Inference of interactions between players based on asynchronously updated evolutionary game data

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 naive mean-field(n MF)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 n MF.Both methods are robust to the asymmetric degree but work better for large payoffs.Compared with MLE,n MF is more sensitive to the strength of couplings and prefers weak couplings.