The robustness of the "Raise-The-Stakes” strategy: Coping with exploitation in noisy Prisoner's Dilemma Games

Recent models of altruism point out the success of a strategy called 'Raise-The-Stakes' (RTS) in situations allowing variability in cooperation. In theory, RTS is difficult to exploit because it begins with a small investment in an iterated Prisoner's Dilemma Game (PDG). When its cooperation is reciprocated, RTS increases its generosity, thereby taking advantage of cooperative opportunities. Previous research has shown that human participants indeed adopt RTS but start out moderately cooperative rather than with a minimal investment. This raises the question how robust RTS is against exploitation, especially in a noisy situation. We investigate whether human participants vary their cooperation in interaction with reciprocators and cheaters in an iterated nondiscrete version of a PDG. When confronted with a strategy that matches the investment of the participant on the previous round, we find that participants are likely to increase cooperation. However, cooperation gradually breaks down in interaction with a strategy that undercuts the level of cooperation of the participants, indicating the robustness of RTS. In line with RTS modeling studies, but in contrast with the cheater detection literature, we find that human participants are less willing to increase cooperation when the perceived likelihood of mistakes increases.     

Why cooperation is not running away

A growing number of experimental and theoretical studies show the importance of partner choice as a mechanism to promote the evolution of cooperation, especially in humans. In this paper, we focus on the question of the precise quantitative level of cooperation that should evolve under this mechanism. When individuals compete to be chosen by others, their level of investment in cooperation evolves towards higher values, a process called competitive altruism, or runaway cooperation. Using a classic adaptive dynamics model, we first show that when the cost of changing partner is low, this runaway process can lead to a profitless escalation of cooperation. In the extreme, when partner choice is entirely frictionless, cooperation even increases up to a level where its cost entirely cancels out its benefit. That is, at evolutionary equilibrium, individuals gain the same payoff than if they had not cooperated at all. Second, importing models from matching theory in economics we, however, show that when individuals can plastically modulate their choosiness in function of their own cooperation level, partner choice stops being a runaway competition to outbid others and becomes a competition to form the most optimal partnerships. In this case, when the cost of changing partner tends towards zero, partner choice leads to the evolution of the socially optimum level of cooperation. This last result could explain the observation that human cooperation seems to be often constrained by considerations of social efficiency.     

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.     

Reputation-based partner choice is an effective alternative to indirect reciprocity in solving social dilemmas

When group interests clash with individual ones, maintaining cooperation poses a problem. However, cooperation can be facilitated by introducing reputational incentives. Through indirect reciprocity, people who cooperate in a social dilemma are more likely to receive cooperative acts from others. Another mechanism that enhances group cooperation is reputation-based partner choice, or competitive altruism. According to this framework, cooperators benefit via increased access to cooperative partners. Our study compared the effectiveness of indirect reciprocity and competitive altruism in re-establishing cooperation after the typical decline found during repeated public goods games. Twenty groups of four participants first played a series of public goods games, which confirmed the expected decline. Subsequently, public goods games were alternated with either indirect reciprocity games (in which participants had an opportunity to give to another individual from whom they would never receive a direct return) or competitive altruism games (in which they could choose partners for directly reciprocal interactions). We found that public goods game contributions increased when interspersed with competitive altruism games; they were also higher than in public goods games interspersed with indirect reciprocity games. Investing in reputation by increasing contributions to public goods was a profitable strategy in that it increased returns in subsequent competitive altruism and indirect reciprocity games. There was also some evidence that these returns were greater under competitive altruism than indirect reciprocity. Our findings indicate that strategic reputation building through competitive altruism provides an effective alternative to indirect reciprocity as a means for restoring cooperation in social dilemmas.     

A model of the interaction between 'good genes' and direct benefits in courtship-feeding animals: when do males of high genetic quality invest less?

Conflict between mates over the amount of parental investment by each partner is probably the rule except in rare cases of genetic monogamy. In systems with parental care, males may frequently benefit by providing smaller investments than are optimal for individual female partners. Females are therefore expected to choose males that will provide the largest amounts of parental investment. In some species, however, the preferred males provide less care than their rivals. Focusing on species in which males invest by feeding their mates, I use a simple model to demonstrate the conditions under which males preferred by females may have optimal donations that are smaller than those of less-preferred rivals. Pre-mating female choice may sufficiently bias the perception of mate availability of preferred males relative to their rivals such that preferred males gain by conserving resources for future matings. Similarly, 'cryptic' biases in favour of high-quality ejaculates by females can compensate for smaller than average donations received from preferred males. However, post-fertilization cryptic choice should not change the optimal donations of preferred males relative to their rivals. I discuss the implications of this work for understanding sexual selection in courtship-feeding animals, and the relevance of these systems to understanding patterns of investment for animals in general.     

The Evolution of Quantitatively Responsive Cooperative Trade

The iterated Prisoner's Dilemma reflects the essence of repeated cooperative interactions with selfish incentives. However, the classical form of this game assumes that individuals either cooperate or defect, whereas in practice different degrees of cooperation are usually possible. To overcome this limitation, we present a model of alternating cooperative trade in which individuals controlled the costs they incurred in benefiting their partners. Since the range of possible strategies is enormous, competitively successful solutions were identified using a genetic algorithm, a powerful search technique in which good performers are iteratively selected and recombined from an initial "strategy soup". Beginning with a population of asocial individuals, altruistic behaviour readily emerged. Like the pre-defined strategy of "Raise-the-Stakes", the emerging strategies evolved protection from cheats by investing relatively little in strangers and subsequently responding quantitatively to a partner's altruism. Unlike "Raise-the-Stakes", they began trading relations at intermediate levels and, when the benefit-to-cost ratio of cooperation was relatively low, mean investment was considerably below the maximum level. Our approach is novel in allowing us to predict not just whether cooperation will occur, but how cooperative individuals will be, in relation to factors such as the number of rounds and the cost effectiveness of cooperative trade.     

Male sexual attractiveness predicts differential ovulatory shifts in female extra-pair attraction and male mate retention

Because ancestral women faced trade-offs in choosing mates, they may have evolved to pursue a dual-mating strategy in which they secured investment through one partner and obtained good genes through others. The dual-mating theory predicts that women will display greater interest in extra-pair sex near ovulation, especially if they are mated to a primary male partner who is low in sexual attractiveness. Forty-three normally ovulating women rated their partner's sexual attractiveness and separately reported their own desires and their partner's mate retention behaviors at high and low fertility (confirmed using luteinizing hormone tests). In the high-fertility session relative to the low, women who assessed their partners as being lower in sexual attractiveness reported greater extra-pair desires and more expressed love and attention from their male partners. Women's desire for their own partners did not differ significantly between high and low-fertility sessions.     

Cooperators benefit through reputation-based partner choice in economic games

Explaining unconditional cooperation, such as donations to charities or contributions to public goods, continues to present a problem. One possibility is that cooperation can pay through developing a reputation that makes one more likely to be chosen for a profitable cooperative partnership, a process termed competitive altruism (CA) or reputation-based partner choice. Here, we show, to our knowledge, for the first time, that investing in a cooperative reputation can bring net benefits through access to more cooperative partners. Participants played a public goods game (PGG) followed by an opportunity to select a partner for a second cooperative game. We found that those who gave more in the PGG were more often selected as desired partners and received more in the paired cooperative game. Reputational competition was even stronger when it was possible for participants to receive a higher payoff from partner choice. The benefits of being selected by a more cooperative partner outweighed the costs of cooperation in the reputation building phase. CA therefore provides an alternative to indirect reciprocity as an explanation for reputation-building behaviour. Furthermore, while indirect reciprocity depends upon individuals giving preference to those of good standing, CA can explain unconditional cooperation.     

Partner Choice Drives the Evolution of Cooperation via Indirect Reciprocity

Indirect reciprocity potentially provides an important means for generating cooperation based on helping those who help others. However, the use of ‘image scores’ to summarize individuals’ past behaviour presents a dilemma: individuals withholding help from those of low image score harm their own reputation, yet giving to defectors erodes cooperation. Explaining how indirect reciprocity could evolve has therefore remained problematic. In all previous treatments of indirect reciprocity, individuals are assigned potential recipients and decide whether to cooperate or defect based on their reputation. A second way of achieving discrimination is through partner choice, which should enable individuals to avoid defectors. Here, I develop a model in which individuals choose to donate to anyone within their group, or to none. Whereas image scoring with random pairing produces cycles of cooperation and defection, with partner choice there is almost maximal cooperation. In contrast to image scoring with random pairing, partner choice results in almost perfect contingency, producing the correlation between giving and receiving required for cooperation. In this way, partner choice facilitates much higher and more stable levels of cooperation through image scoring than previously reported and provides a simple mechanism through which systems of helping those who help others can work.     

Chimpanzees (<Emphasis Type="Italic">Pan troglodytes</Emphasis>) learn to act with other individuals in a cooperative task

We presented two chimpanzees with a task in which they were required to pull each end of a rope simultaneously to drag blocks supporting food into reach. The chimpanzees did not succeed in initial tests. They did not immediately understand the necessity for cooperation, and they did not adjust their behavior to work with the partner. However, the frequency of success gradually increased as the number of sessions increased and the task was varied. They began to look at the partner frequently, wait if the partner was not holding the rope, and pull the rope in synchrony with the partner. However, they did not use interactive behaviors or eye contact to synchronize their behavior. One chimpanzee was then paired with a human partner in the same situation. After initial failures, the chimpanzee began to solicit the human partner for cooperation: looking up at his face, vocalizing, and taking the partner’s hand. When this chimpanzee was again paired with the chimpanzee partner, no soliciting behavior was observed. Thus, the chimpanzees could learn to coordinate their behavior through trial and error. Communicative behavior emerged during the task, but the communication differed according to the identity of the partner.     

The stability of cooperation involving variable investment

In this paper, we attempt to reconcile the results of several studies which have investigated the evolution of cooperation between non-relatives in systems where investment in partners can vary. In contrast to previous proposals, we show for the first time that variable-investment cooperation can be readily maintained in inter-species mutualistic relationships even in the absence of spatial structure, but that the stability of this interaction is dependent on the particular investment-response rule that is employed. By allowing the evolution of investment-response parameters in both inter- and intra-specific versions of the continuous variable-investment Prisoners' Dilemma we show that, in the absence of further factors, the raise-the stakes (RTS) strategy is likely to evolve into a simpler, variable investment form of Give-as-Good-as-you-Get that initially offers a high fixed amount and subsequently matches its partner's investment. Nevertheless, we demonstrate that genuine RTS-like strategies will still be selected if two intuitively reasonable conditions hold: if individuals are limited in terms of the total they can invest in cooperative actions over their lifetimes, and if there are always some individuals in a population that cannot cooperate.     

Female baboons do not raise the stakes but they give as good as they get

We used data from four chacma baboon, Papio cynocephalus ursinus, troops, living in two populations, to test the raise the stakes (RTS) strategy of reciprocity. Female baboons did not raise the stakes either within or across grooming bouts. Instead they time-matched grooming contributions and divided grooming into short episodes. In addition, analysis of the grooming behaviour of frequently versus infrequently grooming dyads did not reveal differences in grooming patterns predicted by the RTS strategy. We suggest time constraints preclude the escalation of grooming bout length as required by RTS; the data were more consistent with a strategy of give as good as you get. However, this strategy could not explain all the patterns observed, and we conclude that biological market theory represents a more appropriate framework for investigating female grooming dynamics than dyadic games based on the iterated prisoner's dilemma. We suggest that competitive altruism among individuals acts as a market force influencing an individual's value as a grooming partner. Copyright 2000 The Association for the Study of Animal Behaviour.     

Long-term social bonds promote cooperation in the iterated Prisoner's Dilemma

Reciprocal altruism, one of the most probable explanations for cooperation among non-kin, has been modelled as a Prisoner''s Dilemma. According to this game, cooperation could evolve when individuals, who expect to play again, use conditional strategies like tit-for-tat or Pavlov. There is evidence that humans use such strategies to achieve mutual cooperation, but most controlled experiments with non-human animals have failed to find cooperation. One reason for this could be that subjects fail to cooperate because they behave as if they were to play only once. To assess this hypothesis, we conducted an experiment with monogamous zebra finches (Taeniopygia guttata) that were tested in a two-choice apparatus, with either their social partner or an experimental opponent of the opposite sex. We found that zebra finches maintained high levels of cooperation in an iterated Prisoner''s Dilemma game only when interacting with their social partner. Although other mechanisms may have contributed to the observed difference between the two treatments, our results support the hypothesis that animals do not systematically give in to the short-term temptation of cheating when long-term benefits exist. Thus, our findings contradict the commonly accepted idea that reciprocal altruism will be rare in non-human animals.     

The evolution of one-shot cooperation: An experiment

Can people rationally advance their own material interests by cooperating in one-shot prisoner's dilemmas, even when there is no possibility of being punished for defection? We outline a model that describes how such cooperation could evolve if the presence of a cooperative disposition can be discerned by others. We test the model's key assumption with an experiment in which we find that subjects who interacted for thirty minutes before playing one-shot prisoner's dilemmas with two others were substantially more accurate than chance in predicting their partner's decisions.     

A positive effect of flowers rather than eye images in a large-scale, cross-cultural dictator game

People often consider how their behaviour will be viewed by others, and may cooperate to avoid gaining a bad reputation. Sensitivity to reputation may be elicited by subtle social cues of being watched: previous studies have shown that people behave more cooperatively when they see images of eyes rather than control images. Here, we tested whether eye images enhance cooperation in a dictator game, using the online labour market Amazon Mechanical Turk (AMT). In contrast to our predictions and the results of most previous studies, dictators gave away more money when they saw images of flowers rather than eye images. Donations in response to eye images were not significantly different to donations under control treatments. Dictator donations varied significantly across cultures but there was no systematic variation in responses to different image types across cultures. Unlike most previous studies, players interacting via AMT may feel truly anonymous when making decisions and, as such, may not respond to subtle social cues of being watched. Nevertheless, dictators gave away similar amounts as in previous studies, so anonymity did not erase helpfulness. We suggest that eye images might only promote cooperative behaviour in relatively public settings and that people may ignore these cues when they know their behaviour is truly anonymous.     

Evolution of Conformity in Social Dilemmas

People often deviate from their individual Nash equilibrium strategy in game experiments based on the prisoner’s dilemma (PD) game and the public goods game (PGG), whereas conditional cooperation, or conformity, is supported by the data from these experiments. In a complicated environment with no obvious “dominant” strategy, conformists who choose the average strategy of the other players in their group could be able to avoid risk by guaranteeing their income will be close to the group average. In this paper, we study the repeated PD game and the repeated m-person PGG, where individuals’ strategies are restricted to the set of conforming strategies. We define a conforming strategy by two parameters, initial action in the game and the influence of the other players’ choices in the previous round. We are particularly interested in the tit-for-tat (TFT) strategy, which is the well-known conforming strategy in theoretical and empirical studies. In both the PD game and the PGG, TFT can prevent the invasion of non-cooperative strategy if the expected number of rounds exceeds a critical value. The stability analysis of adaptive dynamics shows that conformity in general promotes the evolution of cooperation, and that a regime of cooperation can be established in an AllD population through TFT-like strategies. These results provide insight into the emergence of cooperation in social dilemma games.     

Reciprocal preening and food sharing in colour‐polymorphic nestling barn owls

Barn owl (Tyto alba) siblings preen and offer food items to one another, behaviours that can be considered prosocial because they benefit a conspecific by relieving distress or need. In experimental broods, we analysed whether such behaviours were reciprocated, preferentially exchanged between specific phenotypes, performed to avoid harassment and food theft or signals of hierarchy status. Three of the results are consistent with the hypothesis of direct reciprocity. First, food sharing was reciprocated in three‐chick broods but not in pairs of siblings, that is when nestlings could choose a partner with whom to develop a reciprocating interaction. Second, a nestling was more likely to give a prey item to its sibling if the latter individual had preened the former. Third, siblings matched their investment in preening each other. Manipulation of age hierarchy showed that food stealing was directed towards older siblings but was not performed to compensate for a low level of cooperation received. Social behaviours were related to melanin‐based coloration, suggesting that animals may signal their propensity to interact socially. The most prosocial phenotype (darker reddish) was also the phenotype that stole more food, and the effect of coloration on prosocial behaviour depended upon rank and sex, suggesting that colour‐related prosociality is state dependent.     

Reciprocity and communication of partner quality

In a cooperative exchange, the size of a partner''s contribution is likely to depend both on the partner''s ability to supply help and on the partner''s need for help in return. Referring to such needs and abilities as aspects of partner quality, it follows that variation in the amount of help offered in a relationship could transmit information about partner quality. A plausible behaviour might then be to vary the investment in a partner according to available information about partner quality and to invest little in a partner who offers little in return. Thus, regulation of a relationship through communication of partner quality would tend to follow the principle of reciprocity. In an analysis of an iterated game where players have private information about their needs and abilities, I verify this possibility by describing an evolutionarily stable state space strategy, referred to as ''state-dependent reciprocity'', entailing communication of partner quality. Although the evolution of cooperation has been studied in great detail, there has been no previous analysis of communication of needs and abilities in a relationship. It may well be that such communication is of major importance for the evolution of cooperative behaviour in nature.     

Correlates of cooperation in a one-shot high-stakes televised prisoners' dilemma

Explaining cooperation between non-relatives is a puzzle for both evolutionary biology and the social sciences. In humans, cooperation is often studied in a laboratory setting using economic games such as the prisoners' dilemma. However, such experiments are sometimes criticized for being played for low stakes and by misrepresentative student samples. Golden balls is a televised game show that uses the prisoners' dilemma, with a diverse range of participants, often playing for very large stakes. We use this non-experimental dataset to investigate the factors that influence cooperation when "playing" for considerably larger stakes than found in economic experiments. The game show has earlier stages that allow for an analysis of lying and voting decisions. We found that contestants were sensitive to the stakes involved, cooperating less when the stakes were larger in both absolute and relative terms. We also found that older contestants were more likely to cooperate, that liars received less cooperative behavior, but only if they told a certain type of lie, and that physical contact was associated with reduced cooperation, whereas laughter and promises were reliable signals or cues of cooperation, but were not necessarily detected.     

To be or not to be a good social partner?

Cooperation based in mutual benefit provides a perfect scenario to start selfish behaviors aimed to obtain greater benefit at the expense of the partner. Here we investigate if mutual benefit cooperation can be stable between individuals that cooperate with kindness (good partners) or if they will be displaced by other individuals that try to obtain more benefit with less cost (bad partners). Our model assumes an asymmetry between partners in such a way that one of them (actor) proposes the cooperation whereas the other (receiver) always accepts the offer. It also assumes that actors can choose the partner on the basis of their past experiences with the potential partners. With the help of a simple two-locus mathematical model we show that not only the gene that conditions the actor preference to choose good partners can increase in frequency but also the gene responsible of the good partner behavior.