The role of Far-Sighted agents on the evolution of cooperation in social dilemma

Why would natural selection facilitate the prevailing cooperation in selfish groups of individuals? A common framework for studying this problem is evolutionary game theory. Here, we propose a new strategy update rule, called the far-Sighted update rule, that enables agents to take into account the possible responses of their neighbors, which means a far-Sighted agent does not have a short-sighted, static view of the environment but rather a long-term view that considers environmental changes. We study the effect of the far-Sighted update rule on behavioral evolution in two cases. The level of cooperation can be significantly promoted for populations of myopic agents acting with a certain probability with the far-Sighted update rule. The cooperation rate of the population did not drop below a threshold even under very hostile conditions. Moreover, the stronger the intelligence's willingness to consider long-term views is, the larger this threshold will be. The theoretical results of the mean field are consistent with the simulation results. However, for far-Sighted agents, which act exactly as far-Sighted update rule, it shows sensitivity to the network structure. In a mixed population of far-Sighted agents and myopic agents, even if all myopic agents become defectors, the far-Sighted agents can still maintain a certain cooperator ratio. Thus, our work can help to understand the evolution of populations of agents with a higher intelligence that can consider environmental changes.