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Strategic interactions arise in all domains of life. This form of competition often plays out in dynamically changing environments. The strategies employed in a population may alter the state of the environment, which may in turn feedback to change the incentive structure of strategic interactions. Feedbacks between strategies and the environment are common in social-ecological systems, evolutionary-ecological systems, and even psychological-economic systems. Here we develop a framework of ‘eco-evolutionary game theory’ that enables the study of strategic and environmental dynamics with feedbacks. We consider environments governed either by intrinsic growth, decay, or tipping points. We show how the joint dynamics of strategies and the environment depend on the incentives for individuals to lead or follow behavioral changes, and on the relative speed of environmental versus strategic change. Our analysis unites dynamical phenomena that occur in settings as diverse as human decision-making, plant nutrient acquisition, and resource harvesting. We discuss implications in fields ranging from ecology to economics. Strategic game payoffs often depend on the state of the environment, which in turn can be influenced by game strategies. Here, Tilman et al. develop a general framework for modeling strategic games with environmental feedbacks and analyze case studies from decision-making, ecology, and economics.

The authors derive a condition for how natural selection chooses between two competing strategies on any graph for weak selection, elucidating which population structures promote certain behaviours, such as cooperation. Evolution, the great game Evolution is a game that anyone can play. The traits that evolve in a population depend on how the players interact. Students are familiar with toy populations in which every member of the population can interact equally with any other, but as W. S. Gilbert wrote, “When everyone is somebody, then no one's anybody”. In the real world, the numbers and identities of the players can change, and realistic simulations of evolution have proven exceedingly hard to create. Recent models have worked only in special cases in which all individuals have the same number of neighbours. Benjamin Allen and colleagues have now devised a model that works for any number of neighbours, providing that natural selection is weak. They simulate how small changes in population structure can affect evolutionary outcomes, and that cooperation flourishes most in populations with strong ties between pairs of individuals. Evolution occurs in populations of reproducing individuals. The structure of a population can affect which traits evolve 1 , 2 . Understanding evolutionary game dynamics in structured populations remains difficult. Mathematical results are known for special structures in which all individuals have the same number of neighbours 3 , 4 , 5 , 6 , 7 , 8 . The general case, in which the number of neighbours can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class that suggests there is no efficient algorithm 9 . Whether a simple solution for weak selection exists has remained unanswered. Here we provide a solution for weak selection that applies to any graph or network. Our method relies on calculating the coalescence times 10 , 11 of random walks 12 . We evaluate large numbers of diverse population structures for their propensity to favour cooperation. We study how small changes in population structure—graph surgery—affect evolutionary outcomes. We find that cooperation flourishes most in societies that are based on strong pairwise ties.

Cooperation is central to human societies. Yet relatively little is known about the cognitive underpinnings of cooperative decision making. Does cooperation require deliberate self-restraint? Or is spontaneous prosociality reined in by calculating self-interest? Here we present a theory of why (and for whom) intuition favors cooperation: cooperation is typically advantageous in everyday life, leading to the formation of generalized cooperative intuitions. Deliberation, by contrast, adjusts behaviour towards the optimum for a given situation. Thus, in one-shot anonymous interactions where selfishness is optimal, intuitive responses tend to be more cooperative than deliberative responses. We test this ‘social heuristics hypothesis’ by aggregating across every cooperation experiment using time pressure that we conducted over a 2-year period (15 studies and 6,910 decisions), as well as performing a novel time pressure experiment. Doing so demonstrates a positive average effect of time pressure on cooperation. We also find substantial variation in this effect, and show that this variation is partly explained by previous experience with one-shot lab experiments. Whether or not intuition favours cooperative decision making has been controversial. Rand et al. carry out a meta-analysis of 15 studies involving volunteers playing economic games, and confirm a role for intuition in cooperation, which varies according to the volunteers’ previous experience with similar games.

The decoy effect is a cognitive bias documented in behavioural economics by which the presence of a third, (partly) inferior choice causes a significant shift in people’s preference for other items. Here, we performed an experiment with human volunteers who played a variant of the repeated prisoner’s dilemma game in which the standard options of “cooperate” and “defect” are supplemented with a new, decoy option, “reward”. We show that although volunteers rarely chose the decoy option, its availability sparks a significant increase in overall cooperativeness and improves the likelihood of success for cooperative individuals in this game. The presence of the decoy increased willingness of volunteers to cooperate in the first step of each game, leading to subsequent propagation of such willingness by (noisy) tit-for-tat. Our study thus points to decoys as a means to elicit voluntary prosocial action across a spectrum of collective endeavours. The decoy effect refers to the fact that the presence of a third option can shift people’s preferences between two other options even though the third option is inferior to both. Here, the authors show how the decoy effect can enhance cooperation in a social dilemma, the repeated prisoner’s dilemma.

Social dilemmas occur when incentives for individuals are misaligned with group interests 1 – 7 . According to the ‘tragedy of the commons’, these misalignments can lead to overexploitation and collapse of public resources. The resulting behaviours can be analysed with the tools of game theory 8 . The theory of direct reciprocity 9 – 15 suggests that repeated interactions can alleviate such dilemmas, but previous work has assumed that the public resource remains constant over time. Here we introduce the idea that the public resource is instead changeable and depends on the strategic choices of individuals. An intuitive scenario is that cooperation increases the public resource, whereas defection decreases it. Thus, cooperation allows the possibility of playing a more valuable game with higher payoffs, whereas defection leads to a less valuable game. We analyse this idea using the theory of stochastic games 16 – 19 and evolutionary game theory. We find that the dependence of the public resource on previous interactions can greatly enhance the propensity for cooperation. For these results, the interaction between reciprocity and payoff feedback is crucial: neither repeated interactions in a constant environment nor single interactions in a changing environment yield similar cooperation rates. Our framework shows which feedbacks between exploitation and environment—either naturally occurring or designed—help to overcome social dilemmas. Cooperation is more likely to evolve in a public-goods-distribution game when payoffs can change between rounds so that the stakes increase when players cooperate and decrease when players defect.

Bacteria release and sense small molecules called autoinducers in a process known as quorum sensing. The prevailing interpretation of quorum sensing is that by sensing autoinducer concentrations, bacteria estimate population density to regulate the expression of functions that are only beneficial when carried out by a sufficiently large number of cells. However, a major challenge to this interpretation is that the concentration of autoinducers strongly depends on the environment, often rendering autoinducer-based estimates of cell density unreliable. Here we propose an alternative interpretation of quorum sensing, where bacteria, by releasing and sensing autoinducers, harness social interactions to sense the environment as a collective. Using a computational model we show that this functionality can explain the evolution of quorum sensing and arises from individuals improving their estimation accuracy by pooling many imperfect estimates – analogous to the ‘wisdom of the crowds’ in decision theory. Importantly, our model reconciles the observed dependence of quorum sensing on both population density and the environment and explains why several quorum sensing systems regulate the production of private goods. Bacteria release and respond to autoinducers in a process known as quorum sensing. While classically viewed as a strategy to coordinate cell behaviour, Moreno-Gámez et al. demonstrate using modelling that quorum sensing may also be used to sense the environment as a collective by pooling information at relevant scales and harnessing the wisdom of the crowds.

Across societies, humans punish norm violations. To date, research on the antecedents and consequences of punishment has largely relied upon agent-based modeling and laboratory experiments. Here, we report a longitudinal study documenting punishment responses to norm violations in daily life ( k  = 1507; N  = 257) and test pre-registered hypotheses about the antecedents of direct punishment (i.e., confrontation) and indirect punishment (i.e., gossip and social exclusion). We find that people use confrontation versus gossip in a context-sensitive manner. Confrontation is more likely when punishers have been personally victimized, have more power, and value offenders more. Gossip is more likely when norm violations are severe and when punishers have less power, value offenders less, and experience disgust. Findings reveal a complex punishment psychology that weighs the benefits of adjusting others’ behavior against the risks of retaliation. People regularly punish norm violations using gossip and direct confrontation. Here, the authors show that the use of gossip versus direct confrontation is context sensitive, with confrontation used more when punishers have more to gain, and gossip used more when the costs of retaliation loom large.

In human societies, individuals who violate social norms may be punished by third-party observers who have not been harmed by the violator; this study suggests that a reason why the observers are willing to punish is to be seen as more trustworthy by the community. Punishing schedule denotes trustworthiness Human societies appear to be unique in that individuals may be punished for violating social norms — even if the violator has not harmed the punisher and the punishment exerts a cost. Explaining the reasons why this behaviour has evolved has been problematic. These authors offer a model showing that 'third-party punishment' can be an honest signal of trustworthiness. Those who incur a cost by punishing wrongdoers are seen as trustworthy by the community, and behave in a more trustworthy way. But there's a catch: this signal becomes weaker when a more informative signalling mechanism is introduced. That is, when potential punishers have the chance to engage in costly helping, they are less likely to punish, and punishment is perceived as a weaker sign of trustworthiness. Either way, the costs of punishment may be recouped by the long-term reputational benefit of appearing to be trustworthy. Third-party punishment (TPP) 1 , 2 , 3 , 4 , 5 , 6 , 7 , in which unaffected observers punish selfishness, promotes cooperation by deterring defection. But why should individuals choose to bear the costs of punishing? We present a game theoretic model of TPP as a costly signal 8 , 9 , 10 of trustworthiness. Our model is based on individual differences in the costs and/or benefits of being trustworthy. We argue that individuals for whom trustworthiness is payoff-maximizing will find TPP to be less net costly (for example, because mechanisms 11 that incentivize some individuals to be trustworthy also create benefits for deterring selfishness via TPP). We show that because of this relationship, it can be advantageous for individuals to punish selfishness in order to signal that they are not selfish themselves. We then empirically validate our model using economic game experiments. We show that TPP is indeed a signal of trustworthiness: third-party punishers are trusted more, and actually behave in a more trustworthy way, than non-punishers. Furthermore, as predicted by our model, introducing a more informative signal—the opportunity to help directly—attenuates these signalling effects. When potential punishers have the chance to help, they are less likely to punish, and punishment is perceived as, and actually is, a weaker signal of trustworthiness. Costly helping, in contrast, is a strong and highly used signal even when TPP is also possible. Together, our model and experiments provide a formal reputational account of TPP, and demonstrate how the costs of punishing may be recouped by the long-run benefits of signalling one’s trustworthiness.

Multiplayer games on graphs are at the heart of theoretical descriptions of key evolutionary processes that govern vital social and natural systems. However, a comprehensive theoretical framework for solving multiplayer games with an arbitrary number of strategies on graphs is still missing. Here, we solve this by drawing an analogy with the Balls-and-Boxes problem, based on which we show that the local configuration of multiplayer games on graphs is equivalent to distributing k identical co-players among n distinct strategies. We use this to derive the replicator equation for any n -strategy multiplayer game under weak selection, which can be solved in polynomial time. As an example, we revisit the second-order free-riding problem, where costly punishment cannot truly resolve social dilemmas in a well-mixed population. Yet, in structured populations, we derive an accurate threshold for the punishment strength, beyond which punishment can either lead to the extinction of defection or transform the system into a rock-paper-scissors-like cycle. The analytical solution also qualitatively agrees with the phase diagrams that were previously obtained for non-marginal selection strengths. Our framework thus allows an exploration of any multi-strategy multiplayer game on regular graphs. Evolutionary multiplayer games in structured populations illustrate a variety of phenomena in natural and social systems. This research provides a mathematical framework to analyze multiplayer games with an arbitrary number of strategies on regular graphs.

Prosocial punishment has been proved to be a powerful mean to promote cooperation. Recent studies have found that social exclusion, which indeed can be regarded as a kind of punishment, can also support cooperation. However, if prosocial punishment and exclusion are both present, it is still unclear which strategy is more advantageous to curb free-riders. Here we first study the direct competition between different types of punishment and exclusion. We find that pool (peer) exclusion can always outperform pool (peer) punishment both in the optional and in the compulsory public goods game, no matter whether second-order sanctioning is considered or not. Furthermore, peer exclusion does better than pool exclusion both in the optional and in the compulsory game, but the situation is reversed in the presence of second-order exclusion. Finally, we extend the competition among all possible sanctioning strategies and find that peer exclusion can outperform all other strategies in the absence of second-order exclusion and punishment, while pool exclusion prevails when second-order sanctioning is possible. Our results demonstrate that exclusion is a more powerful strategy than punishment for the resolution of social dilemmas.