Coveting thy neighbors fitness as a means to resolve social dilemmas

In spatial evolutionary games the fitness of each individual is traditionally determined by the payoffs it obtains upon playing the game with its neighbors. Since defection yields the highest individual benefits, the outlook for cooperators is gloomy. While network reciprocity promotes collaborative efforts, chances of averting the impending social decline are slim if the temptation to defect is strong. It is, therefore, of interest to identify viable mechanisms that provide additional support for the evolution of cooperation. Inspired by the fact that the environment may be just as important as inheritance for individual development, we introduce a simple switch that allows a player to either keep its original payoff or use the average payoff of all its neighbors. Depending on which payoff is higher, the influence of either option can be tuned by means of a single parameter. We show that, in general, taking into account the environment promotes cooperation. Yet coveting the fitness of one's neighbors too strongly is not optimal. In fact, cooperation thrives best only if the influence of payoffs obtained in the traditional way is equal to that of the average payoff of the neighborhood. We present results for the prisoner's dilemma and the snowdrift game, for different levels of uncertainty governing the strategy adoption process, and for different neighborhood sizes. Our approach outlines a viable route to increased levels of cooperative behavior in structured populations, but one that requires a thoughtful implementation.     

Chimpanzees coordinate in a negotiation game

A crucially important aspect of human cooperation is the ability to negotiate to cooperative outcomes when interests over resources conflict. Although chimpanzees and other social species may negotiate conflicting interests regarding travel direction or activity timing, very little is known about their ability to negotiate conflicting preferences over food. In the current study, we presented pairs of chimpanzees with a choice between two cooperative tasks—one with equal payoffs (e.g., 5-5) and one with unequal payoffs (higher and lower than in the equal option, e.g., 10-1). This created a conflict of interests between partners with failure to work together on the same cooperative task resulting in no payoff for either partner. The chimpanzee pairs cooperated successfully in as many as 78–94% of the trials across experiments. Even though dominant chimpanzees preferred the unequal option (as they would obtain the largest payoff), subordinate chimpanzees were able to get their way (the equal option) in 22–56% of trials across conditions. Various analyses showed that subjects were both strategic and also cognizant of the strategies used by their partners. These results demonstrate that one of our two closest primate relatives, the chimpanzee, can settle conflicts of interest over resources in mutually satisfying ways—even without the social norms of equity, planned strategies of reciprocity, and the complex communication characteristic of human negotiation.     

Optimal Cooperation-Trap Strategies for the Iterated Rock-Paper-Scissors Game

In an iterated non-cooperative game, if all the players act to maximize their individual accumulated payoff, the system as a whole usually converges to a Nash equilibrium that poorly benefits any player. Here we show that such an undesirable destiny is avoidable in an iterated Rock-Paper-Scissors (RPS) game involving two rational players, X and Y. Player X has the option of proactively adopting a cooperation-trap strategy, which enforces complete cooperation from the rational player Y and leads to a highly beneficial and maximally fair situation to both players. That maximal degree of cooperation is achievable in such a competitive system with cyclic dominance of actions may stimulate further theoretical and empirical studies on how to resolve conflicts and enhance cooperation in human societies.     

Temporal discounting predicts risk sensitivity in rhesus macaques

Humans and animals tend both to avoid uncertainty and to prefer immediate over future rewards. The comorbidity of psychiatric disorders such as impulsivity, problem gambling, and addiction suggests that a common mechanism may underlie risk sensitivity and temporal discounting. Nonetheless, the precise relationship between these two traits remains largely unknown. To examine whether risk sensitivity and temporal discounting reflect a common process, we recorded choices made by two rhesus macaques in a visual gambling task while we varied the delay between trials. We found that preference for the risky option declined with increasing delay between sequential choices in the task, even when all other task parameters were held constant. These results were quantitatively predicted by a model that assumed that the subjective expected utility of the risky option is evaluated based on the expected time of the larger payoff. The importance of the larger payoff in this model suggests that the salience of larger payoffs played a critical role in determining the value of risky options. These data suggest that risk sensitivity may be a product of other cognitive processes, and specifically that myopia for the future and the salience of jackpots control the propensity to take a gamble.     

How wealth accumulation can promote cooperation

Explaining the emergence and stability of cooperation has been a central challenge in biology, economics and sociology. Unfortunately, the mechanisms known to promote it either require elaborate strategies or hold only under restrictive conditions. Here, we report the emergence, survival, and frequent domination of cooperation in a world characterized by selfishness and a strong temptation to defect, when individuals can accumulate wealth. In particular, we study games with local adaptation such as the prisoner's dilemma, to which we add heterogeneity in payoffs. In our model, agents accumulate wealth and invest some of it in their interactions. The larger the investment, the more can potentially be gained or lost, so that present gains affect future payoffs. We find that cooperation survives for a far wider range of parameters than without wealth accumulation and, even more strikingly, that it often dominates defection. This is in stark contrast to the traditional evolutionary prisoner's dilemma in particular, in which cooperation rarely survives and almost never thrives. With the inequality we introduce, on the contrary, cooperators do better than defectors, even without any strategic behavior or exogenously imposed strategies. These results have important consequences for our understanding of the type of social and economic arrangements that are optimal and efficient.     

Evolutionary games on networks and payoff invariance under replicator dynamics

The commonly used accumulated payoff scheme is not invariant with respect to shifts of payoff values when applied locally in degree-inhomogeneous population structures. We propose a suitably modified payoff scheme and we show both formally and by numerical simulation, that it leaves the replicator dynamics invariant with respect to affine transformations of the game payoff matrix. We then show empirically that, using the modified payoff scheme, an interesting amount of cooperation can be reached in three paradigmatic non-cooperative two-person games in populations that are structured according to graphs that have a marked degree inhomogeneity, similar to actual graphs found in society. The three games are the Prisoner’s Dilemma, the Hawks-Doves and the Stag-Hunt. This confirms previous important observations that, under certain conditions, cooperation may emerge in such network-structured populations, even though standard replicator dynamics for mixing populations prescribes equilibria in which cooperation is totally absent in the Prisoner’s Dilemma, and it is less widespread in the other two games.     

Women Tend to Defect in a Social Dilemma Game in Southwest China

Cooperation theories assume that interacting individuals can change their strategies under different expected payoffs, depending on their social status or social situations. When looking at sex differences in cooperation, the existing studies have found that the genders cooperate at similar frequencies. However, the majority of the data originate within Western human societies. In this paper, we explore whether there are gender differences in cooperation in China. An Iterated Prisoner’s Dilemma game with a punishment option was used to gather data about Southwest Chinese subjects in a culture in which men have a hierarchical advantage over women. Results indicate that men invested into partners significantly more than women did (34% ♂ vs. 24% ♀) while women, in turn, were more likely to defect (65% ♀ vs. 50% ♂). In this region, women have customarily held less economic power and they are used to obtain a payoff typically lower than men. We suggest that the women’s willingness to invest in cooperation has decreased throughout evolutionary time, providing us with an illustration of a culturally-driven shift towards a disparity in gender cooperation interests.     

The evolution of payoff matrices: providing incentives to cooperate

Most of the work in evolutionary game theory starts with a model of a social situation that gives rise to a particular payoff matrix and analyses how behaviour evolves through natural selection. Here, we invert this approach and ask, given a model of how individuals behave, how the payoff matrix will evolve through natural selection. In particular, we ask whether a prisoner's dilemma game is stable against invasions by mutant genotypes that alter the payoffs. To answer this question, we develop a two-tiered framework with goal-oriented dynamics at the behavioural time scale and a diploid population genetic model at the evolutionary time scale. Our results are two-fold: first, we show that the prisoner's dilemma is subject to invasions by mutants that provide incentives for cooperation to their partners, and that the resulting game is a coordination game similar to the hawk-dove game. Second, we find that for a large class of mutants and symmetric games, a stable genetic polymorphism will exist in the locus determining the payoff matrix, resulting in a complex pattern of behavioural diversity in the population. Our results highlight the importance of considering the evolution of payoff matrices to understand the evolution of animal social systems.     

Adaptive Dynamics of Extortion and Compliance

Direct reciprocity is a mechanism for the evolution of cooperation. For the iterated prisoner’s dilemma, a new class of strategies has recently been described, the so-called zero-determinant strategies. Using such a strategy, a player can unilaterally enforce a linear relationship between his own payoff and the co-player’s payoff. In particular the player may act in such a way that it becomes optimal for the co-player to cooperate unconditionally. In this way, a player can manipulate and extort his co-player, thereby ensuring that the own payoff never falls below the co-player’s payoff. However, using a compliant strategy instead, a player can also ensure that his own payoff never exceeds the co-player’s payoff. Here, we use adaptive dynamics to study when evolution leads to extortion and when it leads to compliance. We find a remarkable cyclic dynamics: in sufficiently large populations, extortioners play a transient role, helping the population to move from selfish strategies to compliance. Compliant strategies, however, can be subverted by altruists, which in turn give rise to selfish strategies. Whether cooperative strategies are favored in the long run critically depends on the size of the population; we show that cooperation is most abundant in large populations, in which case average payoffs approach the social optimum. Our results are not restricted to the case of the prisoners dilemma, but can be extended to other social dilemmas, such as the snowdrift game. Iterated social dilemmas in large populations do not lead to the evolution of strategies that aim to dominate their co-player. Instead, generosity succeeds.     

Natural selection and social preferences

A large number of individuals are randomly matched into groups, where each group plays a finite symmetric game. Individuals breed true. The expected number of surviving offspring depends on own material payoff, but may also, due to cooperative breeding and/or reproductive competition, depend on the material payoffs to other group members. The induced population dynamic is equivalent with the replicator dynamic for a game with payoffs derived from those in the original game. We apply this selection dynamic to a number of examples, including prisoners' dilemma games with and without a punishment option, coordination games, and hawk-dove games. For each of these, we compare the outcomes with those obtained under the standard replicator dynamic. By way of a revealed-preference argument, our selection dynamic can explain certain "altruistic" and "spiteful" behaviors that are consistent with individuals having social preferences.     

Asymmetric interaction will facilitate the evolution of cooperation

Explaining the evolution of cooperation remains one of the greatest problems for both biology and social science. The classical theories of cooperation suggest that cooperation equilibrium or evolutionary stable strategy between partners can be maintained through genetic similarity or reciprocity relatedness. These classical theories are based on an assumption that partners interact symmetrically with equal payoffs in a game of cooperation interaction. However, the payoff between partners is usually not equal and therefore they often interact asymmetrically in real cooperative systems. With the Hawk-Dove model, we find that the probability of cooperation between cooperative partners will depend closely on the payoff ratio. The higher the payoff ratio between recipients and cooperative actors, the greater will be the probability of cooperation interaction between involved partners. The greatest probability of conflict between cooperative partners will occur when the payoff between partners is equal. The results show that this asymmetric relationship is one of the key dynamics of the evolution of cooperation, and that pure cooperation strategy (i.e., Nash equilibrium) does not exist in asymmetrical cooperation systems, which well explains the direct conflict observed in almost all of the well documented cooperation systems. The model developed here shows that the cost-to-benefit ratio of cooperation is also negatively correlated with the probability of cooperation interaction. A smaller cost-to-benefit ratio of cooperation might be created by the limited dispersal ability or exit cost of the partners involved, and it will make the punishment of the non-cooperative individuals by the recipient more credible, and therefore make it more possible to maintain stable cooperation interaction.     

How Feeling Betrayed Affects Cooperation

For a population of interacting self-interested agents, we study how the average cooperation level is affected by some individuals'' feelings of being betrayed and guilt. We quantify these feelings as adjusted payoffs in asymmetric games, where for different emotions, the payoff matrix takes the structure of that of either a prisoner''s dilemma or a snowdrift game. Then we analyze the evolution of cooperation in a well-mixed population of agents, each of whom is associated with such a payoff matrix. At each time-step, an agent is randomly chosen from the population to update her strategy based on the myopic best-response update rule. According to the simulations, decreasing the feeling of being betrayed in a portion of agents does not necessarily increase the level of cooperation in the population. However, this resistance of the population against low-betrayal-level agents is effective only up to some extend that is explicitly determined by the payoff matrices and the number of agents associated with these matrices. Two other models are also considered where the betrayal factor of an agent fluctuates as a function of the number of cooperators and defectors that she encounters. Unstable behaviors are observed for the level of cooperation in these cases; however, we show that one can tune the parameters in the function to make the whole population become cooperative or defective.     

The continuous prisoner's dilemma: I. linear reactive strategies.

We present a general model for the Prisoner's Dilemma in which variable degrees of cooperation are possible, and payoffs are scaled accordingly. We describe a continuous strategy space, and divide this space into strategy families. We derive the payoff function for these families analytically, and study the evolutionary outcome when a wide range of strategies play against each other. Our results show that the initial degree of cooperation offered by a strategy is a decisive factor for evolutionary robustness: the most successful strategies in our model offer full cooperation as an initial move, but thereafter cooperate fully only if their opponent does the same. These strategies gradually raise the stakes when playing a strategy which is initially reticent to cooperate, but differ from the strategies predicted by other continuous models in that they are not only generous, but are also consistently optimistic and uncompromising.     

Stochastic sampling of interaction partners versus deterministic payoff assignment

Evolutionary game dynamics describes how successful strategies spread in a population. In well-mixed populations, the usual assumption, e.g. underlying the replicator dynamics, is that individuals obtain a payoff from interactions with a representative sample of the population. This determines their fitness. Here, we analyze a situation in which payoffs are obtained through a single interaction, so that individuals of the same type can have different payoffs. We show analytically that for weak selection, this scenario is identical to the usual approach in which an individual interacts with the whole population. For strong selection, however, differences arise that are reflected in the fixation probabilities and lead to deviating evolutionary dynamics.     

Pollen dispersal in spatially aggregated populations

We perform a theoretical study of effective pollen dispersal within plant populations exhibiting intraspecific spatial aggregation. We simulate nonuniform distributions of individuals by means of a Poisson cluster process and use an individual-based spatially explicit model of pollen dispersal to assess the effects of different aggregation patterns on the effective pollen pool size (N(ep)) and the axial variance of pollen dispersal (sigma (p)). Results show clear interactions between clumping and both N(ep) and sigma (p), whose precise form and intensity depend on the relative spatial scale of aggregation to pollen dispersal range. If clump size is small relative to dispersal range, clumping results in lower N(ep) and sigma (p) than in randomly distributed populations. Interestingly, by contrast, aggregation may actually enlarge N(ep) and has minimum impact on sigma (p) if clump size is near or above the scale of dispersal. High intraclump to global density ratios enhance the sensitivity of both N(ep) and sigma (p) to clumping, while leptokurtic pollen dispersal generates sharper reductions of both N(ep) and sigma (p) for small clump sizes and stronger increments of N(ep) for larger clump sizes. Overall, our results indicate that isolation-by-distance models in plants should not ignore the effects of intraspecific spatial aggregation on effective dispersal.     

Inhibition of Fibrinogen Reaction by Polysaccharide of Encapsulated Staphylococcus aureus

Encapsulated and nonencapsulated strains of Staphylococcus aureus which lack coagulase or clumping factor (bound coagulase), or both, were examined for the antigen associated with the fibrinogen-cell clumping reaction. Extracts of the cells were tested for the ability to react with fibrinogen or to inhibit fibrinogen precipitation. Antisera prepared against encapsulated (coagulase-positive, clumping factor-negative) variants, as well as against nonencapsulated wild-type (coagulase-positive, clumping factor-positive) S. aureus strains, contained high titers of clumping-inhibiting antibody. When coagulase-negative, clumping factor-negative mutants were the immunizing agents, antisera contained no demonstrable clumping-inhibiting antibody. Phenol extracts of all coagulase-positive strains tested precipitated fibrinogen, regardless of the ability of cells to clump in the presence of fibrinogen. Polysaccharide extracts of encapsulated, clumping factor-negative strains inhibited this fibrinogen-precipitating activity, whereas similar extracts of nonencapsulated staphylococci did not inhibit the fibrinogen reaction. From these results, it appeared that the coagulase-positive, encapsulated staphylococci which do not clump in fibrinogen solution possess clumping factor, but that their capsular polysaccharide inhibits clumping activity. These findings suggested a closer association of clumping factor and coagulase than is now recognized.     

Cooperation,clumping and the evolution of multicellularity

The evolution of multicellular organisms represents one of the major evolutionary transitions in the history of life. A potential advantage of forming multicellular clumps is that it provides an efficiency benefit to pre-existing cooperation, such as the production of extracellular ‘public goods’. However, this is complicated by the fact that cooperation could jointly evolve with clumping, and clumping could have multiple consequences for the evolution of cooperation. We model the evolution of clumping and a cooperative public good, showing that (i) when considered separately, both clumping and public goods production gradually increase with increasing genetic relatedness; (ii) in contrast, when the traits evolve jointly, a small increase in relatedness can lead to a major shift in evolutionary outcome—from a non-clumping state with low public goods production to a cooperative clumping state with high values of both traits; (iii) high relatedness makes it easier to get to the cooperative clumping state and (iv) clumping can be inhibited when it increases the number of cells that the benefits of cooperation must be shared with, but promoted when it increases relatedness between those cells. Overall, our results suggest that public goods sharing can facilitate the formation of well-integrated cooperative clumps as a first step in the evolution of multicellularity.     

Statistical fluctuations in population bargaining in the ultimatum game: Static and evolutionary aspects

We explore the emergent behavior in heterogeneous populations where players negotiate via an ultimatum game: two players are offered a gift, one of them (the proposer) suggests how to divide the offer while the other player (the responder) can either accept or reject the deal. Rejection is detrimental to both players as it results in no earnings. In this context, our contribution is twofold: (i) we consider a population where the distribution of used strategies is constant over time and properties of the random payoff received by the players (average and higher moments) are reported from simple exact methods and corroborated by computer simulations; (ii) the evolution of a population is analyzed via Monte Carlo simulations where agents may change independently the proposing and accepting parameters of their strategy depending on received payoffs. Our results show that evolution leads to a stationary state in which wealth (accumulated payoff) is fairly distributed. As time evolves, an increase in average payoff and a simultaneous variance decrease is observed when we use a dynamics based on a probabilistic version of the saying: “One should not comply with small earnings, but one's greed must be limited.”     

Posterior cingulate cortex mediates outcome-contingent allocation of behavior

Adaptive decision making requires selecting an action and then monitoring its consequences to improve future decisions. The neuronal mechanisms supporting action evaluation and subsequent behavioral modification, however, remain poorly understood. To investigate the contribution of posterior cingulate cortex (CGp) to these processes, we recorded activity of single neurons in monkeys performing a gambling task in which the reward outcome of each choice strongly influenced subsequent choices. We found that CGp neurons signaled reward outcomes in a nonlinear fashion and that outcome-contingent modulations in firing rate persisted into subsequent trials. Moreover, firing rate on any one trial predicted switching to the alternative option on the next trial. Finally, microstimulation in CGp following risky choices promoted a preference reversal for the safe option on the following trial. Collectively, these results demonstrate that CGp directly contributes to the evaluative processes that support dynamic changes in decision making in volatile environments.     

Does evolution lead to maximizing behavior?

A long‐standing question in biology and economics is whether individual organisms evolve to behave as if they were striving to maximize some goal function. We here formalize this “as if” question in a patch‐structured population in which individuals obtain material payoffs from (perhaps very complex multimove) social interactions. These material payoffs determine personal fitness and, ultimately, invasion fitness. We ask whether individuals in uninvadable population states will appear to be maximizing conventional goal functions (with population‐structure coefficients exogenous to the individual's behavior), when what is really being maximized is invasion fitness at the genetic level. We reach two broad conclusions. First, no simple and general individual‐centered goal function emerges from the analysis. This stems from the fact that invasion fitness is a gene‐centered multigenerational measure of evolutionary success. Second, when selection is weak, all multigenerational effects of selection can be summarized in a neutral type‐distribution quantifying identity‐by‐descent between individuals within patches. Individuals then behave as if they were striving to maximize a weighted sum of material payoffs (own and others). At an uninvadable state it is as if individuals would freely choose their actions and play a Nash equilibrium of a game with a goal function that combines self‐interest (own material payoff), group interest (group material payoff if everyone does the same), and local rivalry (material payoff differences).