title: Stochastic win-stay-lose-shift strategy with dynamic aspirations in evolutionary social dilemmas.
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.
authors.affiliation: Departamento de Física, Universidade Federal de Minas Gerais, Caixa Postal 702, CEP 30161-970, Belo Horizonte-MG, Brazil.
authors.forename: Marco A
authors.initials: MA
authors.lastname: Amaral
authors.affiliation: Departamento de Fisica, Universidade Federal de Ouro Preto, Ouro Preto, CEP 35400-000 MG, Brazil.
authors.forename: Lucas
authors.initials: L
authors.lastname: Wardil
authors.affiliation: Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia.|CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia.
authors.forename: Matjaž
authors.initials: M
authors.lastname: Perc
authors.affiliation: Departamento de Física, Universidade Federal de Minas Gerais, Caixa Postal 702, CEP 30161-970, Belo Horizonte-MG, Brazil.
authors.forename: Jafferson K L
authors.initials: JK
authors.lastname: da Silva
mesh_terms: D005075:Biological Evolution; D003198:Computer Simulation; D003299:Cooperative Behavior; D006801:Humans; D008954:Models, Biological; D009010:Monte Carlo Method; D013269:Stochastic Processes