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

Yiyin Cao and Chuangyin Dang

Games and Economic Behavior, 2022, vol. 134, issue C, 127-150

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.

Keywords: Game theory; Nash equilibrium; Perfect equilibrium; Linear tracing procedure; Differentiable homotopy method (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:134:y:2022:i:c:p:127-150

DOI: 10.1016/j.geb.2022.04.004

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