Inference of interactions between players based on asynchronously updated evolutionary game data
Hong-Li Zeng(曾红丽)1, Bo Jing(景浡)2, Yu-Hao Wang(王于豪)1, and Shao-Meng Qin(秦绍萌)3,†
1. College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China; 2. College of Electronic Science and Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210046, China; 3. College of Science, Civil Aviation University of China, Tianjin 300300, China
Abstract The interactions between players of the prisoner's dilemma game are inferred using observed game data. All participants play the game with their counterparts and gain corresponding rewards during each round of the game. The strategies of each player are updated asynchronously during the game. Two inference methods of the interactions between players are derived with naïve mean-field (nMF) approximation and maximum log-likelihood estimation (MLE), respectively. Two methods are tested numerically also for fully connected asymmetric Sherrington-Kirkpatrick models, varying the data length, asymmetric degree, payoff, and system noise (coupling strength). We find that the mean square error of reconstruction for the MLE method is inversely proportional to the data length and typically half (benefit from the extra information of update times) of that by nMF. Both methods are robust to the asymmetric degree but work better for large payoffs. Compared with MLE, nMF is more sensitive to the strength of couplings and prefers weak couplings.
Fund: This work was supported by the National Natural Science Foundation of China (Grant Nos.11705079 and 11705279), the Scientific Research Foundation of Nanjing University of Posts and Telecommunications (Grant Nos.NY221101 and NY222134), and the Science and Technology Innovation Training Program (Grant No. STITP_202210293044Z).
Hong-Li Zeng(曾红丽), Bo Jing(景浡), Yu-Hao Wang(王于豪), and Shao-Meng Qin(秦绍萌) Inference of interactions between players based on asynchronously updated evolutionary game data 2023 Chin. Phys. B 32 080201
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