Cooperative emergence of spatial public goods games with reputation discount accumulation

To address issues like the tragedy of the commons, reputation mechanisms prove effective in promoting the emergence of cooperative behavior in social dilemmas. Previous research assumed that the increment of reputation is a fixed constant, however, the historical behavior of individuals with time preferences affects their reputation fluctuations on different scales. Inspired by this, we propose a framework for spatial public goods game that incorporates a reputation discount accumulation model with time preferences. In this model, players are classified as either long-sighted players or short-sighted players based on the significance of their historical behavior. Compared with short-sighted players, long-sighted players are more concerned with the impact of historical behaviors on the next game. Simulation results show that long-sighted cooperative players can resist the invasion of short-sighted defectors, and short-sighted defection strategies are eventually replaced by long-sighted cooperative strategies. This indicates that a higher discount factor facilitates the generation and maintenance of cooperation.