Game Theory

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1. Competitive Equilibria and Benefit Distributions of Population Production Economies with External Increasing Returns

Zhe Yang, Xian Zhang

Journal of the Operations Research Society of China 2021, 9 (4): 723-740. DOI: 10.1007/s40305-021-00340-1

摘要（2811）

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Inspired by the work of population games, we establish the model of population production economies with external increasing returns and introduce the notion of competitive equilibria. We first prove the existence of competitive equilibria under some regular assumptions. Furthermore, we assume that there exists the cooperative behavior of different populations. By proving the existence of transferable utility (TU) core, we analyze the benefit distributions of population production economies with external increasing returns.

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2. Generalizations of Sobolev’s Consistency and Values for TU-Games

Jun Su, Theo S. H. Driessen, Gen-Jiu Xu

Journal of the Operations Research Society of China 2021, 9 (2): 344-357. DOI: 10.1007/s40305-019-00279-4

摘要（2507）

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In the framework of cooperative game theory, Sobolev (Advances in game theory, Izdat., “Minitis”, Vilnius, pp 151–153, 1973) axiomatized the well-known Shapley value by means of consistency property with reference to a specifically chosen reduced game. The goal of this paper is to generalize Sobolev’s consistency approach to the class of efficient, symmetric and linear values.

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3. The Generic Uniqueness and Well-Posedness of Nash Equilibria for Stable Population Games

Wen-Sheng Jia, Xiao-Ling Qiu, Ding-Tao Peng

Journal of the Operations Research Society of China 2021, 9 (2): 455-464. DOI: 10.1007/s40305-019-00281-w

摘要（2910）

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This paper aims at studying a new kind of stable population games introduced by J. Hofbauer and H. Sandholm in 2009. We first construct a complete distance space M consisting of stable population games and show that most of stable population games have unique Nash equilibrium point that according to Baire’s category theorem. It implies that every stable population game that possesses more than one Nash equilibrium can be approached arbitrarily by a sequence of the stable population game each of which has a unique Nash equilibrium. Then, we construct a bounded rationality function and deduce some results on the generic well-posedness implying Tikhonov well-posedness and Hadamard well-posedness for stable population games.

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4. Bi-level Programming for Stackelberg Game with Intuitionistic Fuzzy Number: a Ranking Approach

Sumit Kumar Maiti, Sankar Kumar Roy

Journal of the Operations Research Society of China 2021, 9 (1): 131-149. DOI: 10.1007/s40305-018-0234-2

摘要（1905）

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This paper introduces a ranking function procedure on a bi-level programming for Stackelberg game involving intuitionistic fuzzy parameters. Intuitionistic fuzzy number is considered in many real-life situations, so it makes perfect sense to address decision-making problem by using some specified intuitionistic fuzzy numbers. In this paper, intuitionistic fuzziness is characterized by a normal generalized triangular intuitionistic fuzzy number. A defuzzification method is introduced based on the proportional probability density function associated with the corresponding membership function, as well as the complement of non-membership function. Using the proposed ranking technique, a methodology is presented for solving bi-level programming for Stackelberg game. An application example is provided to demonstrate the applicability of the proposed methodology, and the achieved results are compared with the existing methods.

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5. Existence of Weakly Cooperative Equilibria for Infinite-Leader-Infinite-Follower Games

Zhe Yang, Qing-Bin Gong

Journal of the Operations Research Society of China 2019, 7 (4): 643-654. DOI: 10.1007/s40305-018-0236-0

摘要（976）

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In this paper, we first generalize Yang and Ju's (J Glob Optim 65:563-573, 2016) result in Hausdorff topological vector spaces. Second, we introduce the model of leader-follower games with infinitely many leaders and followers, that is, infiniteleader-infinite-follower game. We next introduce the notion of weakly cooperative equilibria for infinite-leader-infinite-follower games and prove the existence result.

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6. A Note on Submodularity Preserved Involving the Rank Functions

Min Li, Dong-Lei Du, Da-Chuan Xu, Zhen-Ning Zhang

Journal of the Operations Research Society of China 2019, 7 (3): 399-407. DOI: 10.1007/s40305-019-00255-y

摘要（982）

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In many kinds of games with economic significance, it is very important to study the submodularity of functions. In this paper, we mainly study the problem of maximizing a concave function over an intersection of two matroids. We obtain that the submodularity may not be preserved, but it involves one maximal submodular problem (or minimal supermodular problem) with some conditions. Moreover, we also present examples showing that these conditions can be satisfied.

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7. The Myerson Value on Local Structures of Coalitions

Daniel Li Li, Er-Fang Shan

Journal of the Operations Research Society of China 2019, 7 (3): 461-473. DOI: 10.1007/s40305-019-00254-z

摘要（1327）

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The Myerson value introduced by Mayerson (Math Oper Res 2:225-229, 1977) is a solution for cooperative games under the partial cooperation structures described by graphs, in which feasible coalitions are connected but their structures are ignored. To extend the Myerson value, we define a mapping to describe local structures of coalitions and obtain a new solution for cooperative games, called Myerson value with local structures. We propose an axiomatic characterization of the Myerson value associated with local cooperative structures.

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