Uncovering cooperative behaviors with sparse historical behavior data in the spatial games

For past decades, the main attention of the evolutionary games has been focused on cooperation mechanism with the assumption that the strategy information of all players are known. However, it is difficult for observers to obtain the global information of players’ strategies in the real world, and some players even hide their strategy information to confuse their opponents. Here we try to solve the problem to predicate the hidden strategies with sparse historical behavior data in the evolutionary games. To quantify the similarity of strategies among the players in our method, the Euclidean distance of players is defined from the strategies of the players in the few past rounds. Then, the hidden strategy of a player will be determined from the tendency that players with minimum Euclidean distance will adopt similar strategies. The method has good performance on determining hidden strategy of human beings in both the prisoner’s dilemma game and the public goods game where strategies of twenty five percent players are hidden, and the success rate to determine hidden strategy reaches up to 0.9. It is also found that the success rate to determine hidden strategy depends on both length of historical behavior data and tempting payoff b (the prisoner’s dilemma game) or multiple factor r (the public goods game).