Role-separating ordering in social dilemmas controlled by topological frustration

Abstract

"Three is a crowd" is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models. Accordingly, social relations within a triangle deserve special attention. With this motivation, we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice. This topology provides an irreconcilable frustration, which prevents anticoordination of competing strategies that would be needed for an optimal outcome of the game. By using different strategy updating protocols, we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb-like organization, which helps to minimize the negative consequence of the topological frustration. We relate the emergence of these patterns to the microscopic dynamics of the evolutionary process, both by means of mean-field approximations and Monte Carlo simulations. For comparison, we also consider the same evolutionary dynamics on the square lattice, where of course the topological frustration is absent. However, with the deletion of diagonal links of the triangular lattice, we can gradually bridge the gap to the square lattice. Interestingly, in this case the level of cooperation in the system is a direct indicator of the level of topological frustration, thus providing a method to determine frustration levels in an arbitrary interaction network.

Statistical physics of human cooperation

“…As an alternative to the above-described imitation dynamics we also mention the logit rule, which is mathematically equivalent to the statistics used in physics to describe the dynamics of spins in a Fermi-Dirac distribution [202,203]. The logit rule is also known as the myopic best response rule in evolutionary game theory [204,205]. According to the logit rule, a player will change its strategy s x to another randomly selected strategy s ′ x with probability…”

Heterogeneous update mechanisms in evolutionary games: Mixing innovative and imitative dynamics

“…As reported in previous investigations (e.g. [12,14,[16][17][18]), the application of innovative and non-innovative updat-ing rules leads to results that can be drastically different. As a very interesting and recent example, [19] showed how innovative strategies towards vaccination can lead to different dynamics than the usual imitative ones, changing the vaccination coverage.…”

“…However, in this case, cooperators do not form compact clusters. Instead, they spread out in the lattice and cooperation is sustained because of other mechanisms related to second order spatial effects as seen in [12,16]. Mixing both models, innovative cooperators spread trough the lattice and, in turn, imitative cooperators are not able to form clusters to protect themselves.…”

“…In [16], the authors show that win-stay-lose-shift with dynamic aspiration can lead to the coexistence of cooperation and defection for the whole parameter range while, at the same time, cooperators do not need to form islands to survive. In [12,34,35], a model based on the Glauber dynamics (from magnetism) shows the survival of cooperators while leading the population to global stable patterns, in a process akin to the minimization of energy. Driven by this observation, in this work we propose an evolutionary model for studying the dynamics of a heterogeneous population composed of imitative and innovative agents.…”

Stability of subsystem solutions in agent-based models

“…Although the present example draws on spatial evolutionary games and should be of interest to contemporary statistical physics research on the subject [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63], the concept of stability of subsystem solutions in agent-based models goes far beyond disciplinary boundaries. Whether agents are humans, firms, ants, or ecological entities, whenever more than two states compete in a structured population (represented by a lattice or a network), the stability of subsystem solutions is crucial for a correct and relevant analysis.…”