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A Differentiable Path-Following Method with a Compact Formulation to Compute Proper Equilibria

Cao, Yiyin ; Chen, Yin ; Dang, Chuangyin

INFORMS journal on computing, 2024-03, Vol.36 (2), p.377-396 [Periódico revisado por pares]

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  • Título:
    A Differentiable Path-Following Method with a Compact Formulation to Compute Proper Equilibria
  • Autor: Cao, Yiyin ; Chen, Yin ; Dang, Chuangyin
  • Assuntos: differentiable path-following method ; Nash equilibrium ; noncooperative game ; perfect ; proper equilibrium
  • É parte de: INFORMS journal on computing, 2024-03, Vol.36 (2), p.377-396
  • Descrição: The concept of proper equilibrium was established as a strict refinement of perfect equilibrium. This establishment has significantly advanced the development of game theory and its applications. Nonetheless, it remains a challenging problem to compute such an equilibrium. This paper develops a differentiable path-following method with a compact formulation to compute a proper equilibrium. The method incorporates square-root-barrier terms into payoff functions with an extra variable and constitutes a square-root-barrier game. As a result of this barrier game, we acquire a smooth path to a proper equilibrium. To further reduce the computational burden, we present a compact formulation of an ε -proper equilibrium with a polynomial number of variables and equations. Numerical results show that the differentiable path-following method is numerically stable and efficient. Moreover, by relaxing the requirements of proper equilibrium and imposing Selten’s perfection, we come up with the notion of perfect d -proper equilibrium, which approximates a proper equilibrium and is less costly to compute. Numerical examples demonstrate that even when d is rather large, a perfect d -proper equilibrium remains to be a proper equilibrium. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms-Continuous. Funding: This work was partially supported by General Research Fund (GRF) CityU 11306821 of Hong Kong SAR Government. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0148 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0148 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
  • Editor: INFORMS
  • Idioma: Inglês
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