Continuous Prisoner Research Articles

Dynamic contact effects: Individuals' positive and negative contact history influences intergroup contact effects in a behavioral game.

Positive contact between members of different groups reduces prejudice and increases cooperation, findings known as intergroup contact effects. Yet in real-world settings not only positive, but also negative intergroup contact occurs, which have opposing effects. To date little is known about whether and how an individual's valenced history of intergroup contact influences contact effects and how this dynamic change happens during specific instances of intergroup contact. A pilot study examined the psychological impact of a novel paradigm to assess intergroup contact using a behavioral game. We then conducted two studies, which allowed us to observe a sequence of up to 23 in- and outgroup interactions and their behavioral outcomes in a continuous prisoner's dilemma behavioral game (N = 116, 2,668 interactions; N = 89, 1,513 interactions). As expected, participants showed a clear ingroup bias in expectations and cooperation. Furthermore, the quality of contact history moderated contact effects. Specifically, intergroup contact following a positive history of intergroup contact had a stronger effect on intergroup expectations than contact following a negative history thereof. Findings are discussed in view of the importance of considering the valenced history of intergroup contact, as well as new research questions on intergroup contact that can be addressed with this novel contact paradigm. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Modelling prejudice and its effect on societal prosperity

ABSTRACT Existing studies of the multi-group dynamics of prejudiced societies focus on the social-psychological knowledge behind the relevant processes. We instead create a multi-agent framework that simulates the propagation of prejudice and measures its tangible impact on prosperity. Levels of prosperity are tracked for individuals as well as larger social structures including groups and factions. We model social interactions using the Continuous Prisoner's Dilemma (CPD) and a new agent type called a prejudiced agent. Our simulations show that even modeling prejudice as an exclusively out-group phenomenon nonetheless generates implicit in-group promotion, leading to higher relative prosperity of a prejudiced population. This skew in prosperity is seen to be correlated to factors such as size difference between groups, and the fraction of prejudiced agents in a group. Our model is a step towards a deeper understanding of the origins, propagation, and ramifications of prejudice through simulative studies grounded in apt theoretical backgrounds.

The Power of Tolerance vs. Unselfishness as a Cultural Determinant of Cooperation.

Cooperation in collective action problems and resource dilemmas is often assumed to depend on the values of the individuals involved, such as their degree of unselfishness and tolerance. Societal differences in cooperation and cooperative norms may therefore result from cultural variation in emphasis on these personal values. Here we draw on several cross-national datasets to examine whether society-level emphasis on unselfishness and tolerance and respect for other people predict how societies vary in cooperation [in a continuous prisoner’s dilemma (PD)] and in norms governing cooperation [in a common pool resource dilemma (CPR)]. The results suggest that high levels of cooperation and cooperative norms are promoted specifically by a cultural emphasis on tolerance.

The power of joint decision-making in a finitely-repeated dilemma

A rich body of literature has proposed that pairs behave significantly differently from individuals due to a number of reasons such as group polarization. This paper experimentally compares cooperation behaviors between pairs and individuals in a finitely-repeated two-player public goods game (continuous prisoner’s dilemma game). We show that pairs contribute significantly more than individuals to their group accounts. Especially, when two pairs are matched with each other for the entire periods, they successfully build long-lasting cooperative relationships with their matched pairs. Our detailed analyses suggest that the enhanced cooperation behavior of pairs may be driven by (a) the mere fact that they have partners when they make decisions, (b) group polarization – those who initially prefer to contribute smaller amounts are more affected by the partners in their pairs, and (c) stronger conditional cooperation behavior of pairs to their matched pairs.

Power of Joint Decision-Making in a Finitely-Repeated Dilemma

A rich body of literature has proposed that pairs behave significantly differently from individuals due to a number of reasons such as group polarization. This paper experimentally compares cooperation behaviors between pairs and individuals in a finitely-repeated two-player public goods game (continuous prisoner’s dilemma game). We show that pairs contribute significantly more than individuals to their group accounts. Especially when two pairs are matched with each other for the entire periods, they successfully build long-lasting cooperative relationships with their matched pairs. Our detailed analyses suggest that the enhanced cooperation behavior of pairs may be driven by (a) the mere fact that they have partners as decision-making units when they make decisions, (b) group polarization – those who initially prefer to contribute smaller amounts are more affected by the partners in their pairs, and (c) stronger conditional cooperation behavior of pairs to their matched pairs.

The development of ingroup favoritism in repeated social dilemmas.

In two comprehensive and fully incentivized studies, we investigate the development of ingroup favoritism as one of two aspects of parochial altruism in repeated social dilemmas. Specifically, we test whether ingroup favoritism is a fixed phenomenon that can be observed from the very beginning and remains stable over time, or whether it develops (increases vs. decreases) during repeated contact. Ingroup favoritism is assessed through cooperation behavior in a repeated continuous prisoner's dilemma where participants sequentially interact with 10 members of the ingroup (own city and university) and subsequently with 10 members of the outgroup (other city and university), or vice versa. In none of the experiments do we observe initial differences in cooperation behavior for interaction partners from the ingroup, as compared to outgroup, and we only observe small differences in expectations regarding the interaction partners' cooperation behavior. After repeated interaction, however, including a change of groups, clear ingroup favoritism can be observed. Instead of being due to gradual and potentially biased updating of expectations, we found that these emerging differences were mainly driven by the change of interaction partners' group membership that occurred after round 10. This indicates that in social dilemma settings ingroup favoritism is to some degree dynamic in that it is enhanced and sometimes only observable if group membership is activated by thinking about both the interaction with the ingroup and the outgroup.

Learning Algorithm and the Cooperation Behavior of Continuous Prisoner's Dilemma Game on Complex Networks

The standard evolutionary Prisoner’s Dilemma Game (PDG), which is the most widely used model for investigating the evolution of cooperation, does not allow for changeable degrees of cooperation and the players can either cooperate or defect in each time. In this paper, we study Continuous Prisoner’s Dilemma Games (CPDG) on complex networks (or Spatial Continuous Prisoner’s Dilemma Games (SCPDG)); in which each agent locates on a vertex of the network and interacts with all his neighboring agents by making an investment. Each agent’s investment will benefit all its neighbors and incur a cost to the focus agent. The investment which can be varied continuously exhibits variable degrees of cooperation. The cooperative level of the group is characterized by the average investment of the population. Unlike the imitation of the best neighbors learning rule, the probability based imitation learning rule and the Moran process based learning rule that usually used in the standard evolutionary SPDG, we propose a new learning algorithm in the continuous condition. Three parameters to describe the imitation ability of the best neighbors, the memory length of the individual and uncertainty effect of the environment are introduced. We investigate the co-effect of these parameters on the cooperation level of the population on the Barabasi-Albert (BA) scale-free networks, the nearest-neighbor coupled networks and the Newman-Watts (NW) small-world networks. Our results may provide some new conclusion on the study of evolutionary games on networks.

Evolution of Cooperation in Continuous Prisoner's Dilemma Games on Barabasi—Albert Networks with Degree-Dependent Guilt Mechanism

This paper studies the continuous prisoner's dilemma games (CPDG) on Barabasi—Albert (BA) networks. In the model, each agent on a vertex of the networks makes an investment and interacts with all of his neighboring agents. Making an investment is costly, but which benefits its neighboring agents, where benefit and cost depend on the level of investment made. The payoff of each agent is given by the sum of payoffs it receives in its interactions with all its neighbors. Not only payoff, individual's guilty emotion in the games has also been considered. The negative guilty emotion produced in comparing with its neighbors can reduce the utility of individuals directly. We assume that the reduction amount depends on the individual's degree and a baseline level parameter. The group's cooperative level is characterized by the average investment of the population. Each player makes his investment in the next step based on a convex combination of the investment of his best neighbors in the last step, his best history strategies in the latest steps which number is controlled by a memory length parameter, and a uniformly distributed random number. Simulation results show that this degree-dependent guilt mechanism can promote the evolution of cooperation dramatically comparing with degree-independent guilt or no guilt cases. Imitation, memory, uncertainty coefficients and network structure also play determinant roles in the cooperation level of the population. All our results may shed some new light on studying the evolution of cooperation based on network reciprocity mechanisms.

Heterogeneity in the resistance to learning

In this paper we analyze the effect of heterogeneity in the recently introduced “resistance to learning” (Jimenez et al. in Eur Phys J B 71:273–280, 2009a). In the context of the spatial Continuous Prisoner’s Dilemma, the resistance to learning has become a key mechanism for the emergence and maintenance of cooperation in a wide range of cost regimes. We extend the model to the case in which different individuals may have different levels of resistance. From non-cooperative initial states, the existence of heterogeneity in the resistance affects the cooperative behavior of unconditional imitators. These unconditional imitators, i.e., fast learners or individuals without resistance can achieve due to their interactions with gradual learners significant levels of cooperation. Our results confirm in one of its form the impact of heterogeneity and its role as a fundamental mechanism in promoting the emergence of cooperation.

Punishment Leads to Cooperative Behavior in Structured Societies

Altruistic punishment occurs when an agent incurs a cost to punish another but receives no material benefit for doing so. Despite the seeming irrationality of such behavior, humans in laboratory settings routinely pay to punish others even in anonymous, one-shot settings. Costly punishment is ubiquitous among social organisms in general and is increasingly accepted as a mechanism for the evolution of cooperation. Yet if it is true that punishment explains cooperation, the evolution of altruistic punishment remains a mystery. In a series of computer simulations I give agents the ability to punish one another while playing a continuous prisoner's dilemma. In simulations without social structure, expected behavior evolves-agents do not punish and consequently no cooperation evolves. Likewise, in simulations with social structure but no ability to punish, no cooperation evolves. However, in simulations where agents are both embedded in a social structure and have the option to inflict costly punishment, cooperation evolves quite readily. This suggests a simple and broadly applicable explanation of cooperation for social organisms that have nonrandom social structure and a predisposition to punish one another. Results with scale-free networks further suggest that nodal degree distribution plays an important role in determining whether cooperation will evolve in a structured population.

Gradual learning and the evolution of cooperation in the spatial Continuous Prisoner’s Dilemma

The usual mechanism for modeling learning in spatially structured evolutionary games has to date been imitation of some successful neighbor. However, it seems natural that individuals hesitate to imitate their neighbor’s acts, specially if they can imply high costs. Here we study the effect of incorporating resistance to imitation on these models. Our framework is the spatial Continuous Prisoner’s Dilemma. For this evolutionary game, it has been reported that occasional errors in the imitation process can explain the emergence of cooperation from a non-cooperative initial state. In this work, we show that this only occurs for particular regimes of low costs of cooperation. Furthermore, we display how resistance gets greater the range of scenarios where cooperative individuals can invade selfish populations. In this context, where resistance to imitation can be interpreted as a general rule of gradual learning, our results show that the less that is learnt in a single step from a successful neighbors, the larger the degree of global cooperation finally attained. In general, the effect of step-by-step learning can be more efficient for the evolution of cooperation than a full blast one.

Dual lattice model of the evolution of facultative symbiosis with continuous Prisoner's Dilemma game

Mutualism is ubiquitous in nature and is thought to have played a key role in the history of life. However, how mutualism could evolve despite being prone to unilateral exploitation is a puzzling question in evolutionary ecology. Some theoretical studies have shown that spatial structure of habitat can facilitate the emergence and maintenance of mutualism. However, they are based on the simple assumption that the trait in question is discrete: each individual is either a mutualist or a non-mutualist. In this article I develop a simple simulation model of coevolution of facultative symbiosis using a one-shot continuous Prisoner's Dilemma game to investigate the evolutionary dynamics of mutualism between two species. In this model I assume continuous traits for both species from - 1 (fully deceptive) to 1 (fully cooperative). The habitat has a dual-lattice structure, each layer is inhabited by one species. Interspecific interaction is restricted between two corresponding sites of the two layers. Without limitation on the magnitude of a single mutation, I find that mutualism can arise and persist when the intrinsic reproduction rate is low (but is above a threshold) and the benefit/cost ratio of the cooperative strategy is large, which is consistent with Yamamura et al. [2004. Evolution of mutualism through spatial effects. J. Theor. Biol. 226, 421–428]. In these cases, extreme antagonism often evolves starting from a neutral population that seems nearly stable, but once mutualism arises, the cooperative individuals quickly increase and both the populations eventually become mutualistic on average, although they are polymorphic. However, when the effect of a single mutation was limited to be small, extreme antagonism is much likely to dominate unless the intrinsic reproduction rate is low. When only one species is allowed to evolve, mutualism arises when the initial strategy of the other species is cooperative. Otherwise, excessive deception evolves in the former, and the latter often becomes driven to extinction.

The iterated continuous prisoner's dilemma game cannot explain the evolution of interspecific mutualism in unstructured populations

The evolutionionary origin of inter- and intra-specific cooperation among non-related individuals has been a great challenge for biologists for decades. Recently, the continuous prisoner's dilemma game has been introduced to study this problem. In function of previous payoffs, individuals can change their cooperative investment iteratively in this model system. Killingback and Doebeli (Am. Nat. 160 (2002) 421–438) have shown analytically that intra-specific cooperation can emerge in this model system from originally non-cooperating individuals living in a non-structured population. However, it is also known from an earlier numerical work that inter-specific cooperation (mutualism) cannot evolve in a very similar model. The only difference here is that cooperation occurs among individuals of different species. Based on the model framework used by Killingback and Doebeli (2002), this Note proves analytically that mutualism indeed cannot emerge in this model system. Since numerical results have revealed that mutualism can evolve in this model system if individuals interact in a spatially structured manner, our work emphasizes indirectly the role of spatial structure of populations in the origin of mutualism.

Effects of neighbourhood size and connectivity on the spatial Continuous Prisoner's Dilemma

The Prisoner's Dilemma, a two-person game in which the players can either cooperate or defect, is a common paradigm for studying the evolution of cooperation. In real situations cooperation is almost never all or nothing. This observation is the motivation for the Continuous Prisoner's Dilemma, in which individuals exhibit variable degrees of cooperation. It is known that in the presence of spatial structure, when individuals “play against” (i.e. interact with) their neighbours, and “compare to” (“learn from”) them, cooperative investments can evolve to considerable levels. Here, we examine the effect of increasing the neighbourhood size: we find that the mean-field limit of no cooperation is reached for a critical neighbourhood size of about five neighbours on each side in a Moore neighbourhood, which does not depend on the size of the spatial lattice. We also find the related result that in a network of players, the critical average degree (number of neighbours) of nodes for which defection is the final state does not depend on network size, but only on the network topology. This critical average degree is considerably (about 10 times) higher for clustered (social) networks, than for distributed random networks. This result strengthens the argument that clustering is the mechanism which makes the development and maintenance of the cooperation possible. In the lattice topology, it is observed that when the neighbourhood sizes for “interacting” and “learning” differ by more than 0.5, cooperation is not sustainable, even for neighbourhood sizes that are below the mean-field limit of defection. We also study the evolution of neighbourhood sizes, as well as investment level. Here, we observe that the series of the interaction and learning neighbourhoods converge, and a final cooperative state with considerable levels of average investment is achieved.

The Continuous Prisoner’s Dilemma and the Evolution of Cooperation through Reciprocal Altruism with Variable Investment

Understanding the evolutionary origin and persistence of cooperative behavior is a fundamental biological problem. The standard "prisoner's dilemma," which is the most widely adopted framework for studying the evolution of cooperation through reciprocal altruism between unrelated individuals, does not allow for varying degrees of cooperation. Here we study the continuous iterated prisoner's dilemma, in which cooperative investments can vary continuously in each round. This game has been previously considered for a class of reactive strategies in which current investments are based on the partner's previous investment. In the standard iterated prisoner's dilemma, such strategies are inferior to strategies that take into account both players' previous moves, as is exemplified by the evolutionary dominance of "Pavlov" over "tit for tat." Consequently, we extend the analysis of the continuous prisoner's dilemma to a class of strategies in which current investments depend on previous payoffs and, hence, on both players' previous investments. We show, both analytically and by simulation, that payoff-based strategies, which embody the intuitively appealing idea that individuals invest more in cooperative interactions when they profit from these interactions, provide a natural explanation for the gradual evolution of cooperation from an initially noncooperative state and for the maintenance of cooperation thereafter.

The Continuous Prisoner's Dilemma and the Evolution of Cooperation through Reciprocal Altruism with Variable Investment

The Continuous Prisoner's Dilemma and the Evolution of Cooperation through Reciprocal Altruism with Variable Investment

On discrete dynamical systems associated to games

Dynamical systems corresponding to continuous strategy games are introduced. The steady of the systems corresponding to continuous prisoner's dilemma, hawk-dove and rock-scissors-paper games are found and their stability are discussed. A discrete imitation equation is derived. Smale's payoff memory game formulation is generalized.

The Continuous Prisoner's Dilemma: II. Linear Reactive Strategies with Noise

We present a general model for the Continuous Prisoner's Dilemma and study the effect of errors. We find that cooperative strategies that can resist invasion by defectors are optimistic (make high initial offers),generous (always offer more cooperation than the partner did in the previous round) and uncompromising (offer full cooperation only if the partner does). A necessary condition for the emergence of cooperation in the continuous Prisoner's Dilemma with noise is b (1−p)>c, where b and c denote, respectively, the benefit and cost of cooperation, while p is the error rate. This relation can be reformulated as an error threshold: cooperation can only emerge if the probability of making a mistake is below a critical value. We note, however, that cooperation in the continuous Prisoner's Dilemma with noise does not seem to be evolutionarily stable: while it is possible to find cooperative strategies that resist invasion by defectors, such cooperators are generally invaded by more cooperative strategies which eventually yield to defectors. Thus, the long-term evolution of the continuous Prisoner's Dilemma is either characterized by unending cycles or by stable polymorphisms of cooperators and defectors.

Variable investment, the Continuous Prisoner's Dilemma, and the origin of cooperation.

Cooperation is fundamental to many biological systems. A common metaphor for studying the evolution of cooperation is the Prisoner's Dilemma, a game with two strategies: cooperate or defect. However, cooperation is rare all or nothing, and its evolution probably involves the gradual extension of initially modest degrees of assistance. The inability of the Prisoner's Dilemma to capture this basic aspect limits its use for understanding the evolutionary origins of cooperation. Here we consider a framework for cooperation based on the concept of investment: an act which is costly, but which benefits other individuals, where the cost and benefit depend on the level of investment made. In the resulting Continuous Prisoner's Dilemma the essential problem of cooperation remains: in the absence of any additional structure non-zero levels of investment cannot evolve. However, if investments are considered in a spatially structured context, selfish individuals who make arbitrarily low investments can be invaded by higher-investing mutants. This results in the mean level of investment evolving to significant levels, where it is maintained indefinitely. This approach provides a natural solution to the fundamental problem of how cooperation gradually increases from a non-cooperative state.

Reproductive Sharing in Different Types of Kin Associations

Reproductive Sharing in Different Types of Kin Associations