Journal
GAMES AND ECONOMIC BEHAVIOR
Volume 134, Issue -, Pages 127-150Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.geb.2022.04.004
Keywords
Game theory; Nash equilibrium; Perfect equilibrium; Linear tracing procedure; Differentiable homotopy method
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Funding
- Hong Kong SAR Government [GRF: CityU 11304620]
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The linear tracing procedure is crucial in the equilibrium selection theory but fails to always select a perfect equilibrium when there are more than two players. To address this issue, we develop a variant of the linear tracing procedure by creating a perturbed game and establish the existence of a smooth path from a unique starting point to a perfect equilibrium using optimality conditions and transformations on variables. Additionally, we propose variant procedures to select a perfect equilibrium.
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.
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