Coexistence of fraternity and egoism for spatial social dilemmas

Cooperation in public goods games: Leveraging other-regarding reinforcement learning on hypergraphs

Cooperation is a self-organized collective behavior. It plays a significant role in the evolution of both ecosystems and human society. Reinforcement learning is different from imitation learning, offering a new perspective for exploring cooperation mechanisms. However, most existing studies with the public goods game (PGG) employ a self-regarding setup or are on pairwise interaction networks. Players in the real world, however, optimize their policies based not only on their histories but also on the histories of their coplayers, and the game is played in a group manner. In this work, we investigate the evolution of cooperation in the PGG under the other-regarding reinforcement learning evolutionary game on hypergraph by combining the Q-learning algorithm and evolutionary game framework, where other players' action history is incorporated and the game is played on hypergraphs. Our results show that as the synergy factor r[over ̂] increases, the parameter interval divides into three distinct regions-the absence of cooperation, medium cooperation, and high cooperation-accompanied by two abrupt transitions in the cooperation level near r[over ̂]_{1}^{*} and r[over ̂]_{2}^{*}, respectively. Interestingly, we identify regular and anticoordinated chessboard structures in the spatial pattern that positively contribute to the first cooperation transition but adversely affect the second. Furthermore, we provide a theoretical treatment for the first transition with an approximated r[over ̂]_{1}^{*} and reveal that players with a long-sighted perspective and low exploration rate are more likely to reciprocate kindness with each other, thus facilitating the emergence of cooperation. Our findings contribute to understanding the evolution of human cooperation, where other-regarding information and group interactions are commonplace.

Heterogeneous decision-making dynamics of threshold-switching agents on complex networks

In the classical two-player decision-making scenario, individuals may have different tendencies to take a certain action, given that there exists a sufficient number of neighbors adopting a particular option. This is ubiquitous in many real-life contexts including traffic congestion, crowd evacuation, and minimal vertex cover problem. Under best-response dynamics, we investigate the decision-making behaviors of heterogeneous agents on complex networks. Results of the networked games are twofold: for networks of uniform degree distribution (e.g., the lattice) and fraction of the strategy is of a linear function of the threshold setting. Moreover, the equilibrium analysis is provided and the relationship between the equilibrium dynamics and the change of the threshold value is given quantitatively. Next, if the games are played on networks with non-uniform degree distribution (e.g., random regular and scale-free networks), influence of the threshold-switching will be weakened. Robust experiments indicate that it is not the value of the average degree, but the degree distribution that influences how the strategy evolves affected by the threshold settings. Our result shows that the decision-making behaviors can be effectively manipulated by tuning the parameters in the utility function (i.e., thresholds) of some agents for more regular network structures.

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.

Dynamic aspiration based on Win-Stay-Lose-Learn rule in spatial prisoner's dilemma game

Prisoner’s dilemma game is the most commonly used model of spatial evolutionary game which is considered as a paradigm to portray competition among selfish individuals. In recent years, Win-Stay-Lose-Learn, a strategy updating rule base on aspiration, has been proved to be an effective model to promote cooperation in spatial prisoner’s dilemma game, which leads aspiration to receive lots of attention. In this paper, according to Expected Value Theory and Achievement Motivation Theory, we propose a dynamic aspiration model based on Win-Stay-Lose-Learn rule in which individual’s aspiration is inspired by its payoff. It is found that dynamic aspiration has a significant impact on the evolution process, and different initial aspirations lead to different results, which are called Stable Coexistence under Low Aspiration, Dependent Coexistence under Moderate aspiration and Defection Explosion under High Aspiration respectively. Furthermore, a deep analysis is performed on the local structures which cause defectors’ re-expansion, the concept of END- and EXP-periods are used to justify the mechanism of network reciprocity in view of time-evolution, typical feature nodes for defectors’ re-expansion called Infectors, Infected nodes and High-risk cooperators respectively are found. Compared to fixed aspiration model, dynamic aspiration introduces a more satisfactory explanation on population evolution laws and can promote deeper comprehension for the principle of prisoner’s dilemma.

Strategy equilibrium in dilemma games with off-diagonal payoff perturbations

We analyze the strategy equilibrium of dilemma games considering a payoff matrix affected by small and random perturbations on the off-diagonal. Notably, a recent work [Proc. R. Soc. A 476, 20200116 (2020)1364-502110.1098/rspa.2020.0116] reported that while cooperation is sustained by perturbations acting on the main diagonal, a less clear scenario emerges when perturbations act on the off-diagonal. Thus, the second case represents the core of this investigation, aimed at completing the description of the effects that payoff perturbations have on the dynamics of evolutionary games. Our results, achieved by analyzing the proposed model under a variety of configurations as different update rules, suggest that off-diagonal perturbations actually constitute a nontrivial form of noise. In particular, the most interesting effects are detected near the phase transition, as perturbations tend to move the strategy distribution towards nonordered states of equilibrium, supporting cooperation when defection is pervading the population, and supporting defection in the opposite case. To conclude, we identified a form of noise that, under controlled conditions, could be used to enhance cooperation and greatly delay its extinction.

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

Innovation and evolution are two processes of paramount relevance for social and biological systems. In general, the former allows the introduction of elements of novelty, while the latter is responsible for the motion of a system in its phase space. Often, these processes are strongly related, since an innovation can trigger the evolution, and the latter can provide the optimal conditions for the emergence of innovations. Both processes can be studied by using the framework of evolutionary game theory, where evolution constitutes an intrinsic mechanism. At the same time, the concept of innovation requires an opportune mathematical representation. Notably, innovation can be modeled as a strategy, or it can constitute the underlying mechanism that allows agents to change strategy. Here, we analyze the second case, investigating the behavior of a heterogeneous population, composed of imitative and innovative agents. Imitative agents change strategy only by imitating that of their neighbors, whereas innovative ones change strategy without the need for a copying source. The proposed model is analyzed by means of analytical calculations and numerical simulations in different topologies. Remarkably, results indicate that the mixing of mechanisms can be detrimental to cooperation near phase transitions. In those regions, the spatial reciprocity from imitative mechanisms is destroyed by innovative agents, leading to the downfall of cooperation. Our investigation sheds some light on the complex dynamics emerging from the heterogeneity of strategy revision methods, highlighting the role of innovation in evolutionary games.

Giant Catalytic Effect of Altruists in Schelling's Segregation Model

We study the effect of introducing altruistic agents in a Schelling-like model of residential segregation. We find that even an infinitesimal proportion of altruists has dramatic catalytic effects on the collective utility of the system. Altruists provide pathways that move the system away from the suboptimal equilibrium it would reach if the system included only egoist agents, allowing it to reach the optimal steady state.

Role-separating ordering in social dilemmas controlled by topological frustration

''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.

Extension of a spatial evolutionary coordination game with neutral options

The multiagent evolutionary games on a lattice are equivalent to a kinetic Ising model if the uniform pair interactions are defined by a two-strategy coordination game and the logit rule controls the strategy updates. Now we extend this model by allowing the players to use additional neutral strategies that provide zero payoffs for both players if one of them selects one of the neutral strategies. In the resulting n-strategy evolutionary games the analytical methods and numerical simulations indicate continuous order-disorder phase transitions when increasing the noise level if n does not exceed a threshold value. For larger n the system exhibits a first order phase transition at a critical noise level decreasing asymptotically as 2/ln(n).

Social dilemma alleviated by sharing the gains with immediate neighbors

We study the evolution of cooperation in the evolutionary spatial prisoner's dilemma game (PDG) and snowdrift game (SG), within which a fraction α of the payoffs of each player gained from direct game interactions is shared equally by the immediate neighbors. The magnitude of the parameter α therefore characterizes the degree of the relatedness among the neighboring players. By means of extensive Monte Carlo simulations as well as an extended mean-field approximation method, we trace the frequency of cooperation in the stationary state. We find that plugging into relatedness can significantly promote the evolution of cooperation in the context of both studied games. Unexpectedly, cooperation can be more readily established in the spatial PDG than that in the spatial SG, given that the degree of relatedness and the cost-to-benefit ratio of mutual cooperation are properly formulated. The relevance of our model with the stakeholder theory is also briefly discussed.