  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.
