首页|A variant of Harsanyi?s tracing procedures to select a perfect equilibrium in normal form games
A variant of Harsanyi?s tracing procedures to select a perfect equilibrium in normal form games
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NSTL
Elsevier
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.
Game theoryNash equilibriumPerfect equilibriumLinear tracing procedureDifferentiable homotopy methodCOMPUTING SOLUTIONSNASH EQUILIBRIAFIXED-POINTSHOMOTOPYALGORITHMSCOMPLEXITYPRODUCT
NSTL
Elsevier
