Sucker's Payoff Research Articles

Evaluation and threshold-based mutual supervision promotes the evolution of cooperation on interdependent networks

Inspired by the pivotal role of supervision mechanisms in promoting and maintaining cooperative behavior in human society, we propose a mutual supervision mechanism to explore the evolution of cooperation on an interdependent network. The mechanism adjusts the game type of supervised nodes when their evaluation value falls below a critical threshold. Monte Carlo simulations reveal that the mutual supervision mechanism effectively encourages the emergence of cooperative strategies on interdependent networks. The experimental results show a direct positive linkage between the number of supervised nodes and the fraction of cooperation. In detail, the effect of the sucker's payoff on cooperation is more noticeable when most of the nodes are supervised by the mechanism. However, a higher sucker's payoff discourages cooperation when there are few supervised nodes. Furthermore, the stability of cooperation is closely related to a stricter supervision threshold. Conversely, if the supervision threshold is too lenient, previously stable cooperation levels will suddenly collapse.

Co-evolution of cooperation and extortion with resource allocation in spatial multigame

In nature and human society, some agents want to obtain more payoffs by controlling own and opponents' strategy. The extortion strategy can unilaterally ensure that its own payoffs are not lower than its opponents', which has aroused widespread concern. In this article, based on spatial multigame, an evolutionary dynamics model with extortion strategy is proposed, which can significantly influence the evolution of different dilemma strategies in the system. Moreover, the limited resources as a co-evolutionary factor are also involved in this model. Throughout the entire evolutionary process, individuals in SDG and collaborators are more likely to obtain more resources and the number of resources owned by individuals in PDG is continuously decreasing. By using single square lattice network, we discuss in detail the evolutionary dynamics of the proposed model and study the impact of the sucker's payoff θ and extortion factor λ on different strategies of the system. Through a large number of experiments, it is found that the θ can significantly increase the number of cooperators. And there is an appropriate λ value, which can not increase the number of its own individuals, but also form an alliance with cooperators to jointly resist the intrusion of defectors. Besides, the relationship between θ, λ and network reciprocity is studied. We obtain that the θ and λ can significantly improve network reciprocity. Finally, based on different extortion factor λ, the proportion of different strategy in PDG and SDG is discussed to explain the robustness of the results.

Co-evolution of reputation-based preference selection and resource allocation with multigame on interdependent networks

In nature and human society, individual's reputation and selection of interaction objects play a very important role in explaining the emergence and maintenance of cooperation. Meanwhile, how to make resources allocation more evenly and properly has attracted extensive attention. In this article, based on the multi-game mode of the interdependent network, a reputation-based preference selection mechanism is proposed, where individual's reputation is used as its weight to redefine its individual's fitness and dynamically adjusted. And, the cooperative behavior and dynamic characteristics of different individuals in the system from different perspectives are studied. Moreover, limited resources are also leaded into the network, which has an impact on the reputation of agents. Based on this model, the interdependent strength, reputation, sucker's payoff and strategy choice from different angles is deeply studied, and corresponding evolution dynamics are also discussed. As the results, the optimal interdependent strength is found. Besides, preferential parameter and sucker's payoff not only improve cooperation rate, but also affect the resource allocation of different individuals in the system. Finally, we hope that it can provide some theoretical references for some real systems through this work.

The effect of perceptions competition and learning costs on cooperation in spatial evolutionary multigames

It is a great challenge to correctly understand the evolution and incentives of cooperation. In recent years, the spatial evolutionary multigames have attracted extensive attention from researchers. Actually, for players, not only themselves but also their neighbors will affect their perceptions, which has not been considered in previous works. In addition, changing perceptions has a learning process, which will cause some costs. Inspired by the above facts, we explore the impact of perceptions competition mechanisms and learning costs on the evolution of cooperation in the multigames dilemma, which consists of prisoner game and snowdrift game. Especially, we further explore how different groups can coexist in such a setting. It is found that the heterogeneity of payoffs contributes to network reciprocity and can maintain cooperative behaviors even under unfavorable conditions. Compared with the static multigames mechanism, our perceptions competition mechanism has a higher proportion of cooperators under the same temptation value b and sucker payoff θ, and the cooperators can survive within a larger range of parameters. At the same time, a small cost can effectively maintain a high proportion of cooperators, while an appropriate cost will keep players at a high level of both the proportion of cooperators and the coexistence range. The continuous increase of costs will make our evolutionary mechanism ineffective and turn to static multigames. We also find that the introduction of costs will help different types of players coexist, and with the increase of costs, the coexistence area will first decrease and then increase. Moreover, our main findings are equally applicable to complex networks such as BA networks and random networks.

The Residency Match: Escaping the Prisoner's Dilemma.

The Residency Match: Escaping the Prisoner's Dilemma.

Diversity of interaction intensity enhances the cooperation of spatial multi-games on interdependent lattices

We put forward a novel multi-games model based on the diversity of interaction intensity under the framework of interdependent lattices, where an adjustable variable ω is accustomed to regulate the interaction intensity between players. In detail, when the payoff of the focal player x gaining from his neighbor y is not less than the average payoff of the focal player x from four nearest neighbors, the interaction intensity between them is strengthened; otherwise, this intensity is weakened. In addition, the utility of players is mainly determined by their own payoff and also related to the payoff of that player occupying the same position on another lattice. Through extensive simulations, the results indicate that the diversity of interaction intensity between players can immensely favor the evolution of cooperation. The smaller ω means the stronger diversity of interaction intensity, which leads to the higher level of collective cooperation. Particularly, when the interaction intensity and the sucker's payoff are changed continuously, the cooperative behavior among individuals tends to become more complicated than that only driven by the network reciprocity. We also find that when the diversity is weak (ω>0.5), the utility coupling factor α does not seem to be a decisive element in facilitating the development of cooperation. However, when the diversity is strong (ω<0.5), the promotion of cooperation becomes more remarkable. Our work also illustrates the pivotal role of diversity of interaction intensity in solving complex social dilemmas, which will inspire us to comprehend the cooperation behavior in numerous real-world systems.

Accessing the Role of Trust Profiles for the Economic Growth of Societies: A Stochastic Rule-Based Simulation Using the Prisoner’s Dilemma Game

According to Robert Putnam, trust can be a proxy for social capital. Thus, a higher societal trust could be related to economic growth. To test this hypothesis, we simulated the association between trust and economic growth in two artificial societies. One artificial society (New Zealand) exhibited higher levels of initial trust, and the other (Argentina) had lower levels of trust. Initial starting points for simulations were set using representative survey data (using the global trust inventory). Computational simulation relied on a rule-based model (RBM), integrating time through a stochastic simulation algorithm implemented in PISKaS. Agents in the artificial societies were distributed according to proportions of four trust profiles, with more high trusters (HTs) in New Zealand. In each iteration, the agents played a prisoner's dilemma, earning or losing money according to different payoff matrices, cooperation probabilities, and interaction frequencies, modeling different conditions for economic exchange. We analyzed the economic performance of each country, together with the performance of each trust profile. Results support the notion that societies with high trust perform economically better, on average, than those with low trust, but only if interaction frequency is held constant. Despite the relevance of HTs for economic development, their performance is tightly linked to the type of society in which they interact: they prosper more in a Rule of Law society, and where HTs are more common, compared with a predators' paradise, where the sucker's payoff is more punitive.

The evolution of cooperation affected by aspiration-driven updating rule in multi-games with voluntary participation

Abstract We have demonstrated multi-games with voluntary participation can promote cooperation and found aspiration-driven updating rule can also facilitate cooperation to some degree. Stimulated by these, we combine the two mechanisms and investigate the evolution of cooperation. In our work, the population is randomly divided into two types, one type players play the PDG, while the other type players play SG. At the same time, a part of players randomly select to use the aspiration-driven updating rule, and the other part of players choose to use the Fermi-function based strategy adoption rule. Besides, players have three strategies - cooperation, defection and going it alone- to choose. We reveal that both the diversity of sucker's payoff and updating strategy can facilitate cooperation to some degree. Moreover, larger magnitude of sucker's payoff and less players using the aspiration-driven rule can improve cooperation resulting from spatial distribution of strategies. And players playing SG play a more important role to enhance cooperation than players playing PDG, which is due to the special network reciprocity. Furthermore, the easily satisfied players intend to cooperate, while the greedy players intend to be loners to avoid obtaining nothing.

The mechanism of alliance promotes cooperation in the spatial multi-games

In reality, individuals often tend to enhance their competitiveness by forming alliances with the partners sharing the same view. Motivated by this phenomenon, we propose a novel model considering the mechanism of alliance to investigate the evolution of cooperation in the spatial multi-games, in which the intensity of alliance could be adjusted by a parameter μ. In detail, the focal individual will contribute the ratio μ of his own payoff as a cost of the alliance, and then expect to gain the equal portion of average benefits of the neighbors holding the same strategy, which means that the individual fitness can be tuned by the intensity of alliance. Through extensive numerical simulations, one could find that the mechanism of alliance can significantly promote the prosperity of cooperation. Moreover, the larger the value of μ, the stronger the intensity of alliance, which could lead to the higher the level of cooperation. In particular, the evolutionary dynamics presents a complex situation when the co-changes of the intensity of alliance μ and sucker's payoff δ are commonly considered. Furthermore, we also verify the robustness of the proposed mechanism by using the diversity of the intensity of alliance and different network topologies. The current results are conducive to comprehending the emergence and persistence of cooperation within the real-world population.

Co-evolution of influence-based preferential selection and limited resource with multi-games on interdependent networks

In real life, some individuals generally have more influence than ordinary people. Their behaviors are easily learned by other individuals. In this article, we propose influence-based preferential selection multi-games model on interdependent networks, where influence of players as a factor to be considered is involved in multiple game models and coevolved with cooperation. By using of coupled lattices, the effect of the cooperative behaviors of the system is comprehensively studies. Besides, in real life, resources are always related to the outcome of game. The results in game generally determine the allocation of limited resources, which in turn affects the choice of strategy. Hence, limited resources as a co-evolutionary factor are also introduced into the game model, which mutual interacts with individual's strategy and influence. Based on multi-game model, the evolutionary dynamics of the model in detail is discussed. We find that the preferential selection mechanism based on influence can effectively improve the cooperative behaviors of the system, where the influence growth factor increases and the cooperation evolution also monotonously increases. Furthermore, the interdependent strength, sucker's payoff and the distribution of limited resources would have different effects on the dynamics of the system.

The evolution of cooperation in multi-games with aspiration-driven updating rule

Abstract We introduce multi-games with aspiration-driven updating rule and investigate the evolution of cooperation. In our work, a percentage of players randomly choose to play the PDG, while the remaining players play SG. Meanwhile, a part of players randomly select to use the aspiration-driven updating rule, and the other part of players select to use the Fermi-function updating rule. We find that both the diversity of sucker's payoff and updating rule have a positive effect on the cooperation. Besides, when the contribution of the sucker's payoff is larger or more players use the aspiration-driven rule to update the strategy, more cooperators appear derived from the spatial distribution of strategies and special network reciprocity. What is more, when more players choose to play SG and simultaneously use the aspiration-driven rule, cooperators gradually flourish. In addition, we also reveal that the easily contented players prefer to cooperate.

Coevolution of multi-game resolves social dilemma in network population

It is an open question to understand the emergence and maintenance of cooperation in nature and society. Aim to this issue, evolutionary game theory in networked population and its various derivations, like mixing game and multi-game, have proved an effective way to resolve the social dilemma. In this work, we propose the coevolution framework of strategy and multi-game: if a player, in prisoner's dilemma game, successively keeps its strategy constant for several times (referred as memory step), it will have opportunity to participate in snow drift game, which has lower dilemma strength than prisoner's dilemma game. Of particular, it is unveiled that for short memory step, the larger the value of sucker's payoff is, the higher frequency of cooperation will be. While for long memory step, middle sucker's payoff provides a best environment for cooperation. For all these findings, we also provide theoretical analysis, which guarantees further validation.

Multigames with voluntary participation on interdependent networks and the evolution of cooperation

Multigames with voluntary participation and interdependent networks could facilitate cooperation from different perspectives. Motivated by the two mechanisms, we attempt to perform multigames voluntarily on interdependent networks and investigate the evolution of cooperation. In our work, the sucker's payoff could randomly split population on both networks into two types to play the Prisoner's Dilemma and Snowdrift respectively. Meanwhile, there are three strategies - cooperation, defection and going it alone - to choose. We show that the cooperation on both networks can be improved by the diversity of sucker's payoff and bias in the utility function for the smaller values of temptation to defect. Moreover, with the increasing of magnitude of sucker's payoff within a certain range, more cooperators emerge on both networks arising from spatial distribution of strategies. And a stronger bias in the utility function could promote cooperation on the main network, which is because of the fantastic network reciprocity caused by bias in the utility function. Besides, more players playing SD on one network is able to improve the cooperation on this network regardless of which type game to choose for players on the other network.

The evolution of cooperation in spatial multigame with voluntary participation

In the real life, we often simultaneously encounter various social dilemmas, which are also inclined to be voluntarily participated in, instead of previous assumption's compulsory participation in. Accounting on this realistic scenario, we have introduced the mechanism that the individuals have access to different payoff matrices corresponding to different social dilemmas to participate in the multigame with three strategies to choose, including cooperation, defection, going it alone. Furthermore, we set a proportion ψ/2 of the population to play the Prisoner's Dilemma, a proportion ψ/2 of the population to play Snowdrift and a proportion 1−ψ of the population to play the weak Prisoner's Dilemma, which results in the fact that the mean payoff matrix returns to the basic weak PD. Though numerical simulations, we find that for the smaller temptation to defect, the cooperation can be enhanced by the diversity of the sucker's payoff in the multigame contrast to the basic case. In addition, when the contribution of sucker's payoff is larger or more players choose to play the Prisoner's Dilemma and Snowdrift, the cooperators become more dominated.

Different perceptions of social dilemmas: evolutionary multigames in structured populations.

Motivated by the fact that the same social dilemma can be perceived differently by different players, we here study evolutionary multigames in structured populations. While the core game is the weak prisoner's dilemma, a fraction of the population adopts either a positive or a negative value of the sucker's payoff, thus playing either the traditional prisoner's dilemma or the snowdrift game. We show that the higher the fraction of the population adopting a different payoff matrix the more the evolution of cooperation is promoted. The microscopic mechanism responsible for this outcome is unique to structured populations, and it is due to the payoff heterogeneity, which spontaneously introduces strong cooperative leaders that give rise to an asymmetric strategy imitation flow in favor of cooperation. We demonstrate that the reported evolutionary outcomes are robust against variations of the interaction network, and they also remain valid if players are allowed to vary which game they play over time. These results corroborate existing evidence in favor of heterogeneity-enhanced network reciprocity, and they reveal how different perceptions of social dilemmas may contribute to their resolution.

Ordering in spatial evolutionary games for pairwise collective strategy updates

Evolutionary 2×2 games are studied with players located on a square lattice. During the evolution the randomly chosen neighboring players try to maximize their collective income by adopting a random strategy pair with a probability dependent on the difference of their summed payoffs between the final and initial states assuming quenched strategies in their neighborhood. In the case of the anticoordination game this system behaves like an antiferromagnetic kinetic Ising model. Within a wide region of social dilemmas this dynamical rule supports the formation of similar spatial arrangement of the cooperators and defectors ensuring the optimum total payoff if the temptation to choose defection exceeds a threshold value dependent on the sucker's payoff. The comparison of the results with those achieved for pairwise imitation and myopic strategy updates has indicated the relevant advantage of pairwise collective strategy update in the maintenance of cooperation.

A systematic analysis of the N‐person chicken game

AbstractWe report computer simulation experiments based on our agent‐based simulation tool to model the multiperson Chicken dilemma game for the case when the agents are greedy simpletons who imitate the action of that of their neighbors who received the highest payoff for its previous action. The individual agents may cooperate with each other for the collective interest or may defect, i.e., pursue their selfish interests only. After a certain number of iterations the proportion of cooperators stabilizes to either a constant value or oscillates around such a value. The payoff (reward/penalty) functions are given as two straight lines: one for the cooperators and another for the defectors. The payoff curves are functions of the ratio of cooperators to the total number of agents. Even for linear payoff functions, we have four free parameters that determine the payoff functions that have the following properties: (1) Both payoff functions increase with the increasing number of cooperators. (2) In the region of low cooperation the cooperators have a higher reward than the defectors. (3) When the cooperation rate is high, there is a higher payoff for defecting behavior than for cooperating behavior. (4) As a consequence, the slope of the D function is greater than that of the C function and the two payoff functions intersect. (5) All agents receive a lower payoff if all defect than if all cooperate. We have investigated the behavior of the agents systematically. The results show that the solutions have predictable tendencies but they are nontrivial and quite irregular. The solutions show drastic changes in the parameter ranges 0.6 ≤ R ≤ 0.65 for all values of S and 0 ≤ S ≤ 0.2 when R &lt; 0.6 (R is the reward for mutual cooperation and S is the sucker's payoff to a lonely cooperator). © 2010 Wiley Periodicals, Inc. Complexity, 2010

Exploring the cooperative regimes in an agent-based model: indirect reciprocity vs. selfish incentives

The self-organization in cooperative regimes in a simple mean-field version of a model based on “selfish” agents which play the Prisoner's Dilemma (PD) game is studied. The agents have no memory and use strategies not based on direct reciprocity nor “tags”. Two variables are assigned to each agent k at time t, measuring its capital C( k; t) and its probability of cooperation p( k; t). At each time step t a pair of agents interact by playing the PD game. These two agents update their probability of cooperation p( k; t) as follows: they compare the profits they made in this interaction δC( k; t) with an estimator ε( k; t) and, if δC( k; t)⩾ ε( k; t), agent i increases its p( k; t) while if δC( k; t)< ε( k; t) the agent decreases p( k; t). The 4!=24 different cases produced by permuting the four Prisoner's Dilemma canonical payoffs 3, 0, 1, and 5—corresponding, respectively, to R (reward), S (sucker's payoff), T (temptation to defect) and P (punishment)—are analyzed. It turns out that for all these 24 possibilities, after a transient, the system self-organizes into a stationary state with average equilibrium probability of cooperation p ̄ ∞= constant>0 . Depending on the payoff matrix, there are different equilibrium states characterized by their average probability of cooperation and average equilibrium per capita income ( p ̄ ∞, δC ̄ ∞) .

Experiments with Social Traps IV

In a long sequence of iterated Prisoner's Dilemma played by a pair of subjects, "lock-in " effects are frequently observed both on the CC and on the DD outcome. That is, in the course of the sequence either CC or DD becomes predominant sometimes persisting to the end. A lock-in on CC can be explained by a deterrence effect: The subjects learn that defection to D, although immediately advantageous if the co-player continues with C, is likely to be followed by retaliation. A lock-in on DD can be explained by the inhibition of unilateral C (the "peace initiative"), which is associated with the sucker's payoff In the present experiment, subjects played repeated round robin sequences of Prisoner's Dilemma with other subjects in their experimental group. Prominent lock-in effects were observed when the subjects were informed on each play how their current co-players chose when paired with other subjects but not when no such information was given.

Axelrod's "The Evolution of Cooperation"

* Most economists who have studied the behavior of firms have at one time or another wrestled with such questions as: How is collusion among firms sustained? Why do firms sometimes maintain product quality, when cheating on quality would lower costs? and Why do customers sometimes stick with suppliers who do not offer the lowest price? In general, why do firms and individuals sometimes engage in behavior that is plainly unprofitable from a short-run point of view? How do these behaviors emerge, and what sustains them? To the economist's list of questions about cooperative behavior, Axelrod would add several more drawn from other disciplines: How did cooperation emerge between the fungi and algae that compose lichens, or between fig trees and fig wasps, or between certain small fishes and their potential predators, whose mouths the small fishes clean? How did the Live-and-Let-Live system-a system in which opposing German and Allied battalions in trench warfare avoided shooting seriously at each other between major battles-emerge in World War I? What lessons can be drawn from these examples that might be useful in promoting cooperation and reducing conflict among people and nations? Axelrod's approach to studying these questions is based on an analysis of the famous Prisoners' Dilemma game. In that game, each player has two strategies available, labelled Cooperate and Defect, or C and D for short. The payoffs to the players are summarized in Table 1. The first entry in each pair designates the payoff to the row player and the second the payoff to the column player. The letters used in the payoff table are mnemonics: R designates the reward for cooperation, T the temptation to defect, S the sucker's payoff, and P the punishment for mutual defection. It is assumed that T > R, P > S, and R > P. No matter what move one player makes, the other player does best for himself by defecting. Simple self-interest would lead both players to defect and garner a payoff of P. The dilemma is that the pair would be better off if they could agree to cooperate. It is also assumed that mutual cooperation is better for both players than alternating defection and cooperation, that is, T + S < 2R. The Prisoners' Dilemma game has been widely studied by economists, psychologists, game theorists, and others. From the game theorist's point of view the main facts are: (i) the unique Nash equilibrium of the game involves mutual defection, and (ii) cooperation can be supported as an equilibrium phenomenon if the game is repeated infinitely many times without too much discounting (Rubinstein, 1980), or if the game is repeated finitely many times but the players are uncertain about each other's motivation or strategies (Kreps, Milgrom, Roberts, and Wilson, 1982).