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

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

Information transmission in oscillatory neural activity

Periodic neural activity not locked to the stimulus or to motor responses is usually ignored. Here, we present new tools for modeling and quantifying the information transmission based on periodic neural activity that occurs with quasi-random phase relative to the stimulus. We propose a model to reproduce characteristic features of oscillatory spike trains, such as histograms of inter-spike intervals and phase locking of spikes to an oscillatory influence. The proposed model is based on an inhomogeneous Gamma process governed by a density function that is a product of the usual stimulus-dependent rate and a quasi-periodic function. Further, we present an analysis method generalizing the direct method (Rieke et al, 1999; Brenner et al, 2000) to assess the information content in such data. We demonstrate these tools on recordings from relay cells in the lateral geniculate nucleus of the cat.Comment: 18 pages, 8 figures, to appear in Biological Cybernetic

Robot life: simulation and participation in the study of evolution and social behavior.

This paper explores the case of using robots to simulate evolution, in particular the case of Hamilton's Law. The uses of robots raises several questions that this paper seeks to address. The first concerns the role of the robots in biological research: do they simulate something (life, evolution, sociality) or do they participate in something? The second question concerns the physicality of the robots: what difference does embodiment make to the role of the robot in these experiments. Thirdly, how do life, embodiment and social behavior relate in contemporary biology and why is it possible for robots to illuminate this relation? These questions are provoked by a strange similarity that has not been noted before: between the problem of simulation in philosophy of science, and Deleuze's reading of Plato on the relationship of ideas, copies and simulacra