Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything

Zero Determinant (ZD) strategies are a new class of probabilistic and conditional strategies that are able to unilaterally set the expected payoff of an opponent in iterated plays of the Prisoner's Dilemma irrespective of the opponent's strategy, or else to set the ratio between a ZD player's and their opponent's expected payoff. Here we show that while ZD strategies are weakly dominant, they are not evolutionarily stable and will instead evolve into less coercive strategies. We show that ZD strategies with an informational advantage over other players that allows them to recognize other ZD strategies can be evolutionarily stable (and able to exploit other players). However, such an advantage is bound to be short-lived as opposing strategies evolve to counteract the recognition.Comment: 14 pages, 4 figures. Change in title (again!) to comply with Nature Communications requirements. To appear in Nature Communication

Lightweight Interactions for Reciprocal Cooperation in a Social Network Game

The construction of reciprocal relationships requires cooperative interactions during the initial meetings. However, cooperative behavior with strangers is risky because the strangers may be exploiters. In this study, we show that people increase the likelihood of cooperativeness of strangers by using lightweight non-risky interactions in risky situations based on the analysis of a social network game (SNG). They can construct reciprocal relationships in this manner. The interactions involve low-cost signaling because they are not generated at any cost to the senders and recipients. Theoretical studies show that low-cost signals are not guaranteed to be reliable because the low-cost signals from senders can lie at any time. However, people used low-cost signals to construct reciprocal relationships in an SNG, which suggests the existence of mechanisms for generating reliable, low-cost signals in human evolution.Comment: 13 pages, 2 figure

Generosity Pays in the Presence of Direct Reciprocity: A Comprehensive Study of 2×2 Repeated Games

By applying a technique previously developed to study ecosystem assembly [Capitán et al., Phys. Rev. Lett. 103, 168101 (2009)] we study the evolutionary stable strategies of iterated 22 games. We focus on memory-one strategies, whose probability to play a given action depends on the actions of both players in the previous time step. We find the asymptotically stable populations resulting from all possible invasions of any known stable population. The results of this invasion process are interpreted as transitions between different populations that occur with a certain probability. Thus the whole process can be described as a Markov chain whose states are the different stable populations. With this approach we are able to study the whole space of symmetric 22 games, characterizing the most probable results of evolution for the different classes of games. Our analysis includes quasi-stationary mixed equilibria that are relevant as very long-lived metastable states and is compared to the predictions of a fixation probability analysis. We confirm earlier results on the success of the Pavlov strategy in a wide range of parameters for the iterated Prisoner's Dilemma, but find that as the temptation to defect grows there are many other possible successful strategies. Other regions of the diagram reflect the equilibria structure of the underlying one-shot game, albeit often some non-expected strategies arise as well. We thus provide a thorough analysis of iterated 22 games from which we are able to extract some general conclusions. Our most relevant finding is that a great deal of the payoff parameter range can still be understood by focusing on win-stay, lose-shift strategies, and that very ambitious ones, aspiring to obtaining always a high payoff, are never evolutionary stable

Transition from reciprocal cooperation to persistent behaviour in social dilemmas at the end of adolescence.

While human societies are extraordinarily cooperative in comparison with other social species, the question of why we cooperate with unrelated individuals remains open. Here we report results of a lab-in-the-field experiment with people of different ages in a social dilemma. We find that the average amount of cooperativeness is independent of age except for the elderly, who cooperate more, and a behavioural transition from reciprocal, but more volatile behaviour to more persistent actions towards the end of adolescence. Although all ages react to the cooperation received in the previous round, young teenagers mostly respond to what they see in their neighbourhood regardless of their previous actions. Decisions then become more predictable through midlife, when the act of cooperating or not is more likely to be repeated. Our results show that mechanisms such as reciprocity, which is based on reacting to previous actions, may promote cooperation in general, but its influence can be hindered by the fluctuating behaviour in the case of children

If players are sparse social dilemmas are too: Importance of percolation for evolution of cooperation

Spatial reciprocity is a well known tour de force of cooperation promotion. A thorough understanding of the effects of different population densities is therefore crucial. Here we study the evolution of cooperation in social dilemmas on different interaction graphs with a certain fraction of vacant nodes. We find that sparsity may favor the resolution of social dilemmas, especially if the population density is close to the percolation threshold of the underlying graph. Regardless of the type of the governing social dilemma as well as particularities of the interaction graph, we show that under pairwise imitation the percolation threshold is a universal indicator of how dense the occupancy ought to be for cooperation to be optimally promoted. We also demonstrate that myopic updating, due to the lack of efficient spread of information via imitation, renders the reported mechanism dysfunctional, which in turn further strengthens its foundations.Comment: 6 two-column pages, 5 figures; accepted for publication in Scientific Reports [related work available at http://arxiv.org/abs/1205.0541

Growth dynamics and the evolution of cooperation in microbial populations

Microbes providing public goods are widespread in nature despite running the risk of being exploited by free-riders. However, the precise ecological factors supporting cooperation are still puzzling. Following recent experiments, we consider the role of population growth and the repetitive fragmentation of populations into new colonies mimicking simple microbial life-cycles. Individual-based modeling reveals that demographic fluctuations, which lead to a large variance in the composition of colonies, promote cooperation. Biased by population dynamics these fluctuations result in two qualitatively distinct regimes of robust cooperation under repetitive fragmentation into groups. First, if the level of cooperation exceeds a threshold, cooperators will take over the whole population. Second, cooperators can also emerge from a single mutant leading to a robust coexistence between cooperators and free-riders. We find frequency and size of population bottlenecks, and growth dynamics to be the major ecological factors determining the regimes and thereby the evolutionary pathway towards cooperation.Comment: 26 pages, 6 figure

Cooperation and Contagion in Web-Based, Networked Public Goods Experiments

A longstanding idea in the literature on human cooperation is that cooperation should be reinforced when conditional cooperators are more likely to interact. In the context of social networks, this idea implies that cooperation should fare better in highly clustered networks such as cliques than in networks with low clustering such as random networks. To test this hypothesis, we conducted a series of web-based experiments, in which 24 individuals played a local public goods game arranged on one of five network topologies that varied between disconnected cliques and a random regular graph. In contrast with previous theoretical work, we found that network topology had no significant effect on average contributions. This result implies either that individuals are not conditional cooperators, or else that cooperation does not benefit from positive reinforcement between connected neighbors. We then tested both of these possibilities in two subsequent series of experiments in which artificial seed players were introduced, making either full or zero contributions. First, we found that although players did generally behave like conditional cooperators, they were as likely to decrease their contributions in response to low contributing neighbors as they were to increase their contributions in response to high contributing neighbors. Second, we found that positive effects of cooperation were contagious only to direct neighbors in the network. In total we report on 113 human subjects experiments, highlighting the speed, flexibility, and cost-effectiveness of web-based experiments over those conducted in physical labs

Evolution of cooperation without reciprocity

A long-standing problem in biological and social sciences is to understand the conditions required for the emergence and maintenance of cooperation in evolving populations. For many situations, kin selection(1) is an adequate explanation, although kin-recognition may still be a problem. Explanations of cooperation between non-kin include continuing interactions that provide a shadow of the future (that is, the expectation of an ongoing relationship) that can sustain reciprocity(2-4), possibly supported by mechanisms to bias interactions such as embedding the agents in a two-dimensional space(4-6) or other context-preserving networks(7). Another explanation, indirect reciprocity(8), applies when benevolence to one agent increases the chance of receiving help from others. Here we use computer simulations to show that cooperation can arise when agents donate to others who are sufficiently similar to themselves in some arbitrary characteristic. Such a characteristic, or 'tag', can be a marking, display, or other observable trait. Tag-based donation can lead to the emergence of cooperation among agents who have only rudimentary ability to detect environmental signals and, unlike models of direct(3,4) or indirect reciprocity(9,10), no memory of past encounters is required.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62686/1/414441a0.pd

Network Homophily and the Evolution of the Pay-It-Forward Reciprocity

The pay-it-forward reciprocity is a type of cooperative behavior that people who have benefited from others return favors to third parties other than the benefactors, thus pushing forward a cascade of kindness. The phenomenon of the pay-it-forward reciprocity is ubiquitous, yet how it evolves to be part of human sociality has not been fully understood. We develop an evolutionary dynamics model to investigate how network homophily influences the evolution of the pay-it-forward reciprocity. Manipulating the extent to which actors carrying the same behavioral trait are linked in networks, the computer simulation model shows that strong network homophily helps consolidate the adaptive advantage of cooperation, yet introducing some heterophily to the formation of network helps advance cooperation's scale further. Our model enriches the literature of inclusive fitness theory by demonstrating the conditions under which cooperation or reciprocity can be selected for in evolution when social interaction is not confined exclusively to relatives