Stochastic win-stay-lose-shift strategy with dynamic aspirations in evolutionary social dilemmas

TL;DR

This paper introduces a stochastic win-stay-lose-shift strategy with dynamic aspirations in evolutionary social dilemmas, demonstrating persistent cooperation across different network topologies through local interactions rather than network reciprocity.

Contribution

It develops a novel dynamic aspiration model for social dilemmas, analytically and numerically analyzing its effects on cooperation in various network structures.

Findings

Cooperation persists even at high temptation levels.

Cooperation spreads through second-order neighbors, not network reciprocity.

Local patterns remain stable regardless of network topology.

Abstract

In times of plenty expectations rise, just as in times of crisis they fall. This can be mathematically described as a Win-Stay-Lose-Shift strategy with dynamic aspiration levels, where individuals aspire to be as wealthy as their average neighbor. Here we investigate this model in the realm of evolutionary social dilemmas on the square lattice and scale-free networks. By using the master equation and Monte Carlo simulations, we find that cooperators coexist with defectors in the whole phase diagram, even at high temptations to defect. We study the microscopic mechanism that is responsible for the striking persistence of cooperative behavior and find that cooperation spreads through second-order neighbors, rather than by means of network reciprocity that dominates in imitation-based models. For the square lattice the master equation can be solved analytically in the large temperature limit of the Fermi function, while for other cases the resulting differential equations must be solved numerically. Either way, we find good qualitative agreement with the Monte Carlo simulation results. Our analysis also reveals that the evolutionary outcomes are to a large degree independent of the network topology, including the number of neighbors that are considered for payoff determination on lattices, which further corroborates the local character of the microscopic dynamics. Unlike large-scale spatial patterns that typically emerge due to network reciprocity, here local checkerboard-like patterns remain virtually unaffected by differences in the macroscopic properties of the interaction network.