2021-12-05T03:06:22Zhttps://tsukuba.repo.nii.ac.jp/oaioai:tsukuba.repo.nii.ac.jp:000228732021-03-02T07:42:35ZStructural Analysis of Two Person Game with Mixed Strategy for Energy SupplyTakahashi, KazukiSumita, UshioEnergytwo person gamemixed strategylimiting strategyStructural models for analyzing competitive markets characterized by homogeneous products\nand services such as the energy supply can be traced back to 1920’s. To the authors’ best knowledge, the\nliterature focuses on pure strategies and analysis for mixed strategies are largely ignored. However, the\ncharacteristic of the energy supply often allows only mixed strategies as a meaningful basis for analyzing\nthe price competition. The purpose of this paper is to fill this gap by developing a duopoly model with two\nsymmetric customers allowing mixed strategies. Nash equilibriums are constructed explicitly when mixed\nstrategies are defined on a finite set of L discrete points spread in a finite interval and their reciprocals are\nequally distanced. Those equilibriums consist of two different types. One is that two players offer the same\nstarategy, and the other is that each player takes the strategy different from the other. Limiting strategies\nas L → ∞ are derived explicitly. These limiting strategies are also shown to be Nash equilibriums in the\ncontext of mixed strategies defined on continuum.technical reportUniversity of Tsukuba. Graduate School of Systems and Information Engineering. Doctoral Program in Social Systems & Management2008-05application/pdfhttp://hdl.handle.net/2241/100229https://tsukuba.repo.nii.ac.jp/record/22873/files/1206.pdfengDepartment of Social Systems and Management Discussion Paper Series ~ no. 1206