title: A belief-based evolutionarily stable strategy.
abstract: As an equilibrium refinement of the Nash equilibrium, evolutionarily stable strategy (ESS) is a key concept in evolutionary game theory and has attracted growing interest. An ESS can be either a pure strategy or a mixed strategy. Even though the randomness is allowed in mixed strategy, the selection probability of pure strategy in a mixed strategy may fluctuate due to the impact of many factors. The fluctuation can lead to more uncertainty. In this paper, such uncertainty involved in mixed strategy has been further taken into consideration: a belief strategy is proposed in terms of Dempster-Shafer evidence theory. Furthermore, based on the proposed belief strategy, a belief-based ESS has been developed. The belief strategy and belief-based ESS can reduce to the mixed strategy and mixed ESS, which provide more realistic and powerful tools to describe interactions among agents.
authors.affiliation: School of Computer and Information Science, Southwest University, Chongqing 400715, China.
authors.forename: Xinyang
authors.initials: X
authors.lastname: Deng
authors.affiliation: Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China; Center for Nonlinear Studies, Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex systems, Hong Kong; Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China.
authors.forename: Zhen
authors.initials: Z
authors.lastname: Wang
authors.affiliation: Center for Quantitative Sciences, Vanderbilt University School of Medicine, Nashville, TN 37232, USA; Department of Biomedical Informatics, Vanderbilt University School of Medicine, Nashville, TN 37232, USA.
authors.forename: Qi
authors.initials: Q
authors.lastname: Liu
authors.affiliation: School of Computer and Information Science, Southwest University, Chongqing 400715, China; School of Automation, Northwestern Polytechnical University, Xi׳an, Shaanxi 710072, China; School of Engineering, Vanderbilt University, Nashville, TN 37235, USA. Electronic address: prof.deng@hotmail.com.
authors.forename: Yong
authors.initials: Y
authors.lastname: Deng
authors.affiliation: School of Engineering, Vanderbilt University, Nashville, TN 37235, USA.
authors.forename: Sankaran
authors.initials: S
authors.lastname: Mahadevan
mesh_terms: D005716:Game Theory; D008962:Models, Theoretical
keywords: Belief function; Dempster–Shafer evidence theory; Evolutionary game; Mixed strategy