finite games with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 4-10.
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