Computing perfect stationary equilibria in stochastic games

Peixuan Li (), Chuangyin Dang () and P. Jean-Jacques Herings
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Peixuan Li: Southeast University
Chuangyin Dang: City University of Hong Kong

Economic Theory, 2024, vol. 78, issue 2, No 1, 347-387

Abstract: Abstract The notion of stationary equilibrium is one of the most crucial solution concepts in stochastic games. However, a stochastic game can have multiple stationary equilibria, some of which may be unstable or counterintuitive. As a refinement of stationary equilibrium, we extend the concept of perfect equilibrium in strategic games to stochastic games and formulate the notion of perfect stationary equilibrium (PeSE). To further promote its applications, we develop a differentiable homotopy method to compute such an equilibrium. We incorporate vanishing logarithmic barrier terms into the payoff functions, thereby constituting a logarithmic-barrier stochastic game. As a result of this barrier game, we attain a continuously differentiable homotopy system. To reduce the number of variables in the homotopy system, we eliminate the Bellman equations through a replacement of variables and derive an equivalent system. We use the equivalent system to establish the existence of a smooth path, which starts from an arbitrary total mixed strategy profile and ends at a PeSE. Extensive numerical experiments, including relevant applications like dynamic oligopoly models and dynamic legislative voting, further affirm the effectiveness and efficiency of the method.

Keywords: Stochastic games; Stationary equilibria; Perfectness; Logarithmic barrier differentiable homotopy method (search for similar items in EconPapers)
JEL-codes: C02 C72 C73 (search for similar items in EconPapers)
Date: 2024
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Working Paper: Computing Perfect Stationary Equilibria in Stochastic Games (2023)
Working Paper: Computing Perfect Stationary Equilibria in Stochastic Games (2023)
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DOI: 10.1007/s00199-024-01565-w

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