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Extended proper equilibrium

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  • Milgrom, Paul
  • Mollner, Joshua

Abstract

We introduce extended proper equilibrium, which refines proper equilibrium (Myerson, 1978) by adding across-player restrictions on trembles. This refinement coincides with proper equilibrium in games with two players but adds new restrictions in games with three or more players. One implication of these additional restrictions is that any tremble that is costless in equilibrium is regarded by all as more likely than any costly tremble, even one by a different player. At least one extended proper equilibrium exists in every finite game. The refinement can also be characterized in terms of a symmetric, meta-version of the game in which players originate from a common pool: if these players tremble symmetrically and in the way of proper equilibrium, then the induced play in the original game is an extended proper equilibrium.

Suggested Citation

  • Milgrom, Paul & Mollner, Joshua, 2021. "Extended proper equilibrium," Journal of Economic Theory, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:jetheo:v:194:y:2021:i:c:s0022053121000752
    DOI: 10.1016/j.jet.2021.105258
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    References listed on IDEAS

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    2. Yeu-Shiang Huang & Min-Sheng Yang & Jyh-Wen Ho, 2022. "Bundling Decisions for Selling Multiple Items in Online Auctions," Decision Analysis, INFORMS, vol. 19(1), pages 44-62, March.

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    More about this item

    Keywords

    Equilibrium refinement; Trembles; Extended proper equilibrium; Proper equilibrium; Generalized second-price auction;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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