Evidential reasoning based on imitation and aspiration information in strategy learning promotes cooperation in optional spatial public goods game

Abstract

Abstract Mechanisms of strategy learning have significant impact on the equilibrium state of the system in evolutionary games. As two common individual strategy updating rules, pairwise imitation and aspiration-driven updating have been widely used in various models of evolutionary games. In previous studies, it is generally assumed that individuals only adopt a single rule to update their strategies. Recently, there have been researches on the combination of the two rules, such as choosing one rule with a certain probability and choosing the other with its complementary probability. Under this combination rule, however, each individual still utilizes single-source information for strategy selection each time. In this paper, we extend the combination of the two rules from the perspective of multi-source information fusion and also consider the ignorance situation that may be contained in the obtained information. Since evidence theory has the advantage in representing knowledge with uncertainty and unknown, we introduce the tool of evidential reasoning to construct a new strategy learning rule where information from imitation and aspiration-driven updating is taken as two pieces of evidence, and individuals update strategies via evidence reasoning. The effect of the evidential-reasoning-based new rule is investigated in detail in the spatial public goods game with optional participation, where individuals have three alternative strategies, namely, cooperation, defection, and loner strategy. Through numerical simulations, we find that evidential reasoning can effectively improve the performance of both imitation and aspiration-driven updating in promoting the emergence of cooperation within a wide range of fusion weights. Particularly, in the region of low-synergy factors, cooperation can also be enhanced. These results can complement our understanding of the emergence of cooperation from the perspective of individual learning.