By-product mutualism and the ambiguous effects of harsher environments - A game-theoretic model

Cooperating elephants mitigate competition until the stakes get too high

Cooperation is ubiquitous in the animal kingdom as it aims to maximize benefits through joint action. Selection, however, may also favor competitive behaviors that could violate cooperation. How animals mitigate competition is hotly debated, with particular interest in primates and little attention paid thus far to nonprimates. Using a loose-string pulling apparatus, we explored cooperative and competitive behavior, as well as mitigation of the latter, in semi-wild Asian elephants (Elephas maximus). Our results showed that elephants first maintained a very high cooperation rate (average = 80.8% across 45 sessions). Elephants applied “block,” “fight back,” “leave,” “move side,” and “submission” as mitigation strategies and adjusted these strategies according to their affiliation and rank difference with competition initiators. They usually applied a “fight back” mitigation strategy as a sanction when competition initiators were low ranking or when they had a close affiliation, but were submissive if the initiators were high ranking or when they were not closely affiliated. However, when the food reward was limited, the costly competitive behaviors (“monopoly” and “fight”) increased significantly, leading to a rapid breakdown in cooperation. The instability of elephant cooperation as a result of benefit reduction mirrors that of human society, suggesting that similar fundamental principles may underlie the evolution of cooperation across species.

This study shows that in a task requiring coordinated pulling, elephants compete for access to food but work to mitigate competition in order to maintain cooperation. If the cost of competition becomes too high, however, cooperation breaks down entirely. This behavior mirrors that seen in humans and other great apes, suggesting that certain cooperative mechanisms are not unique to primates.

The consequences of switching strategies in a two-player iterated survival game

We consider two-player iterated survival games in which players are able to switch from a more cooperative behavior to a less cooperative one at some step of an n-step game. Payoffs are survival probabilities and lone individuals have to finish the game on their own. We explore the potential of these games to support cooperation, focusing on the case in which each single step is a Prisoner’s Dilemma. We find that incentives for or against cooperation depend on the number of defections at the end of the game, as opposed to the number of steps in the game. Broadly, cooperation is supported when the survival prospects of lone individuals are relatively bleak. Specifically, we find three critical values or cutoffs for the loner survival probability which, in concert with other survival parameters, determine the incentives for or against cooperation. One cutoff determines the existence of an optimal number of defections against a fully cooperative partner, one determines whether additional defections eventually become disfavored as the number of defections by the partner increases, and one determines whether additional cooperations eventually become favored as the number of defections by the partner increases. We obtain expressions for these switch-points and for optimal numbers of defections against partners with various strategies. These typically involve small numbers of defections even in very long games. We show that potentially long stretches of equilibria may exist, in which there is no incentive to defect more or cooperate more. We describe how individuals find equilibria in best-response walks among n-step strategies.

Social rank modulates how environmental quality influences cooperation and conflict within animal societies

Although dominance hierarchies occur in most societies, our understanding of how these power structures influence individual investment in cooperative and competitive behaviours remains elusive. Both conflict and cooperation in animal societies are often environmentally regulated, yet how individuals alter their cooperative and competitive investments as environmental quality changes remain unclear. Using game theoretic modelling, we predict that individuals of all ranks will invest more in cooperation and less in social conflict in harsh environments than individuals of the same ranks in benign environments. Counterintuitively, low-ranking subordinates should increase their investment in cooperation proportionally more than high-ranking dominants, suggesting that subordinates contribute relatively more when facing environmental challenges. We then test and confirm these predictions experimentally using the Asian burying beetle Nicrophorus nepalensis. Ultimately, we demonstrate how social rank modulates the relationships between environmental quality and cooperative and competitive behaviours, a topic crucial for understanding the evolution of complex societies.

High thresholds encouraging the evolution of cooperation in threshold public-good games

For a well-mixed population, we consider a threshold public good game where group members only obtain benefits from a public good if a sufficiently large number of them cooperates. We investigate the effect of an increase in the threshold on the level of cooperation that evolves. It is shown that for sufficiently large participation costs, the level of cooperation is higher for low and for high thresholds, than it is for intermediate thresholds – where in the latter case cooperation may not evolve at all. The counterintuitive effect where an increase in the threshold from an intermediate to a high one decreases the probability of cooperation, is related to the so-called common-enemy hypothesis of the evolution of cooperation. We further apply our analysis to assess the relative weight of different game types across the parameter space, and show that game types where either a small, or a large fraction of the population evolves as cooperators, receive more weight compared to game types where an intermediate fraction of cooperators evolves.

Adversity and cooperation in heterogeneous pairs

This paper provides a game-theoretic model of the effect of higher adversity on the evolution of cooperation. The focus lies on how this effect of higher adversity is impacted when there is transient, non-genetic heterogeneity in the form of differences in the players' capabilities of contributing to the public good, in the benefits they obtain from the public good, or in their cooperation costs. A framework is provided that identifies the common mechanisms that are at work across two models of cooperation (jointly producing a public good, and jointly defending an existing public good), and across the mentioned types of heterogeneity. With relatively small heterogeneity, higher adversity generates a common-enemy effect for large cooperation costs and a deterrence effect for small cooperation costs. Yet, these results on the effect of higher adversity are completely reversed for relatively large heterogeneity.

Harsh environments: Multi-player cooperation with excludability and congestion

The common-enemy hypothesis of by-product mutualism proposes that organisms are more likely to cooperate when facing the common enemy of a harsher environment. Micro-foundations of this hypothesis have so far focused on the case where cooperation consists of the production of a pure public good. In this case, the effect of a harsher environment is ambiguous: not only a common-enemy effect is possible, but also an opposite, competing effect where the harsher environment reduces the probability of cooperation. This paper shows that unambiguous effects of a harsher environment are predicted when considering the realistic case where the collective good produced is excludable (in the sense that whether or not a player benefits from the collective good depends on whether or not he is contributing) and/or congestible (in the sense that the benefits the individual player obtains from the collective good are affected by the number of contributing players). In particular, the competing effect is systematically predicted for club goods, where defectors are excluded from the benefits of the collective good. A common-enemy effect is instead systematically predicted for charity goods, where cooperators are excluded from the benefits of the collective good. These effects are maintained for congestible club goods and for congestible charity goods. As the degree to which a collective good is excludable can be meaningfully compared across different instances of cooperation, these contrasting predictions for public good, charity goods and club goods yield testable hypotheses for the common-enemy hypothesis of by-product mutualism.

A two-player iterated survival game

We describe an iterated game between two players, in which the payoff is to survive a number of steps. Expected payoffs are probabilities of survival. A key feature of the game is that individuals have to survive on their own if their partner dies. We consider individuals with hardwired, unconditional behaviors or strategies. When both players are present, each step is a symmetric two-player game. The overall survival of the two individuals forms a Markov chain. As the number of iterations tends to infinity, all probabilities of survival decrease to zero. We obtain general, analytical results for n-step payoffs and use these to describe how the game changes as n increases. In order to predict changes in the frequency of a cooperative strategy over time, we embed the survival game in three different models of a large, well-mixed population. Two of these models are deterministic and one is stochastic. Offspring receive their parent's type without modification and fitnesses are determined by the game. Increasing the number of iterations changes the prospects for cooperation. All models become neutral in the limit (n→∞). Further, if pairs of cooperative individuals survive together with high probability, specifically higher than for any other pair and for either type when it is alone, then cooperation becomes favored if the number of iterations is large enough. This holds regardless of the structure of pairwise interactions in a single step. Even if the single-step interaction is a Prisoner's Dilemma, the cooperative type becomes favored. Enhanced survival is crucial in these iterated evolutionary games: if players in pairs start the game with a fitness deficit relative to lone individuals, the prospects for cooperation can become even worse than in the case of a single-step game.

The evolution of extreme cooperation via shared dysphoric experiences

Willingness to lay down one's life for a group of non-kin, well documented historically and ethnographically, represents an evolutionary puzzle. Building on research in social psychology, we develop a mathematical model showing how conditioning cooperation on previous shared experience can allow individually costly pro-group behavior to evolve. The model generates a series of predictions that we then test empirically in a range of special sample populations (including military veterans, college fraternity/sorority members, football fans, martial arts practitioners, and twins). Our empirical results show that sharing painful experiences produces "identity fusion" - a visceral sense of oneness - which in turn can motivate self-sacrifice, including willingness to fight and die for the group. Practically, our account of how shared dysphoric experiences produce identity fusion helps us better understand such pressing social issues as suicide terrorism, holy wars, sectarian violence, gang-related violence, and other forms of intergroup conflict.

Harsh environments and the evolution of multi-player cooperation

The game-theoretic model in this paper provides micro-foundations for the effect a harsher environment on the probability of cooperation among multiple players. The harshness of the environment is alternatively measured by the degree of complementarity between the players' cooperative efforts in producing a public good, and by the number of attacks on an existing public good that the players can collectively defend, where it is shown that these two measures of the degree of adversity facing the players operate in a similar fashion. We show that the effect of the degree of adversity on the probability of cooperation is monotonous, and has an opposite sign for smaller and for larger cooperation costs. For intermediate cooperation costs, we show that the effect of a harsher environment on the probability of cooperation is hill-shaped.