Discontinuous stochastic games

He, Wei

doi:10.1007/s00199-021-01374-5

Cited by 2 publications

(1 citation statement)

References 46 publications

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“…The existence of SSPEs was discussed in Fink (1964), Takahashi (1964), and Sobel (1971), which provided a solid theoretical foundation for the development of stochastic games. He (2022) proved that an SSPE exists for stochastic games with discontinuous payoffs under the condition that a player can identify another action at the current stage with the payoff not much worse than her current one. The computation of SSPEs has been substantially studied in the literature as well.…”

Section: Introductionmentioning

confidence: 99%

Computing perfect stationary equilibria in stochastic games

Li,

Dang,

Herings

2024

Econ Theory

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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.

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