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A variant of Harsanyi's tracing procedures to select a perfect equilibrium in normal form games

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  • Cao, Yiyin
  • Dang, Chuangyin

Abstract

The linear tracing procedure plays a central role in the equilibrium selection theory of Harsanyi and Selten (1988). Nevertheless, it fails to always select a perfect equilibrium when there are more than two players. To fill this gap, we develop a variant of the linear tracing procedure by constituting a perturbed game in which each player maximizes her payoff against a linear convex combination between a totally mixed prior belief profile and a given mixed strategy profile of other players. Applying the optimality conditions to the integration of the perturbed game and a convex-quadratic-penalty game, we establish with a fixed-point argument and transformations on variables the existence of a smooth path from a unique starting point to a perfect equilibrium. Moreover, we present a variant of Harsanyi's logarithmic tracing procedure and a simplicial linear tracing procedure to select a perfect equilibrium.

Suggested Citation

  • Cao, Yiyin & Dang, Chuangyin, 2022. "A variant of Harsanyi's tracing procedures to select a perfect equilibrium in normal form games," Games and Economic Behavior, Elsevier, vol. 134(C), pages 127-150.
    • Handle: RePEc:eee:gamebe:v:134:y:2022:i:c:p:127-150
    DOI: 10.1016/j.geb.2022.04.004
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