Willingness intensity and co-evolution of decision rationality depending on aspiration enhance cooperation in the spatial public goods game.

The Fermi rule states that rational or irrational sentiment affects individual decision-making. Existing studies have assumed that individuals' irrational sentiments and behavior willingness have fixed values and do not change with time. In reality, people's rationality sentiment and behavior willingness may be influenced by some factors. Therefore, we propose a spatial public goods game mechanism, in which individuals' rational sentiment is co-evolution synchronously depending on the difference between aspiration and payoff. Moreover, the intensity of their subjective willingness to change the status quo depends on the gap between aspiration and payoff. We likewise compare the combined promotion effect of the stochastic "Win-Stay-Lose-Shift" (WSLS) and random imitation (IM) rules. Simulation experiments indicate that high enhancement factors are not conducive to cooperation under the IM rules. When aspiration is small, WSLS is more conducive to promoting cooperation than IM, while increasing aspiration, and the opposite phenomenon will appear. The heterogeneous strategic update rule is beneficial to the evolution of cooperation. Lastly, we find that this mechanism performs better than the traditional case in enhancing cooperation.