Te Wu

Partner selections in public goods games with constant group size.

Most of previous studies concerning the public goods game assume either participation is unconditional or the number of actual participants in a competitive group changes over time. How the fixed group size, prescribed by social institutions, affects the evolution of cooperation is still unclear. We propose a model where individuals with heterogeneous social ties might well engage in differing numbers of public goods games, yet with each public goods game being constant size during the course of evolution. To do this, we assume that each focal individual unidirectionally selects a constant number of interaction partners from his immediate neighbors with probabilities proportional to the degrees or the reputations of these neighbors, corresponding to degree-based partner selection or reputation-based partner selection, respectively. Because of the stochasticity the group formation is dynamical. In both selection regimes, monotonical dependence of the stationary density of cooperators on the group size was found, the latter over the whole range but the former over a restricted range of the renormalized enhancement factor. Moreover, the reputation-based regime can substantially improve cooperation. To interpret these differences, the microscopic characteristics of individuals are probed. We later extend the degree-based partner selection to general cases where focal individuals have preferences toward their neighbors of varying social ties to form groups. As a comparison, we as well investigate the situation where individuals locating on the degree regular graphs choose their coplayers at random. Our results may give some insights into better understanding the widespread teamwork and cooperation in the real world.

Individual's expulsion to nasty environment promotes cooperation in public goods games

Previous studies of games on dynamic graphs have almost specified pairwise interactions using the prisoners dilemma game. We instead here for the first time explore coevolutionary dynamics in the context of interactions being characterized by the public goods game. Individuals are endowed with the capacity to adjust both their strategy and their social ties, occurring exclusively dependent on their payoffs. Under strategy updating, focal individuals are more likely to imitate their neighbors performing better. Meanwhile, they would abstain from engaging in the most defective neighborhoods if the opportunities of adjusting social ties arise, representing trait of individuals that they prefer better but exclude nasty environments. How often strategy dynamics and adaptation of social ties separately progress is governed by a tunable parameter. We experimentally found that opportune tradeoff of these two dynamics peaks cooperation, an observation absent whenever either dynamics is considered. We confirm that the stabilization of cooperation resulting from the partner switching remains effective under some more realistic situation where the maximal number of social ties one can admit is restrained.

The coevolutionary ultimatum game

We develop a minimal model to explore coevolutionary dynamics on spatial ultimatum game. Individuals are endowed with the capacity to adjust both their strategy and their social ties. Under strategy dynamics, individuals preferentially imitate the strategy of more successful neighbors. Meanwhile, the egoists, whose offers do not satisfy the partners, run the risk of being dismissed. We find that individuals make fairer offers when they are allowed to switch adverse partnerships. Remarkably, the promotion of fairness by partner rewiring is offset in a certain extent by the emergence of isolated individuals. We also investigate the influence of the average degree on the evolution of fairness under our coevolutionary rules. It is found that a smaller average degree leads to a fairer society under the condition of low partner rewiring frequency. However, if partner rewiring frequency is high, a dense network where isolated individuals are not apt to emerge, is favorable for the establishment of fairness.

Adaptive role switching promotes fairness in networked ultimatum game

In recent years, mechanisms favoring fair split in the ultimatum game have attracted growing interests because of its practical implications for international bargains. In this game, two players are randomly assigned two different roles respectively to split an offer: the proposer suggests how to split and the responder decides whether or not to accept it. Only when both agree is the offer successfully split; otherwise both get nothing. It is of importance and interest to break the symmetry in role assignment especially when the game is repeatedly played in a heterogeneous population. Here we consider an adaptive role assignment: whenever the split fails, the two players switch their roles probabilistically. The results show that this simple feedback mechanism proves much more effective at promoting fairness than other alternatives (where, for example, the role assignment is based on the number of neighbors).

A tale of two contribution mechanisms for nonlinear public goods

Amounts of empirical evidence, ranging from microbial cooperation to collective hunting, suggests public goods produced often nonlinearly depend on the total amount of contribution. The implication of such nonlinear public goods for the evolution of cooperation is not well understood. There is also little attention paid to the divisibility nature of individual contribution amount, divisible vs. non-divisible ones. The corresponding strategy space in the former is described by a continuous investment while in the latter by a continuous probability to contribute all or nothing. Here, we use adaptive dynamics in finite populations to quantify and compare the roles nonlinearity of public-goods production plays in cooperation between these two contribution mechanisms. Although under both contribution mechanisms the population can converge into a coexistence equilibrium with an intermediate cooperation level, the branching phenomenon only occurs in the divisible contribution mechanism. The results shed insight into understanding observed individual difference in cooperative behavior.

Mixed strategy under generalized public goods games.

The relationship between groups contribution and public goods produced often exhibits nonlinearity, which constitutes the generalized public goods game. Far less attention has been paid to how the mixed strategy evolves in such generalized games. Here, we study the effects of nonlinear production functions on the evolution of the mixed strategy in finite populations for the first time. When the group size and the population size are comparable, cooperation is doomed irrespective of the production function. Otherwise, nonlinear production functions may induce a convergent evolutionary stable strategy (CESS) or a repeller, but cannot yield the evolutionary branching. Moreover, we particularly consider three representative families of production functions, intriguingly which all display the hysteresis effect. For two families of production functions including concave and convex curves, a unique CESS or a unique repeller may occur even if the group size is two. Whereas for the third class encompassing symmetrically sigmoidal and inverse sigmoidal curves, the coexistence of a CESS and a repeller only occurs if group size is above two, and two saddle-node bifurcations appear. Our work includes some evidently different results by comparing with the evolution of continuous investment or binary strategy.

Adaptive tag switching reinforces the coevolution of contingent cooperation and tag diversity.

Most of the previous studies concerning the similarity-based interaction have assumed that the change of tags just happens in the imitation stage. Individuals actually can adjust their tags whenever the environments related to these tags grow nasty. We institute a spatial model to investigate the effect of the coevolution of tag and strategy on the evolution of cooperation in the context of the Prisoners Dilemma game. Interactions just happen between tag-identical neighbors. Individuals exploited by defectors change their current tags at a certain cost. The time-scale ratio controls how fast interaction happens relatively to selection. Results show that whenever individuals have enough chance to adapt to the environment, cooperation is greatly improved even for quite large temptation to defect. Intensive exploration reveals that both little and large costs of tag switching can further favor the establishment of cooperation. Our work may add more into the literature concerning games on adaptive networks.

The increased risk of joint venture promotes social cooperation.

The joint venture of many members is common both in animal world and human society. In these public enterprizes, highly cooperative groups are more likely to while low cooperative groups are still possible but not probable to succeed. Existent literature mostly focuses on the traditional public goods game, in which cooperators create public wealth unconditionally and benefit all group members unbiasedly. We here institute a model addressing this public goods dilemma with incorporating the public resource foraging failure risk. Risk-averse individuals tend to lead a autarkic life, while risk-preferential ones tend to participate in the risky public goods game. For participants, groups success relies on its cooperativeness, with increasing contribution leading to increasing success likelihood. We introduce a function with one tunable parameter to describe the risk removal pattern and study in detail three representative classes. Analytical results show that the widely replicated population dynamics of cyclical dominance of loner, cooperator and defector disappear, while most of the time loners act as savors while eventually they also disappear. Depending on the way that groups success relies on its cooperativeness, either cooperators pervade the entire population or they coexist with defectors. Even in the later case, cooperators still hold salient superiority in number as some defectors also survive by parasitizing. The harder the joint venture succeeds, the higher level of cooperation once cooperators can win the evolutionary race. Our work may enrich the literature concerning the risky public goods games.

Bluffing promotes overconfidence on social networks

The overconfidence, a well-established bias, in fact leads to unrealistic expectations or faulty assessment. So it remains puzzling why such psychology of self-deception is stabilized in human society. To investigate this problem, we draw lessons from evolutionary game theory which provides a theoretical framework to address the subtleties of cooperation among selfish individuals. Here we propose a spatial resource competition model showing that, counter-intuitively, moderate values rather than large values of resource-to-cost ratio boost overconfidence level most effectively. In contrast to theoretical results in infinite well-mixed populations, network plays a role both as a “catalyst” and a “depressant” in the spreading of overconfidence, especially when resource-to-cost ratio is in a certain range. Moreover, when bluffing is taken into consideration, overconfidence evolves to a higher level to counteract its detrimental effect, which may well explain the prosperity of this “erroneous” psychology.