Social dilemmas in multistrategy evolutionary potential games

Neighborhood size effects on the evolution of cooperation under myopic dynamics

We study the evolution of cooperation in 2×2 social dilemma games in which players are located on a two-dimensional square lattice. During the evolution, each player modifies her strategy by means of myopic update dynamic to maximize her payoff while composing neighborhoods of different sizes, which are characterized by the corresponding radius, r. An investigation of the sublattice-ordered spatial structure for different values of r reveals that some patterns formed by cooperators and defectors can help the former to survive, even under untoward conditions. In contrast to individuals who resist the invasion of defectors by forming clusters due to network reciprocity, innovators spontaneously organize a socially divisive structure that provides strong support for the evolution of cooperation and advances better social systems.

Environmental feedback promotes the evolution of cooperation in the structured populations

Environment plays a vital role in individual decision-making. In the game process, employing the strategy of the opponent who behaves better is nontrivial for the evolution and maintenance of cooperation, in that such a behavior may assist the player in achieving higher personal interests and more competitive superiorities. Enlightened by this thought, a coevolutionary model where the mechanisms of dynamic environment and preference selection are introduced in the networked prisoner's dilemma game is considered. Individual preference selection is introduced in the strategy update process to probe how the preferences of the latent strategy sources interfere with individual behaviors. The environment defined in the model is not only heterogeneous, but also evolves with the evolution of individual strategies. Through conducting large-scale Monte Carlo simulations, we draw a conclusion that the introduction of evolutionary environment-related preference selection is an effective promoter of cooperation even under a severe temptation. Our exploration indicates that the coevolutionary model may have a practical significance and provide a new insight into the analysis of the origin of cooperation in structured populations for further research.

Statistical analyses of cyclic and starlike hierarchical dominances in directed graphs

The mathematical framework of matrix decomposition implies the possibility to perform statistical analyses of directed graphs focused on the distributions of the independent cyclic and starlike hierarchical components. In this approach the weighted directed graphs with n nodes are built up as a linear combination of starlike graphs with n outgoing edges and a suitable set of three-edge cyclic subgraphs. The applicability of this approach is illustrated by quantifying several general features: e.g., ratio of the cyclic and hierarchical components and asymmetry in the hierarchical components. The applicability of these methods is illustrated by considering the averages over random directed graphs and comparing these values with those characterizing simple directed graphs of tournaments.

Cooperation dynamics of generalized reciprocity in state-based social dilemmas

We introduce a framework for studying social dilemmas in networked societies where individuals follow a simple state-based behavioral mechanism based on generalized reciprocity, which is rooted in the principle "help anyone if helped by someone." Within this general framework, which applies to a wide range of social dilemmas including, among others, public goods, donation, and snowdrift games, we study the cooperation dynamics on a variety of complex network examples. By interpreting the studied model through the lenses of nonlinear dynamical systems, we show that cooperation through generalized reciprocity always emerges as the unique attractor in which the overall level of cooperation is maximized, while simultaneously exploitation of the participating individuals is prevented. The analysis elucidates the role of the network structure, here captured by a local centrality measure which uniquely quantifies the propensity of the network structure to cooperation by dictating the degree of cooperation displayed both at the microscopic and macroscopic level. We demonstrate the applicability of the analysis on a practical example by considering an interaction structure that couples a donation process with a public goods game.