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Interactions among the underlying agents of a complex system are not only limited to dyads but can also occur in larger groups. Currently, no generic model has been developed to capture high-order interactions (HOI), which, along with pairwise interactions, portray a detailed landscape of complex systems. Here, we integrate evolutionary game theory and behavioral ecology into a unified statistical mechanics framework, allowing all agents (modeled as nodes) and their bidirectional, signed, and weighted interactions at various orders (modeled as links or hyperlinks) to be coded into hypernetworks. Such hypernetworks can distinguish between how pairwise interactions modulate a third agent (active HOI) and how the altered state of each agent in turn governs interactions between other agents (passive HOI). The simultaneous occurrence of active and passive HOI can drive complex systems to evolve at multiple time and space scales. We apply the model to reconstruct a hypernetwork of hexa-species microbial communities, and by dissecting the topological architecture of the hypernetwork using GLMY homology theory, we find distinct roles of pairwise interactions and HOI in shaping community behavior and dynamics. The statistical relevance of the hypernetwork model is validated using a series of in vitro mono-, co-, and tricultural experiments based on three bacterial species. [ABSTRACT FROM AUTHOR]

Epigenetic mechanisms can generate bacterial lineages capable of spontaneously switching between distinct phenotypes. Currently, mathematical models and simulations propose epigenetic switches as a mechanism of adaptation to deal with fluctuating environments. However, bacterial evolution experiments for testing these predictions are lacking. Here, we exploit an epigenetic switch in Salmonella enterica, the opvAB operon, to show clear evidence that OpvAB bistability persists in changing environments but not in stable conditions. Epigenetic control of transcription in the opvAB operon produces OpvABOFF (phage-sensitive) and OpvABON (phage-resistant) cells in a reversible manner and may be interpreted as an example of bet-hedging to preadapt Salmonella populations to the encounter with phages. Our experimental observations and computational simulations illustrate the adaptive value of epigenetic variation as an evolutionary strategy for mutation avoidance in fluctuating environments. In addition, our study provides experimental support to game theory models predicting that phenotypic heterogeneity is advantageous in changing and unpredictable environments. [ABSTRACT FROM AUTHOR]

Models of indirect reciprocity study how social norms promote cooperation. In these models, cooperative individuals build up a positive reputation, which in turn helps them in their future interactions. The exact reputational benefits of cooperation depend on the norm in place, which may change over time. Previous research focused on the stability of social norms. Much less is known about how social norms initially evolve when competing with many others. A comprehensive evolutionary analysis, however, has been difficult. Even among the comparably simple space of so-called third-order norms, there are thousands of possibilities, each one inducing its own reputation dynamics. To address this challenge, we use large-scale computer simulations. We study the reputation dynamics of each third-order norm and all evolutionary transitions between them. In contrast to established work with only a handful of norms, we find that cooperation is hard to maintain in well-mixed populations. However, within group-structured populations, cooperation can emerge. The most successful norm in our simulations is particularly simple. It regards cooperation as universally positive, and defection as usually negative--unless defection takes the form of justified punishment. This research sheds light on the complex interplay of social norms, their induced reputation dynamics, and population structure. [ABSTRACT FROM AUTHOR]

Humans update their social behavior in response to past experiences and changing environments. Behavioral decisions are further complicated by uncertainty in the outcome of social interactions. Faced with uncertainty, some individuals exhibit risk aversion while others seek risk. Attitudes toward risk may depend on socioeconomic status; and individuals may update their risk preferences over time, which will feedback on their social behavior. Here, we study how uncertainty and risk preferences shape the evolution of social behaviors. We extend the game-theoretic framework for behavioral evolution to incorporate uncertainty about payoffs and variation in how individuals respond to this uncertainty. We find that different attitudes toward risk can substantially alter behavior and long-term outcomes, as individuals seek to optimize their rewards from social interactions. In a standard setting without risk, for example, defection always overtakes a well-mixed population engaged in the classic Prisoner's Dilemma, whereas risk aversion can reverse the direction of evolution, promoting cooperation over defection. When individuals update their risk preferences along with their strategic behaviors, a population can oscillate between periods dominated by risk-averse cooperators and periods of risk-seeking defectors. Our analysis provides a systematic account of how risk preferences modulate, and even coevolve with, behavior in an uncertain social world. [ABSTRACT FROM AUTHOR]

In ecological contexts, it is conventionally expected that increased food availability would boost consumption, particularly when animals prioritize maximizing their food intake. This paper challenges this conventional wisdom by conducting an in-depth game-theoretic analysis of a basic foraging model, in which animals must choose between intensive food searching as producers or moderate searching while relying on group members as scroungers. Our study reveals that, under certain circumstances, increasing food availability can amplify the inclination to scrounge to such an extent that it leads to a reduction in animals' food consumption compared to scenarios with limited food availability. We further illustrate a similar phenomenon in a model capturing free-riding dynamics among workers in a company. We demonstrate that, under certain reward mechanisms, enhancing workers' production capacities can inadvertently trigger a surge in free-riding behavior, leading to both diminished group productivity and reduced individual payoffs. Our findings provide intriguing insights into the complex relationships between individual and group performances, as well as the intricate mechanisms underlying the emergence of free-riding behavior in competitive environments. [ABSTRACT FROM AUTHOR]

Empiricists often struggle to apply game theory models to real-life cases of animal cooperation. One reason is that many examples of cooperation occur in stable groups, where individuals form social bonds that influence exchanges of help in ways that are not well described by previous models, including the extent of reciprocity and how relationships are initiated. We present a game theory model exploring the conditions under which social bonds between group members promote cooperation. In the model, bonds build up from exchanges of help in a similar way as the strength of association increases in learning, as in the Rescorla--Wagner rule. The bonds in turn affect partner choice and influence helping amounts. The model has a mechanism of reciprocity for bonded pairs, which can evolve toward either loose or strict reciprocation. Several aspects of the model are inspired by observations of food sharing in vampire bats. We find that small social neighborhoods are required for the evolutionary stability of helping, either as small group sizes, or if bonded members of larger groups can form temporary (daily) smaller groupings. The costs of helping need to be fairly low, while the benefits can be substantial. The form of reciprocity that evolves is neither immediate nor very strict. Individuals in need request help based on bond strength, but there is also an evolved preference for initiating bonds with new group members. In contrast, if different groups come into temporary contact, the evolved tendency is to avoid forming bonds between groups. [ABSTRACT FROM AUTHOR]

A great deal of empirical research has examined who falls for misinformation and why. Here, we introduce a formal game-theoretic model of engagement with news stories that captures the strategic interplay between (mis)information consumers and producers. A key insight from the model is that observed patterns of engagement do not necessarily reflect the preferences of consumers. This is because producers seeking to promote misinformation can use strategies that lead moderately inattentive readers to engage more with false stories than true ones--even when readers prefer more accurate over less accurate information. We then empirically test people's preferences for accuracy in the news. In three studies, we find that people strongly prefer to click and share news they perceive as more accurate--both in a general population sample, and in a sample of users recruited through Twitter who had actually shared links to misinformation sites online. Despite this preference for accurate news--and consistent with the predictions of our model--we find markedly different engagement patterns for articles from misinformation versus mainstream news sites. Using 1,000 headlines from 20 misinformation and 20 mainstream news sites, we compare Facebook engagement data with 20,000 accuracy ratings collected in a survey experiment. Engagement with a headline is negatively correlated with perceived accuracy for misinformation sites, but positively correlated with perceived accuracy for mainstream sites. Taken together, these theoretical and empirical results suggest that consumer preferences cannot be straightforwardly inferred from empirical patterns of engagement. [ABSTRACT FROM AUTHOR]

The evolution of cooperation is a major question in the biological and behavioral sciences. While most theoretical studies model cooperation in the context of an isolated interaction (e.g., a Prisoner's Dilemma), humans live in heterogeneous social environments, characterized by large variations in fitness interdependence--the extent to which one's fitness is affected by others. Theoretical and experimental work indicates that humans can infer, and respond to, variations in interdependence. In a heterogeneous ancestral environment, these psychological mechanisms to infer fitness interdependence could have provided a selective advantage, allowing individuals to maximize their fitness by deciding when and with whom to cooperate. Yet, to date, the link between cognitive inference, variation in fitness interdependence, and cooperation remains unclear. Here we introduce a theoretical framework to study the evolution of inference and cooperation in heterogeneous social environments, where individuals experience interactions with varying levels of corresponding interests. Using a combination of evolutionary game theory and agent-based modeling, we model the evolution of adaptive agents, who incur a cost to infer interdependence, in populations of fixed-behavior agents who always cooperate or defect. Our results indicate that natural selection could promote the evolution of psychological mechanisms to infer fitness interdependence, provided that there is enough variation in fitness interdependence to offset the cost of inference. Under certain conditions, the fixation of adaptive agents results in higher levels of cooperation. This depends crucially on the type of inference performed and the features of the interdependence landscape. [ABSTRACT FROM AUTHOR]

Orbital space enables many essential services, such as weather forecasting, global communication, navigation, Earth observation for environmental and agricultural management, and national security applications. Orbit use is increasingly defined by firms launching coordinated fleets—“constellations”—of satellites into low-Earth orbit. These firms operate in markets with few or no competitors, such as the market for broadband internet provision to rural areas. How will oligopolistic competition shape the allocation of orbital space? We analyze orbital-use patterns and economic welfare when two profit-maximizing firms operate satellite constellations with sophisticated collision avoidance systems. We compare this duopoly equilibrium to public utility constellations designed and regulated to maximize economic welfare from orbit use. We show that imperfect competition reduces economic welfare from orbit use by up to 12%—$1.1 billion USD—per year and distorts the allocation of orbital space. The nature of the distortion depends on the magnitude of constellation-related environmental damages. When damages are low, economic welfare is maximized by larger-than-equilibrium constellations. When damages are high, economic welfare is maximized by smaller-than-equilibrium constellations. Between the growing commercial and national interests in outer space and the importance of low-Earth orbit to space exploration, orbit-use management is likely to be a fruitful and policy-relevant area for economic research. We conclude with a discussion of future research directions in orbit-use management relevant to policymakers around the world. [ABSTRACT FROM AUTHOR]

Human diseases involve metabolic alterations. Metabolomic profiles have served as a vital biomarker for the early identification of high-risk individuals and disease prevention. However, current approaches can only characterize individual key metabolites, without taking into account the reality that complex diseases are multifactorial, dynamic, heterogeneous, and interdependent. Here, we leverage a statistical physics model to combine all metabolites into bidirectional, signed, and weighted interaction networks and trace how the flow of information from one metabolite to the next causes changes in health state. Viewing a disease outcome as the consequence of complex interactions among its interconnected components (metabolites), we integrate concepts from ecosystem theory and evolutionary game theory to model how the health state-dependent alteration of a metabolite is shaped by its intrinsic properties and through extrinsic influences from its conspecifics. We code intrinsic contributions as nodes and extrinsic contributions as edges into quantitative networks and implement GLMY homology theory to analyze and interpret the topological change of health state from symbiosis to dysbiosis and vice versa. The application of this model to real data allows us to identify several hub metabolites and their interaction webs, which play a part in the formation of inflammatory bowel diseases. The findings by our model could provide important information on drug design to treat these diseases and beyond. [ABSTRACT FROM AUTHOR]

The Nash equilibrium—a, combination of choices by the players of a game from which no self-interested player would deviate—is the predominant solution concept in game theory. Even though every game has a Nash equilibrium, it is not known whether there are deterministic behaviors of the players who play a game repeatedly that are guaranteed to converge to a Nash equilibrium of the game from all starting points. If one assumes that the players’ behavior is a discrete-time or continuous-time rule whereby the current mixed strategy profile is mapped to the next, this question becomes a problem in the theory of dynamical systems. We apply this theory, and in particular Conley index theory, to prove a general impossibility result: There exist games, for which all game dynamics fail to converge to Nash equilibria from all starting points. The games which help prove this impossibility result are degenerate, but we conjecture that the same result holds, under computational complexity assumptions, for nondegenerate games. We also prove a stronger impossibility result for the solution concept of approximate Nash equilibria: For a set of games of positive measure, no game dynamics can converge to the set of approximate Nash equilibria for a sufficiently small yet substantial approximation bound. Our results establish that, although the notions of Nash equilibrium and its computation-inspired approximations are universally applicable in all games, they are fundamentally incomplete as predictors of long-term player behavior. [ABSTRACT FROM AUTHOR]

Individual and societal reactions to an ongoing pandemic can lead to social dilemmas: In some cases, each individual is tempted to not follow an intervention, but for the whole society, it would be best if they did. Now that in most countries, the extent of regulations to reduce SARS-CoV-2 transmission is very small, interventions are driven by individual decision-making. Assuming that individuals act in their best own interest, we propose a framework in which this situation can be quantified, depending on the protection the intervention provides to a user and to others, the risk of getting infected, and the costs of the intervention. We discuss when a tension between individual and societal benefits arises and which parameter comparisons are important to distinguish between different regimes of intervention use. [ABSTRACT FROM AUTHOR]

In fighting infectious diseases posing a global health threat, ranging from influenza to Zika, nonpharmaceutical interventions (NPI), such as social distancing and face covering, remain mitigation measures public health can resort to. However, the success of NPI lies in sufficiently high levels of collective compliance, otherwise giving rise to recurrent infections that are not only driven by pathogen evolution but also changing vigilance in the population. Here, we show that compliance with each NPI measure can be highly dynamic and context-dependent during an ongoing epidemic, where individuals may prefer one to another or even do nothing, leading to intricate temporal switching behavior of NPI adoptions. By characterizing dynamic regimes through the perceived costs of NPI measures and their effectiveness in particular regarding face covering and social distancing, our work offers insights into overcoming barriers in NPI adoptions., Competing Interests: Competing interests statement:The authors declare no competing interest.

Direct reciprocity is a wide-spread mechanism for the evolution of cooperation. In repeated interactions, players can condition their behavior on previous outcomes. A well-known approach is given by reactive strategies, which respond to the coplayer's previous move. Here, we extend reactive strategies to longer memories. A reactive- n strategy takes into account the sequence of the last n moves of the coplayer. A reactive- n counting strategy responds to how often the coplayer cooperated during the last n rounds. We derive an algorithm to identify the partner strategies within these strategy sets. Partner strategies are those that ensure mutual cooperation without exploitation. We give explicit conditions for all partner strategies among reactive-2, reactive-3 strategies, and reactive- n counting strategies. To further explore the role of memory, we perform evolutionary simulations. We vary several key parameters, such as the cost-to-benefit ratio of cooperation, the error rate, and the strength of selection. Within the strategy sets we consider, we find that longer memory tends to promote cooperation. This positive effect of memory is particularly pronounced when individuals take into account the precise sequence of moves., Competing Interests: Competing interests statement:The authors declare no competing interest.

Traditional models of social learning by imitation are based on simple contagion-where an individual may imitate a more successful neighbor following a single interaction. But real-world contagion processes are often complex, meaning that multiple exposures may be required before an individual considers changing their type. We introduce a framework that combines the concepts of simple payoff-biased imitation with complex contagion, to describe how social behaviors spread through a population. We formulate this model as a discrete time and state stochastic process in a finite population, and we derive its continuum limit as an ordinary differential equation that generalizes the replicator equation, a widely used dynamical model in evolutionary game theory. When applied to linear frequency-dependent games, social learning with complex contagion produces qualitatively different outcomes than traditional imitation dynamics: it can shift the Prisoner's Dilemma from a unique all-defector equilibrium to either a stable mixture of cooperators and defectors in the population, or a bistable system; it changes the Snowdrift game from a single to a bistable equilibrium; and it can alter the Coordination game from bistability at the boundaries to two internal equilibria. The long-term outcome depends on the balance between the complexity of the contagion process and the strength of selection that biases imitation toward more successful types. Our analysis intercalates the fields of evolutionary game theory with complex contagions, and it provides a synthetic framework to describe more realistic forms of behavioral change in social systems., Competing Interests: Competing interests statement:The authors declare no competing interest.

Stylized experiments, the public goods game and its variants thereof, have taught us the peculiar reproducible fact that humans tend to cooperate (or contribute to shared resources) more than expected from economically rational assumptions. There have been two competing explanations for this phenomenon: Either cooperating is an innate human trait (the prosocial preference hypothesis) or a transitory effect while learning the game (the confused learner hypothesis). We use large-scale experimental data in the two-player version of the public goods game-the prisoner's dilemma-from an experimental design to distinguish between these two hypotheses. By monitoring the effects of zealots (persistently cooperating bots) and varying the participants' awareness of them, we find a considerably more complex scenario than previously reported. People indeed have a prosocial bias, but not to the degree that they always forego taking action to increase their profit. While our findings end the simplistic theorizing of prosociality, an observed positive, cooperative response to zealots has actionable policy implications., Competing Interests: Competing interests statement:The authors declare no competing interest.

Indirect reciprocity is a key explanation for the exceptional magnitude of cooperation among humans. This literature suggests that a large proportion of human cooperation is driven by social norms and individuals' incentives to maintain a good reputation. This intuition has been formalized with two types of models. In public assessment models, all community members are assumed to agree on each others' reputations; in private assessment models, people may have disagreements. Both types of models aim to understand the interplay of social norms and cooperation. Yet their results can be vastly different. Public assessment models argue that cooperation can evolve easily and that the most effective norms tend to be stern. Private assessment models often find cooperation to be unstable, and successful norms show some leniency. Here, we propose a model that can organize these differing results within a single framework. We show that the stability of cooperation depends on a single quantity: the extent to which individual opinions turn out to be correlated. This correlation is determined by a group's norms and the structure of social interactions. In particular, we prove that no cooperative norm is evolutionarily stable when individual opinions are statistically independent. These results have important implications for our understanding of cooperation, conformity, and polarization., Competing Interests: Competing interests statement:The authors declare no competing interest.

We develop a game-theoretic model of strategic interdependence and tipping in public policy choices and show that the model can be estimated by probit and logit estimators. We test its validity and applicability by using daily data on state-level COVID-19 responses in the United States. Social distancing via shelter-in-place (SIP) strategies and wearing masks emerged as the most effective nonpharmaceutical ways of combatting COVID-19. In the United States, choices about these policies are made by individual states. We develop a game-theoretic model of such choices and test it econometrically, confirming strong interdependence in the implementation of these policies. If enough states engage in social distancing or mask wearing, others will be tipped to follow suit. Policy choices are influenced mainly by the choices of other states, especially those of similar political orientation and to a lesser degree by the number of new COVID-19 cases. The choice of mask-wearing policies is more sensitive to peer choices than the choice of SIP policies, and Republican states are much less likely than Democratic to introduce mask-wearing policies. The choices of policies are influenced more by political than public health considerations. These findings emphasize strategic interdependence in policy choice and offer an analytical framework for these complex dynamics., Competing Interests: Competing interests statement:The authors declare no competing interest.

Interactions among the underlying agents of a complex system are not only limited to dyads but can also occur in larger groups. Currently, no generic model has been developed to capture high-order interactions (HOI), which, along with pairwise interactions, portray a detailed landscape of complex systems. Here, we integrate evolutionary game theory and behavioral ecology into a unified statistical mechanics framework, allowing all agents (modeled as nodes) and their bidirectional, signed, and weighted interactions at various orders (modeled as links or hyperlinks) to be coded into hypernetworks. Such hypernetworks can distinguish between how pairwise interactions modulate a third agent (active HOI) and how the altered state of each agent in turn governs interactions between other agents (passive HOI). The simultaneous occurrence of active and passive HOI can drive complex systems to evolve at multiple time and space scales. We apply the model to reconstruct a hypernetwork of hexa-species microbial communities, and by dissecting the topological architecture of the hypernetwork using GLMY homology theory, we find distinct roles of pairwise interactions and HOI in shaping community behavior and dynamics. The statistical relevance of the hypernetwork model is validated using a series of in vitro mono-, co-, and tricultural experiments based on three bacterial species., Competing Interests: Competing interests statement:The authors declare no competing interest.

In order to accommodate the empirical fact that population structures are rarely simple, modern studies of evolutionary dynamics allow for complicated and highly heterogeneous spatial structures. As a result, one of the most difficult obstacles lies in making analytical deductions, either qualitative or quantitative, about the long-term outcomes of evolution. The “structure-coefficient” theorem is a well-known approach to this problem for mutation–selection processes under weak selection, but a general method of evaluating the terms it comprises is lacking. Here, we provide such a method for populations of fixed (but arbitrary) size and structure, using easily interpretable demographic measures. This method encompasses a large family of evolutionary update mechanisms and extends the theorem to allow for asymmetric contests to provide a better understanding of the mutation–selection balance under more realistic circumstances. We apply the method to study social goods produced and distributed among individuals in spatially heterogeneous populations, where asymmetric interactions emerge naturally and the outcome of selection varies dramatically, depending on the nature of the social good, the spatial topology, and the frequency with which mutations arise. [ABSTRACT FROM AUTHOR]

Temperate bacteriophages lyse or lysogenize host cells depending on various parameters of infection, a key one being the ratio of the number of free viruses to the number of host cells. However, the effect of different propensities of phages for lysis and lysogeny on phage fitness remains an open problem. We explore a nonlinear dynamic evolution model of competition between two phages, one of which is disadvantaged in both the lytic and lysogenic phases. We show that the disadvantaged phage can win the competition by alternating between the lytic and lysogenic phases, each of which individually is a "loser." This counterintuitive result is analogous to Parrondo's paradox in game theory, whereby individually losing strategies combine to produce a winning outcome. The results suggest that evolution of phages optimizes the ratio between the lysis and lysogeny propensities rather than the phage burst size in any individual phase. These findings are likely to broadly apply to the evolution of host-parasite interactions. [ABSTRACT FROM AUTHOR]

Models of indirect reciprocity study how social norms promote cooperation. In these models, cooperative individuals build up a positive reputation, which in turn helps them in their future interactions. The exact reputational benefits of cooperation depend on the norm in place, which may change over time. Previous research focused on the stability of social norms. Much less is known about how social norms initially evolve when competing with many others. A comprehensive evolutionary analysis, however, has been difficult. Even among the comparably simple space of so-called third-order norms, there are thousands of possibilities, each one inducing its own reputation dynamics. To address this challenge, we use large-scale computer simulations. We study the reputation dynamics of each third-order norm and all evolutionary transitions between them. In contrast to established work with only a handful of norms, we find that cooperation is hard to maintain in well-mixed populations. However, within group-structured populations, cooperation can emerge. The most successful norm in our simulations is particularly simple. It regards cooperation as universally positive, and defection as usually negative-unless defection takes the form of justified punishment. This research sheds light on the complex interplay of social norms, their induced reputation dynamics, and population structure., Competing Interests: Competing interests statement:The authors declare no competing interest.

Humans update their social behavior in response to past experiences and changing environments. Behavioral decisions are further complicated by uncertainty in the outcome of social interactions. Faced with uncertainty, some individuals exhibit risk aversion while others seek risk. Attitudes toward risk may depend on socioeconomic status; and individuals may update their risk preferences over time, which will feedback on their social behavior. Here, we study how uncertainty and risk preferences shape the evolution of social behaviors. We extend the game-theoretic framework for behavioral evolution to incorporate uncertainty about payoffs and variation in how individuals respond to this uncertainty. We find that different attitudes toward risk can substantially alter behavior and long-term outcomes, as individuals seek to optimize their rewards from social interactions. In a standard setting without risk, for example, defection always overtakes a well-mixed population engaged in the classic Prisoner's Dilemma, whereas risk aversion can reverse the direction of evolution, promoting cooperation over defection. When individuals update their risk preferences along with their strategic behaviors, a population can oscillate between periods dominated by risk-averse cooperators and periods of risk-seeking defectors. Our analysis provides a systematic account of how risk preferences modulate, and even coevolve with, behavior in an uncertain social world., Competing Interests: Competing interests statement:The authors declare no competing interest.

Political theorists have long argued that enlarging the political sphere to include a greater diversity of interests would cure the ills of factions in a pluralistic society. While the scope of politics has expanded dramatically over the past 75 y, polarization is markedly worse. Motivated by this paradox, we take a bottom–up approach to explore how partisan individual-level dynamics in a diverse (multidimensional) issue space can shape collective-level factionalization via an emergent dimensionality reduction. We extend a model of cultural evolution grounded in evolutionary game theory, in which individuals accumulate benefits through pairwise interactions and imitate (or learn) the strategies of successful others. The degree of partisanship determines the likelihood of learning from individuals of the opposite party. This approach captures the coupling between individual behavior, partisan-mediated opinion dynamics, and an interaction network that changes endogenously according to the evolving interests of individuals. We find that while expanding the diversity of interests can indeed improve both individual and collective outcomes, increasingly high partisan bias promotes a reduction in issue dimensionality via party-based assortment that leads to increasing polarization. When party bias becomes extreme, it also boosts interindividual cooperation, thereby further entrenching extreme polarization and creating a tug-of-war between individual cooperation and societal cohesion. These dangers of extreme partisanship are highest when individuals’ interests and opinions are heavily shaped by peers and there is little independent exploration. Overall, our findings highlight the urgency to study polarization in a coupled, multilevel context. [ABSTRACT FROM AUTHOR]

One of the best-known and most replicated laboratory results in behavioral economics is that bargainers frequently reject low offers, even when it harms their material self-interest. This finding could have important implications for international negotiations on many problems facing humanity today, because models of international bargaining assume exactly the opposite: that policy makers are rational and self-interested. However, it is unknown whether elites who engage in diplomatic bargaining will similarly reject low offers because past research has been based almost exclusively on convenience samples of undergraduates, members of the general public, or small-scale societies rather than highly experienced elites who design and bargain over policy. Using a unique sample of 102 policy and business elites who have an average of 21 y of practical experience conducting international diplomacy or policy strategy, we show that, compared with undergraduates and the general public, elites are actually more likely to reject low offers when playing a standard "ultimatum game" that assesses how players bargain over a fixed resource. Elites with more experience tend to make even higher demands, suggesting that this tendency only increases as policy makers advance to leadership positions. This result contradicts assumptions of rational self-interested behavior that are standard in models of international bargaining, and it suggests that the adoption of global agreements on international trade, climate change, and other important problems will not depend solely on the interests of individual countries, but also on whether these accords are seen as equitable to all member states.

The evolution of cooperation in network-structured populations has been a major focus of theoretical work in recent years. When players are embedded in fixed networks, cooperators are more likely to interact with, and benefit from, other cooperators. In theory, this clustering can foster cooperation on fixed networks under certain circumstances. Laboratory experiments with humans, however, have thus far found no evidence that fixed network structure actually promotes cooperation. Here, we provide such evidence and help to explain why others failed to find it. First, we show that static networks can lead to a stable high level of cooperation, outperforming well-mixed populations. We then systematically vary the benefit that cooperating provides to one's neighbors relative to the cost required to cooperate (b/c), as well as the average number of neighbors in the network (k). When b/c > k, we observe high and stable levels of cooperation. Conversely, when b/c ≤ k or players are randomly shuffled, cooperation decays. Our results are consistent with a quantitative evolutionary game theoretic prediction for when cooperation should succeed on networks and, for the first time to our knowledge, provide an experimental demonstration of the power of static network structure for stabilizing human cooperation.

Information transfer is a basic feature of life that includes signaling within and between organisms. Owing to its interactive nature, signaling can be investigated by using game theory. Game theoretic models of signaling have a long tradition in biology, economics, and philosophy. For a long time the analyses of these games has mostly relied on using static equilibrium concepts such as Pareto optimal Nash equilibria or evolutionarily stable strategies. More recently signaling games of various types have been investigated with the help of game dynamics, which includes dynamical models of evolution and individual learning. A dynamical analysis leads to more nuanced conclusions as to the outcomes of signaling interactions. Here we explore different kinds of signaling games that range from interactions without conflicts of interest between the players to interactions where their interests are seriously misaligned. We consider these games within the context of evolutionary dynamics (both infinite and finite population models) and learning dynamics (reinforcement learning). Some results are specific features of a particular dynamical model, whereas others turn out to be quite robust across different models. This suggests that there are certain qualitative aspects that are common to many real-world signaling interactions.

Game theory describes strategic interactions where success of players' actions depends on those of coplayers. In humans, substantial progress has been made at the neural level in characterizing the dopaminergic and frontostriatal mechanisms mediating such behavior. Here we combined computational modeling of strategic learning with a pathway approach to characterize association of strategic behavior with variations in the dopamine pathway. Specifically, using gene-set analysis, we systematically examined contribution of different dopamine genes to variation in a multistrategy competitive game captured by (i) the degree players anticipate and respond to actions of others (belief learning) and (ii) the speed with which such adaptations take place (learning rate). We found that variation in genes that primarily regulate prefrontal dopamine clearance--catechol-O-methyl transferase (COMT) and two isoforms of monoamine oxidase--modulated degree of belief learning across individuals. In contrast, we did not find significant association for other genes in the dopamine pathway. Furthermore, variation in genes that primarily regulate striatal dopamine function--dopamine transporter and D2 receptors--was significantly associated with the learning rate. We found that this was also the case with COMT, but not for other dopaminergic genes. Together, these findings highlight dissociable roles of frontostriatal systems in strategic learning and support the notion that genetic variation, organized along specific pathways, forms an important source of variation in complex phenotypes such as strategic behavior.

The paper models evolution in pecunia--in the realm of finance. Financial markets are explored as evolving biological systems. Diverse investment strategies compete for the market capital invested in long-lived dividend-paying assets. Some strategies survive and some become extinct. The basis of our paper is that dividends are not exogenous but increase with the wealth invested in an asset, as is the case in a production economy. This might create a positive feedback loop in which more investment in some asset leads to higher dividends which in turn lead to higher investments. Nevertheless, we are able to identify a unique evolutionary stable investment strategy. The problem is studied in a framework combining stochastic dynamics and evolutionary game theory. The model proposed employs only objectively observable market data, in contrast with traditional settings relying upon unobservable investors' characteristics (utilities and beliefs). Our method is analytical and based on mathematical reasoning. A numerical illustration of the main result is provided. [ABSTRACT FROM AUTHOR]

Previous models suggest that indirect reciprocity (reputation) can stabilize large-scale human cooperation [K. Panchanathan, R. Boyd, Nature 432 , 499-502 (2004)]. The logic behind these models and experiments [J. Gross et al. , Sci. Adv. 9 , eadd8289 (2023) and O. P. Hauser, A. Hendriks, D. G. Rand, M. A. Nowak, Sci. Rep. 6 , 36079 (2016)] is that a strategy in which individuals conditionally aid others based on their reputation for engaging in costly cooperative behavior serves as a punishment that incentivizes large-scale cooperation without the second-order free-rider problem. However, these models and experiments fail to account for individuals belonging to multiple groups with reputations that can be in conflict. Here, we extend these models such that individuals belong to a smaller, "local" group embedded within a larger, "global" group. This introduces competing strategies for conditionally aiding others based on their cooperative behavior in the local or global group. Our analyses reveal that the reputation for cooperation in the smaller local group can undermine cooperation in the larger global group, even when the theoretical maximum payoffs are higher in the larger global group. This model reveals that indirect reciprocity alone is insufficient for stabilizing large-scale human cooperation because cooperation at one scale can be considered defection at another. These results deepen the puzzle of large-scale human cooperation., Competing Interests: Competing interests statement:The authors declare no competing interest.

Regions with insufficient vaccination have hindered worldwide poliomyelitis eradication, as they are vulnerable to sporadic outbreaks through reintroduction of the disease. Despite Israel's having been declared polio-free in 1988, a routine sewage surveillance program detected polio in 2013. To curtail transmission, the Israel Ministry of Health launched a vaccine campaign to vaccinate children--who had only received the inactivated polio vaccine--with the oral polio vaccine (OPV). Determining the degree of prosocial motivation in vaccination behavior is challenging because vaccination typically provides direct benefits to the individual as well as indirect benefits to the community by curtailing transmission. However, the Israel OPV campaign provides a unique and excellent opportunity to quantify and model prosocial vaccination as its primary objective was to avert transmission. Using primary survey data and a game-theoretical model, we examine and quantify prosocial behavior during the OPV campaign. We found that the observed vaccination behavior in the Israeli OPV campaign is attributable to prosocial behavior and heterogeneous perceived risk of paralysis based on the individual's comprehension of the prosocial nature of the campaign. We also found that the benefit of increasing comprehension of the prosocial nature of the campaign would be limited if even 24% of the population acts primarily from self-interest, as greater vaccination coverage provides no personal utility to them. Our results suggest that to improve coverage, communication efforts should also focus on alleviating perceived fears surrounding the vaccine. [ABSTRACT FROM AUTHOR]

Mean field games (MFG) and mean field control (MFC) are critical classes of multiagent models for the efficient analysis of massive populations of interacting agents. Their areas of application span topics in economics, finance, game theory, industrial engineering, crowd motion, and more. In this paper, we provide a flexible machine learning framework for the numerical solution of potential MFG and MFC models. State-of-the-art numerical methods for solving such problems utilize spatial discretization that leads to a curse of dimensionality. We approximately solve high-dimensional problems by combining Lagrangian and Eulerian viewpoints and leveraging recent advances from machine learning. More precisely, we work with a Lagrangian formulation of the problem and enforce the underlying Hamilton– Jacobi–Bellman (HJB) equation that is derived from the Eulerian formulation. Finally, a tailored neural network parameterization of the MFG/MFC solution helps us avoid any spatial discretization. Our numerical results include the approximate solution of 100-dimensional instances of optimal transport and crowd motion problems on a standard work station and a validation using a Eulerian solver in two dimensions. These results open the door to much-anticipated applications of MFG and MFC models that are beyond reach with existing numerical methods. [ABSTRACT FROM AUTHOR]

Direct reciprocity is a powerful mechanism for cooperation in social dilemmas. The very logic of reciprocity, however, seems to require that individuals are symmetric, and that everyone has the same means to influence each others' payoffs. Yet in many applications, individuals are asymmetric. Herein, we study the effect of asymmetry in linear public good games. Individuals may differ in their endowments (their ability to contribute to a public good) and in their productivities (how effective their contributions are). Given the individuals' productivities, we ask which allocation of endowments is optimal for cooperation. To this end, we consider two notions of optimality. The first notion focuses on the resilience of cooperation. The respective endowment distribution ensures that full cooperation is feasible even under the most adverse conditions. The second notion focuses on efficiency. The corresponding endowment distribution maximizes group welfare. Using analytical methods, we fully characterize these two endowment distributions. This analysis reveals that both optimality notions favor some endowment inequality: More productive players ought to get higher endowments. Yet the two notions disagree on how unequal endowments are supposed to be. A focus on resilience results in less inequality. With additional simulations, we show that the optimal endowment allocation needs to account for both the resilience and the efficiency of cooperation., Competing Interests: Competing interests statement:The authors declare no competing interest.

Some scholars find that behavioral variation in the public goods game is explained by variations in participants' understanding of how to maximize payoff and that confusion leads to cooperation. Their findings lead them to question the common assumption in behavioral economics experiments that choices reflect motivations. We conduct two experiments, in which we minimize confusion by providing participants with increased training. We also introduce a question that specifically assesses participants' understanding of payoff maximization choices. Our experimental results show that the distribution of behavior types is significantly different when participants play with computers versus humans. A significant increase in contributions is also observed when participants play with humans compared to when they play with computers. Moreover, social norms may be the main motive for contributions when playing with computers. Our findings suggest that social preferences, rather than confusion, play a crucial role in determining contributions in public goods games when playing with humans. We therefore argue that the assumption in behavioral economics experiments that choices reveal motivations is indeed valid., Competing Interests: Competing interests statement:The authors declare no competing interest.

Deployment of autonomous vehicles on public roads promises increased efficiency and safety. It requires understanding the intent of human drivers and adapting to their driving styles. Autonomous vehicles must also behave in safe and predictable ways without requiring explicit communication. We integrate tools from social psychology into autonomous-vehicle decision making to quantify and predict the social behavior of other drivers and to behave in a socially compliant way. A key component is Social Value Orientation (SVO), which quantifies the degree of an agent's selfishness or altruism, allowing us to better predict how the agent will interact and cooperate with others. We model interactions between agents as a best-response game wherein each agent negotiates to maximize their own utility. We solve the dynamic game by finding the Nash equilibrium, yielding an online method of predicting multiagent interactions given their SVOs. This approach allows autonomous vehicles to observe human drivers, estimate their SVOs, and generate an autonomous control policy in real time.We demonstrate the capabilities and performance of our algorithm in challenging traffic scenarios: merging lanes and unprotected left turns. We validate our results in simulation and on human driving data from the NGSIM dataset. Our results illustrate how the algorithm's behavior adapts to social preferences of other drivers. By incorporating SVO, we improve autonomous performance and reduce errors in human trajectory predictions by 25%. [ABSTRACT FROM AUTHOR]

Cooperation can be sustained by institutions that punish free-riders. Such institutions, however, tend to be subverted by corruption if they are not closely watched. Monitoring can uphold the enforcement of binding agreements ensuring cooperation, but this usually comes at a price. The temptation to skip monitoring and take the institution's integrity for granted leads to outbreaks of corruption and the breakdown of cooperation. We model the corresponding mechanism by means of evolutionary game theory, using analytical methods and numerical simulations, and find that it leads to sustained or damped oscillations. The results confirm the view that corruption is endemic and transparency a major factor in reducing it. [ABSTRACT FROM AUTHOR]

Healthcare-associated infections (HAIs) pose a significant burden to patient safety. Institutions can implement hospital infection control (HIC) measures to reduce the impact of HAIs. Since patients can carry pathogens between institutions, there is an economic incentive for hospitals to free ride on the HIC investments of other facilities. Subsidies for infection control by public health authorities could encourage regional spending on HIC. We develop coupled mathematical models of epidemiology and hospital behavior in a game-theoretic framework to investigate how hospitals may change spending behavior in response to subsidies. We demonstrate that under a limited budget, a dollar-for-dollar matching grant outperforms both a fixed-amount subsidy and a subsidy on uninfected patients in reducing the number of HAIs in a single institution. Additionally, when multiple hospitals serve a community, funding priority should go to the hospital with a lower transmission rate. Overall, subsidies incentivize HIC spending and reduce the overall prevalence of HAIs. [ABSTRACT FROM AUTHOR]

The presence of prosocial preferences is thought to reduce significantly the difficulty of solving societal collective action problems such as providing public goods (or reducing public bads). However, prosociality is often limited to members of an in-group. We present a general theoretical model where society is split into subgroups and people care more about the welfare of others in their own subgroup than they do about those in out-groups. Individual contributions to the public good spill over and benefit members in each group to different degrees. We then consider special cases of our general model under which we can examine the consequences of localized prosociality for the economic outcomes of society as a whole. We ask to what extent prosociality closes the welfare gap between the Nash equilibrium without prosociality and the social optimum. The answer depends on whether private and public inputs are good or poor substitutes in producing final output. Critically, the degree to which this welfare gap closes is a concave function of the level of prosociality in the case of poor substitutes, so even low levels of prosociality can lead to social welfare near the social optimum. [ABSTRACT FROM AUTHOR]

COMMENTARY Towardecoevolutionarydynamics Karl Sigmund a,1 and Robert D. Holt b  AsbiologistAndrewHendryrecentlywrote,"research initiatives in ecology and evolution have periodically dated but never married" (1). Maynard Smith was the first to apply this insight to the frequency-dependent selection of phenotypic traits, using game theory (5). Ecoevolution The relation of evolution with ecology seems more promising (1, 9).Thesuccessofagiventraitoftendependsonthefrequencyof some trait in another population, as well as on population densities. Evolutionary Game Theory Often, the success of a trait depends on the trait values of other members of its population, and on their abundance. [Extracted from the article]

Coordinated pair bonds are common in birds and also occur in many other taxa. How do animals solve the social dilemmas they face in coordinating with a partner? We developed an evolutionary model to explore this question, based on observations that a) neuroendocrine feedback provides emotional bookkeeping which is thought to play a key role in vertebrate social bonds and b) these bonds are developed and maintained via courtship interactions that include low-stakes social dilemmas. Using agent-based simulation, we found that emotional bookkeeping and courtship sustained cooperation in the iterated prisoner's dilemma in noisy environments, especially when combined. However, when deceitful defection was possible at low cost, courtship often increased cooperation, whereas emotional bookkeeping decreased it.

Contributing to cooperation is typically costly, while its rewards are often available to all members of a social group. So why should individuals be willing to pay these costs, especially if they could cheat by exploiting the investments of others? Kin selection theory broadly predicts that individuals should investmore into cooperation if their relatedness to group members is high (assuming they can discriminate kin fromnonkin). To better understand howrelatedness affects cooperation, we derived the "Collective Investment" game, which provides quantitative predictions for patterns of strategic investment depending on the level of relatedness. We then tested these predictions by experimentally manipulating relatedness (genotype frequencies) in mixed cooperative aggregations of the social amoeba Dictyostelium discoideum, which builds a stalk to facilitate spore dispersal. Measurements of stalk investment by natural strains correspond to the predicted patterns of relatedness-dependent strategic investment, wherein investment by a strain increases with its relatedness to the group. Furthermore, if overall group relatedness is relatively low (i.e., no strain is at high frequency in a group) strains face a scenario akin to the "Prisoner's Dilemma" and suffer from insufficient collective investment. We find that strains employ relatedness-dependent segregation to avoid these pernicious conditions. These findings demonstrate that simple organisms like D. discoideum are not restricted to being "cheaters" or "cooperators" but instead measure their relatedness to their group and strategically modulate their investment into cooperation accordingly. Consequently, all individuals will sometimes appear to cooperate and sometimes cheat due to the dynamics of strategic investing. [ABSTRACT FROM AUTHOR]

Natural selection designs some social behaviors to depend on flexible learning processes, whereas others are relatively rigid or reflexive. What determines the balance between these two approaches? We offer a detailed case study in the context of a two-player game with antisocial behavior and retaliatory punishment. We show that each player in this game--a "thief" and a "victim"--must balance two competing strategic interests. Flexibility is valuable because it allows adaptive differentiation in the face of diverse opponents. However, it is also risky because, in competitive games, it can produce systematically suboptimal behaviors. Using a combination of evolutionary analysis, reinforcement learning simulations, and behavioral experimentation, we show that the resolution to this tension--and the adaptation of social behavior in this game--hinges on the game's learning dynamics. Our findings clarify punishment's adaptive basis, offer a case study of the evolution of social preferences, and highlight an important connection between natural selection and learning in the resolution of social conflicts. [ABSTRACT FROM AUTHOR]

Kin selection theory predicts that, where kin discrimination is possible, animals should typically act more favorably toward closer genetic relatives and direct aggression toward less closely related individuals. Contrary to this prediction, we present data from an 18-y study of wild banded mongooses, Mungos mungo, showing that females that are more closely related to dominant individuals are specifically targeted for forcible eviction from the group, often suffering severe injury, and sometimes death, as a result. This pattern cannot be explained by inbreeding avoidance or as a response to more intense local competition among kin. Instead, we use game theory to show that such negative kin discrimination can be explained by selection for unrelated targets to invest more effort in resisting eviction. Consistent with our model, negative kin discrimination is restricted to eviction attempts of older females capable of resistance; dominants exhibit no kin discrimination when attempting to evict younger females, nor do they discriminate between more closely or less closely related young when carrying out infanticidal attacks on vulnerable infants who cannot defend themselves. We suggest that in contexts where recipients of selfish acts are capable of resistance, the usual prediction of positive kin discrimination can be reversed. Kin selection theory, as an explanation for social behavior, can benefit from much greater exploration of sequential social interactions. [ABSTRACT FROM AUTHOR]

Collective intelligence is the ability of a group to perform more effectively than any individual alone. Diversity among group members is a key condition for the emergence of collective intelligence, but maintaining diversity is challenging in the face of social pressure to imitate one's peers. Through an evolutionary game-theoretic model of collective prediction, we investigate the role that incentives may play in maintaining useful diversity. We show that market-based incentive systems produce herding effects, reduce information available to the group, and restrain collective intelligence. Therefore, we propose an incentive scheme that rewards accurate minority predictions and show that this produces optimal diversity and collective predictive accuracy. We conclude that real world systems should reward those who have shown accuracy when the majority opinion has been in error. [ABSTRACT FROM AUTHOR]

We study how much data a Bayesian observer needs to correctly infer the relative likelihoods of two events when both events are arbitrarily rare. Each period, either a blue die or a red die is tossed. The two dice land on side 1 with unknown probabilities p1 and q1, which can be arbitrarily low. Given a data-generating process where p1≥cq1, we are interested in how much data are required to guarantee that with high probability the observer’s Bayesian posterior mean for p1 exceeds (1−δ)c times that for q1. If the prior densities for the two dice are positive on the interior of the parameter space and behave like power functions at the boundary, then for every ϵ>0, there exists a finite N so that the observer obtains such an inference after n periods with probability at least 1−ϵ whenever np1≥N. The condition on n and p1 is the best possible. The result can fail if one of the prior densities converges to zero exponentially fast at the boundary. [ABSTRACT FROM AUTHOR]

Microbes often live in dense communities called biofilms, where competition between strains and species is fundamental to both evolution and community function. Although biofilms are commonly found in soil-like porous environments, the study of microbial interactions has largely focused on biofilms growing on flat, planar surfaces. Here, we use microfluidic experiments, mechanistic models, and game theory to study how porous media hydrodynamics can mediate competition between bacterial genotypes. Our experiments reveal a fundamental challenge faced by microbial strains that live in porous environments: cells that rapidly form biofilms tend to block their access to fluid flow and redirect resources to competitors. To understand how these dynamics influence the evolution of bacterial growth rates, we couple a model of flow–biofilm interaction with a game theory analysis. This investigation revealed that hydrodynamic interactions between competing genotypes give rise to an evolutionarily stable growth rate that stands in stark contrast with that observed in typical laboratory experiments: cells within a biofilm can outcompete other genotypes by growing more slowly. Our work reveals that hydrodynamics can profoundly affect how bacteria compete and evolve in porous environments, the habitat where most bacteria live. [ABSTRACT FROM AUTHOR]

The question of how cooperation evolves and is maintained among nonkin is central to the biological, social, and behavioral sciences. Previous research has focused on explaining how cooperation in social dilemmas can be maintained by direct and indirect reciprocity among the participants of the social dilemma. However, in complex human societies, both modern and ancient, cooperation is frequently maintained by means of specialized third-party enforcement. We provide an evolutionary-game-theoretic model that explains how specialized third-party enforcement of cooperation (specialized reciprocity) can emerge. A population consists of producers and enforcers. First, producers engage in a joint undertaking represented by a prisoner's dilemma. They are paired randomly and receive no information about their partner's history, which precludes direct and indirect reciprocity. Then, enforcers tax producers and may punish their clients. Finally, the enforcers are randomly paired and may try to grab resources from each other. In order to sustain producer cooperation, enforcers must punish defecting producers, but punishing is costly to enforcers. We show that the threat of potential intraenforcer conflict can incentivize enforcers to engage in costly punishment of producers, provided they are sufficiently informed to maintain a reputation system. That is, the "guards" are guarded by the guards themselves. We demonstrate the key mechanisms analytically and corroborate our results with numerical simulations.