Chunyan Zhang

Resolution of the Stochastic Strategy Spatial Prisoner's Dilemma by Means of Particle Swarm Optimization

We study the evolution of cooperation among selfish individuals in the stochastic strategy spatial prisoners dilemma game. We equip players with the particle swarm optimization technique, and find that it may lead to highly cooperative states even if the temptations to defect are strong. The concept of particle swarm optimization was originally introduced within a simple model of social dynamics that can describe the formation of a swarm, i.e., analogous to a swarm of bees searching for a food source. Essentially, particle swarm optimization foresees changes in the velocity profile of each player, such that the best locations are targeted and eventually occupied. In our case, each player keeps track of the highest payoff attained within a local topological neighborhood and its individual highest payoff. Thus, players make use of their own memory that keeps score of the most profitable strategy in previous actions, as well as use of the knowledge gained by the swarm as a whole, to find the best available strategy for themselves and the society. Following extensive simulations of this setup, we find a significant increase in the level of cooperation for a wide range of parameters, and also a full resolution of the prisoners dilemma. We also demonstrate extreme efficiency of the optimization algorithm when dealing with environments that strongly favor the proliferation of defection, which in turn suggests that swarming could be an important phenomenon by means of which cooperation can be sustained even under highly unfavorable conditions. We thus present an alternative way of understanding the evolution of cooperative behavior and its ubiquitous presence in nature, and we hope that this study will be inspirational for future efforts aimed in this direction.

Evolution of interactions and cooperation in the spatial prisoner's dilemma game.

We study the evolution of cooperation in the spatial prisoners dilemma game where players are allowed to establish new interactions with others. By employing a simple coevolutionary rule entailing only two crucial parameters, we find that different selection criteria for the new interaction partners as well as their number vitally affect the outcome of the game. The resolution of the social dilemma is most probable if the selection favors more successful players and if their maximally attainable number is restricted. While the preferential selection of the best players promotes cooperation irrespective of game parametrization, the optimal number of new interactions depends somewhat on the temptation to defect. Our findings reveal that the “making of new friends” may be an important activity for the successful evolution of cooperation, but also that partners must be selected carefully and their number limited.

How insurance affects altruistic provision in threshold public goods games

The occurrence and maintenance of cooperative behaviors in public goods systems have attracted great research attention across multiple disciplines. A threshold public goods game requires a minimum amount of contributions to be collected from a group of individuals for provision to occur. Here we extend the common binary-strategy combination of cooperation and defection by adding a third strategy, called insured cooperation, which corresponds to buying an insurance covering the potential loss resulted from the unsuccessful public goods game. Particularly, only the contributing agents can opt to be insured, which is an effort decreasing the amount of the potential loss occurring. Theoretical computations suggest that when agents face the potential aggregate risk in threshold public goods games, more contributions occur with increasing compensation from insurance. Moreover, permitting the adoption of insurance significantly enhances individual contributions and facilitates provision, especially when the required threshold is high. This work also relates the strategy competition outcomes to different allocation rules once the resulted contributions exceed the threshold point in populations nested within a dilemma.

Different reactions to adverse neighborhoods in games of cooperation

In social dilemmas, cooperation among randomly interacting individuals is often difficult to achieve. The situation changes if interactions take place in a network where the network structure jointly evolves with the behavioral strategies of the interacting individuals. In particular, cooperation can be stabilized if individuals tend to cut interaction links when facing adverse neighborhoods. Here we consider two different types of reaction to adverse neighborhoods, and all possible mixtures between these reactions. When faced with a gloomy outlook, players can either choose to cut and rewire some of their links to other individuals, or they can migrate to another location and establish new links in the new local neighborhood. We find that in general local rewiring is more favorable for the evolution of cooperation than emigration from adverse neighborhoods. Rewiring helps to maintain the diversity in the degree distribution of players and favors the spontaneous emergence of cooperative clusters. Both properties are known to favor the evolution of cooperation on networks. Interestingly, a mixture of migration and rewiring is even more favorable for the evolution of cooperation than rewiring on its own. While most models only consider a single type of reaction to adverse neighborhoods, the coexistence of several such reactions may actually be an optimal setting for the evolution of cooperation.

Fixation of strategies driven by switching probabilities in evolutionary games

We study the evolutionary dynamics of strategies in finite populations which are homogeneous and well mixed by means of the pairwise comparison process, the core of which is the proposed switching probability. Previous studies about this subject are usually based on the known payoff comparison of the related players, which is an ideal assumption. In real social systems, acquiring the accurate payoffs of partners at each round of interaction may be not easy. So we bypass the need of explicit knowledge of payoffs, and encode the payoffs into the willingness of any individual shift from her current strategy to the competing one, and the switching probabilities are wholly independent of payoffs. Along this way, the strategy updating can be performed when game models are fixed and payoffs are unclear, expected to extend ideal assumptions to be more realistic one. We explore the impact of the switching probability on the fixation probability and derive a simple formula which determines the fixation probability. Moreover we find that cooperation dominates defection if the probability of cooperation replacing defection is always larger than the probability of defection replacing cooperation in finite populations. Last, we investigate the influences of model parameters on the fixation of strategies in the framework of three concrete game models: prisoners dilemma, snowdrift game and stag-hunt game, which effectively portray the characteristics of cooperative dilemmas in real social systems.

Containment control of multi-agent systems with fixed time-delays in fixed directed networks

Containment control of multi-agent system with time-delays is a meaningful topic with considerable realistic significance in the research of multi-agent systems. This paper investigates the distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders, when considering the fixed time-delay under fixed directed network topologies. In the case of studying the multi-agent delayed system with continuous-time, Laplace transform and final value theorem are employed. Specifically some sufficient conditions are obtained which can ensure the containment of the first-order multi-agent systems. Moreover, an effective control protocol is designed for the first-order discrete-time systems with fixed time-delays. Finally, simulation examples are given to verify the effectiveness of the theoretical results and conclusions.

The evolution of altruism in spatial threshold public goods games via an insurance mechanism

The persistence of cooperation in public goods situations has become an important puzzle for researchers. This paper considers the threshold public goods games where the option of insurance is provided for players from the standpoint of diversification of risk, envisaging the possibility of multiple strategies in such scenarios. In this setting, the provision point is defined in terms of the minimum number of contributors in one threshold public goods game, below which the game fails. In the presence of risk and insurance, more contributions are motivated if (1) only cooperators can opt to be insured and thus their contribution loss in the aborted games can be (partly or full) covered by the insurance; (2) insured cooperators obtain larger compensation, at lower values of the threshold point (the required minimum number of contributors). Moreover, results suggest the dominance of insured defectors who get a better promotion by more profitable benefits from insurance. We provide results of extensive computer simulations in the realm of spatial games (random regular networks and scale-free networks here), and support this study with analytical results for well-mixed populations. Our study is expected to establish a causal link between the widespread altruistic behaviors and the existing insurance system.

Cooperation in networks where the learning environment differs from the interaction environment

We study the evolution of cooperation in a structured population, combining insights from evolutionary game theory and the study of interaction networks. In earlier studies it has been shown that cooperation is difficult to achieve in homogeneous networks, but that cooperation can get established relatively easily when individuals differ largely concerning the number of their interaction partners, such as in scale-free networks. Most of these studies do, however, assume that individuals change their behaviour in response to information they receive on the payoffs of their interaction partners. In real-world situations, subjects do not only learn from their interaction partners, but also from other individuals (e.g. teachers, parents, or friends). Here we investigate the implications of such incongruences between the ‘interaction network’ and the ‘learning network’ for the evolution of cooperation in two paradigm examples, the Prisoners Dilemma game (PDG) and the Snowdrift game (SDG). Individual-based simulations and an analysis based on pair approximation both reveal that cooperation will be severely inhibited if the learning network is very different from the interaction network. If the two networks overlap, however, cooperation can get established even in case of considerable incongruence between the networks. The simulations confirm that cooperation gets established much more easily if the interaction network is scale-free rather than random-regular. The structure of the learning network has a similar but much weaker effect. Overall we conclude that the distinction between interaction and learning networks deserves more attention since incongruences between these networks can strongly affect both the course and outcome of the evolution of cooperation.

Group penalty on the evolution of cooperation in spatial public goods games

We study the evolution of cooperation in spatial public goods games, whereby a coevolutionary rule is introduced that aims to integrate group penalty into the framework of evolutionary games. Existing groups are deleted whenever the collective gains of the focal individuals are less than a deletion threshold value. Meanwhile, newcomers are added after each game iteration to maintain the fixed population size. The networking effect is also studied via four representative interaction networks which are associated with the population structure. We conclude that the cooperation level has a strong dependence on the deletion threshold, and the suitable value range of the deletion threshold which is associated with the maximal cooperation frequency has been found. Simulation results also show that optimum values of the deletion threshold can still warrant the most potent promotion of cooperation, irrespective of which of the four topologies is applied.

Diversity of game strategies promotes the evolution of cooperation in public goods games

We propose a mechanism allowing strategy diversity instead of a common combination of cooperation and defection to study how cooperation evolves in public goods games. Each individual is assigned a variable valued in the unit interval as its cooperation degree. Thus, diverse cooperation degrees express the diversity of game strategies in the way of multiple contributions of players, and the investment in the common pool is positively correlated with cooperation degrees correspondingly. Moreover, we also define two particular roles named altruist and egotist defined locally since they depend on the behavior of their neighboring players. Numerical simulations show that the proposed diversity of strategies can substantially evoke the emergence and maintenance of cooperation. Notably, we also find that no player will act as a long-term exploiter (egotist) or exploitee (altruist) in the whole evolutionary process.