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Finite-order type spaces and applications

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  • Qin, Cheng-Zhong
  • Yang, Chun-Lei

Abstract

We propose a framework of consistent finite-order priors to facilitate the incorporation of higher-order uncertainties into Bayesian game analysis, without invoking the concept of a universal type space. Several recent models, which give rise to stunning results with higher-order uncertainties, turn out to operate with certain consistent order-2 priors. We introduce canonical representations of consistent finite-order priors, which we apply to establish a criterion for determining the orders of strategically relevant beliefs for abstract Harsanyi type spaces. We derive finite-order projections of type spaces and discuss convergence of BNEs based on them as the projection order increases. Finally, we introduce finite-order total variation distances between priors, which are suitable for analyzing the issues on equilibrium continuity and robustness. We revisit recent advancements of Bayesian game theory and develop new insights based on our framework.

Suggested Citation

  • Qin, Cheng-Zhong & Yang, Chun-Lei, 2013. "Finite-order type spaces and applications," Journal of Economic Theory, Elsevier, vol. 148(2), pages 689-719.
  • Handle: RePEc:eee:jetheo:v:148:y:2013:i:2:p:689-719
    DOI: 10.1016/j.jet.2012.08.007
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    References listed on IDEAS

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    Keywords

    Bayesian game; Common prior; Complete information; Consistent prior; Finite-order type space; Payoff type space; Projection type space; Robustness; Total variation distance;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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