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- W4387567874 abstract "Abstract In this paper, we propose a reverse game approach to network-modeled games in order to determine the network structure between players that can achieve a desired Nash equilibrium. We consider three network games: the majority game, the minority game, and the best-shot public goods game. For any hypothetical Nash equilibrium, we determine the conditions and constraints of the network structure that can create the desired Nash equilibrium in each game. The first step in the mechanism design is to identify the network between players that can reach the desired Nash equilibrium. This is important because there exist structures between players that will not generate the considered Nash equilibrium under any circumstances. Acceptable networks are not unique and their numbers grow exponentially based on the number of players and the combination of strategies. We provide mathematical relations to obtain the exact number of networks that can create the considered Nash equilibrium in the best-shot public goods game. Moreover, in the majority and minority games, the relations presented under special conditions specify the number of networks. We also investigate the distribution of acceptable networks as microsystems associated with the existing Nash equilibrium and the probability of their occurrence. The results of our simulations show that the distribution of acceptable networks according to the density is normal, and the probability of their occurrence is increasing. In other words, dense networks are more likely to lead to the desired Nash equilibrium." @default.
- W4387567874 created "2023-10-13" @default.
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- W4387567874 date "2023-10-12" @default.
- W4387567874 modified "2023-10-13" @default.
- W4387567874 title "Reverse Game: From Nash equilibrium to network structure, number, and probability of occurrence" @default.
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- W4387567874 doi "https://doi.org/10.21203/rs.3.rs-3419378/v1" @default.
- W4387567874 hasPublicationYear "2023" @default.
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