A differentiable homotopy method to compute perfect equilibria
成果类型：
Article
署名作者：
Chen, Yin; Dang, Chuangyin
署名单位：
City University of Hong Kong
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-019-01422-y
发表日期：
2021
页码：
77-109
关键词：
摘要：
The notion of perfect equilibrium was formulated by Selten (Int J Game Theory 4(1):25-55, 1975) as a strict refinement of Nash equilibrium. For an extensive-form game with perfect recall, every perfect equilibrium of its agent normal-form game yields a perfect equilibrium of the extensive-form game. This paper aims to develop a differentiable homotopy method for computing perfect equilibria of normal-form games. To accomplish this objective, we constitute an artificial game by introducing a continuously differentiable function of an extra variable. The artificial game defines a differentiable homotopy mapping and establishes the existence of a smooth path to a perfect equilibrium. For numerical comparison, we also describe a simplicial homotopy method. Numerical results show that the differentiable homotopy method is numerically stable and efficient and significantly outperforms the simplicial homotopy method especially when the problem is large.
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