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

Mesoscopic structure conditions the emergence of cooperation on social networks

We study the evolutionary Prisoner's Dilemma on two social networks obtained from actual relational data. We find very different cooperation levels on each of them that can not be easily understood in terms of global statistical properties of both networks. We claim that the result can be understood at the mesoscopic scale, by studying the community structure of the networks. We explain the dependence of the cooperation level on the temptation parameter in terms of the internal structure of the communities and their interconnections. We then test our results on community-structured, specifically designed artificial networks, finding perfect agreement with the observations in the real networks. Our results support the conclusion that studies of evolutionary games on model networks and their interpretation in terms of global properties may not be sufficient to study specific, real social systems. In addition, the community perspective may be helpful to interpret the origin and behavior of existing networks as well as to design structures that show resilient cooperative behavior.Comment: Largely improved version, includes an artificial network model that fully confirms the explanation of the results in terms of inter- and intra-community structur

Critical dynamics in the evolution of stochastic strategies for the iterated Prisoner's Dilemma

The observed cooperation on the level of genes, cells, tissues, and individuals has been the object of intense study by evolutionary biologists, mainly because cooperation often flourishes in biological systems in apparent contradiction to the selfish goal of survival inherent in Darwinian evolution. In order to resolve this paradox, evolutionary game theory has focused on the Prisoner's Dilemma (PD), which incorporates the essence of this conflict. Here, we encode strategies for the iterated Prisoner's Dilemma (IPD) in terms of conditional probabilities that represent the response of decision pathways given previous plays. We find that if these stochastic strategies are encoded as genes that undergo Darwinian evolution, the environmental conditions that the strategies are adapting to determine the fixed point of the evolutionary trajectory, which could be either cooperation or defection. A transition between cooperative and defective attractors occurs as a function of different parameters such a mutation rate, replacement rate, and memory, all of which affect a player's ability to predict an opponent's behavior.Comment: 27 pages, including supplementary information. 5 figures, 4 suppl. figures. Version accepted for publication in PLoS Comp. Bio

Exhaled and nasal nitric oxide in laryngectomized patients

<p>Abstract</p> <p>Background</p> <p>Nitric oxide (NO) shows differing concentrations in lower and upper airways. Patients after total laryngectomy are the only individuals, in whom a complete separation of upper and lower airways is guaranteed. Thus the objective of our study was to assess exhaled and nasal NO in these patients.</p> <p>Methods</p> <p>Exhaled bronchial NO (FE_NO) and nasal nitric oxide (nNO) were measured in patients after total laryngectomy (n = 14) and healthy controls (n = 24). To assess lung function we additionally performed spirometry. Co-factors possibly influencing NO, such as smoking, infections, and atopy were excluded.</p> <p>Results</p> <p>There was a markedly (p < 0.001) lower FE_NOin patients after total laryngectomy (median (range): 4 (1-22) ppb) compared to healthy controls 21 (9-41) ppb). In contrast, nNO was comparable between groups (1368 <it>versus </it>1380 in controls) but showed higher variability in subjects after laryngectomy.</p> <p>Conclusions</p> <p>Our data suggest that either bronchial NO production in patients who underwent laryngectomy is very low, possibly due to alterations of the mucosa or oxidant production/inflammation, or that substantial contributions to FE_NOarise from the larynx, pharynx and mouth, raising FE_NOdespite velum closure. The data fit to those indicating a substantial contribution to FE_NOby the mouth in healthy subjects. The broader range of nNO values found in subjects after laryngectomy may indicate chronic alteration or oligo-symptomatic inflammation of nasal mucosa, as frequently found after total laryngectomy.</p

Resolution of the stochastic strategy spatial prisoner's dilemma by means of particle swarm optimization

We study the evolution of cooperation among selfish individuals in the stochastic strategy spatial prisoner's dilemma game. We equip players with the particle swarm optimization technique, and find that it may lead to highly cooperative states even if the temptations to defect are strong. The concept of particle swarm optimization was originally introduced within a simple model of social dynamics that can describe the formation of a swarm, i.e., analogous to a swarm of bees searching for a food source. Essentially, particle swarm optimization foresees changes in the velocity profile of each player, such that the best locations are targeted and eventually occupied. In our case, each player keeps track of the highest payoff attained within a local topological neighborhood and its individual highest payoff. Thus, players make use of their own memory that keeps score of the most profitable strategy in previous actions, as well as use of the knowledge gained by the swarm as a whole, to find the best available strategy for themselves and the society. Following extensive simulations of this setup, we find a significant increase in the level of cooperation for a wide range of parameters, and also a full resolution of the prisoner's dilemma. We also demonstrate extreme efficiency of the optimization algorithm when dealing with environments that strongly favor the proliferation of defection, which in turn suggests that swarming could be an important phenomenon by means of which cooperation can be sustained even under highly unfavorable conditions. We thus present an alternative way of understanding the evolution of cooperative behavior and its ubiquitous presence in nature, and we hope that this study will be inspirational for future efforts aimed in this direction.Comment: 12 pages, 4 figures; accepted for publication in PLoS ON

Evolutionary Games with Affine Fitness Functions: Applications to Cancer

We analyze the dynamics of evolutionary games in which fitness is defined as an affine function of the expected payoff and a constant contribution. The resulting inhomogeneous replicator equation has an homogeneous equivalent with modified payoffs. The affine terms also influence the stochastic dynamics of a two-strategy Moran model of a finite population. We then apply the affine fitness function in a model for tumor-normal cell interactions to determine which are the most successful tumor strategies. In order to analyze the dynamics of concurrent strategies within a tumor population, we extend the model to a three-strategy game involving distinct tumor cell types as well as normal cells. In this model, interaction with normal cells, in combination with an increased constant fitness, is the most effective way of establishing a population of tumor cells in normal tissue.Comment: The final publication is available at http://www.springerlink.com, http://dx.doi.org/10.1007/s13235-011-0029-

Apology and forgiveness evolve to resolve failures in cooperative agreements

Making agreements on how to behave has been shown to be an evolutionarily viable strategy in one-shot social dilemmas. However, in many situations agreements aim to establish long-term mutually beneficial interactions. Our analytical and numerical results reveal for the first time under which conditions revenge, apology and forgiveness can evolve and deal with mistakes within ongoing agreements in the context of the Iterated Prisoners Dilemma. We show that, when the agreement fails, participants prefer to take revenge by defecting in the subsisting encounters. Incorporating costly apology and forgiveness reveals that, even when mistakes are frequent, there exists a sincerity threshold for which mistakes will not lead to the destruction of the agreement, inducing even higher levels of cooperation. In short, even when to err is human, revenge, apology and forgiveness are evolutionarily viable strategies which play an important role in inducing cooperation in repeated dilemmas.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Incipient Cognition Solves the Spatial Reciprocity Conundrum of Cooperation

Background: From the simplest living organisms to human societies, cooperation among individuals emerges as a paradox difficult to explain and describe mathematically, although very often observed in reality. Evolutionary game theory offers an excellent toolbar to investigate this issue. Spatial structure has been one of the first mechanisms promoting cooperation; however, alone it only opens a narrow window of viability. Methodology/Principal Findings: Here we equip individuals with incipient cognitive abilities, and investigate the evolution of cooperation in a spatial world where retaliation, forgiveness, treason and mutualism may coexist, as individuals engage in Prisoner’s Dilemma games. In the model, individuals are able to distinguish their partners and act towards them based on previous interactions. We show how the simplest level of cognition, alone, can lead to the emergence of cooperation. Conclusions/Significance: Despite the incipient nature of the individuals ’ cognitive abilities, cooperation emerges for unprecedented values of the temptation to cheat, being also robust to invasion by cheaters, errors in decision making an

Exhaled nitric oxide: Independent effects of atopy, smoking, respiratory tract infection, gender and height

SummaryMeasurement of exhaled nitric oxide is widely used in respiratory research and clinical practice, especially in patients with asthma. However, interpretation is often difficult, due to common interfering factors, and little is known about interactions between factors. We assessed the influences and interactions of factors such as smoking, respiratory tract infections and respiratory allergy concerning exhaled nitric oxide values, with the aim to derive a scheme for adjustment. We studied 897 subjects (514 females, 383 males; mean age±standard deviation 34.5±13.0 years) with and without respiratory allergy (allergic rhinitis and/or asthma), smoking and respiratory tract infection. Logarithmic nitric oxide levels were described by an additive model comprising respiratory allergy, smoking, respiratory tract infection, gender and height (p⩽0.001 each), without significant interaction terms. Geometric mean was 17.5ppb in a healthy female non smoker of height 170cm, whereby respiratory allergy corresponded to a change by factor 1.50, smoking 0.63, infection 1.24, male gender 1.17, and each 10cm increase (decrease) in height to 1.11 (0.90). Factors were virtually identical when excluding asthma and using the category allergic rhinitis instead of respiratory allergy (n=863). Within each category formed by combinations of these different predictors, the range of residual variation was approximately constant. We conclude that the factors influencing exhaled nitric oxide, which we analyzed, act independently of each other. Thus, circumstances such as smoking and respiratory tract infection do not appear to affect the usefulness of exhaled nitric oxide, provided that appropriate factors for adjustment are applied