Emergence of cooperation with reputation-updating timescale in spatial public goods game

The evaluation and updating of individual reputation plays a significant role in the evolution of game cooperation under the framework of reputation-based indirect reciprocity. However, the reputation-updating timescale is not necessarily consistent with the strategy-selection timescale. In this letter, we explore the effect of reputation-updating timescale on the cooperation behavior of second-order reputation-based public goods game, and it is assumed that the reputation-updating timescale is slower than the strategy-selection timescale. We observe that the low-frequency of reputation updating will result in some delay, and further hamper the emergency of cooperation behavior. Thus, we propose a novel adaptive reputation-update rule by combining the number of cooperative strategy in the historical memory. Through extensive numerical simulations, we find that under the appropriate reputation-updating timescale (not too fast or too slow), the emergence of cooperation behavior will be improved greatly, even the cooperation level is better than that under the conventional second-order reputation-based PGG. Taking together, the current results will be conducive to understanding the emergency of cooperation in theory and design a reasonable reputation-updating rule in practice. (C) 2021 Elsevier B.V. All rights reserved.