arXiv subjects

Joshua B. Plotkin

Publications and source records attributed to Joshua B. Plotkin.

At least 19 recordsLinked to original sources

arXiv2026

A model of local and global reciprocity

We often decide how to treat friends based on observations of their past behavior, whereas actions toward strangers are typically guided by their public reputations. These two kinds of information underlie two classical mechanisms for the evolution of cooperation$\unicode{x2014}$direct and indirect reciprocity$\unicode{x2014}$which have largely been studied in isolation. They are not interchangeable: we can recall the past actions of only a small circle of close contacts, whereas for the far larger pool of strangers we must rely on public reputations. Here we develop a mathematical framework built on this distinction. Each individual engages in direct reciprocity in local games within a finite neighborhood of friends, whose actions they observe directly, and in indirect reciprocity in global games with a large population of strangers, known only by reputation. Separating local and global interactions allows us to address two questions. First, can cooperation persist under a cognitively simple norm of judgment? We show that combining direct and indirect reciprocity resolves the scoring dilemma: conditional cooperators resist invasion by both unconditional cooperators and unconditional defectors, where indirect reciprocity alone would fail. Second, how should one treat a friend whose past behavior conflicts with their public reputation? We find that the strategies that maximize cooperation are forgiving$\unicode{x2014}$overlooking whichever piece of information is unfavorable$\unicode{x2014}$and that these forgiving strategies can often remain robust to invasion. By distinguishing between local and global scales of interaction and integrating information across them, our framework offers a more cognitively realistic account of how reciprocity sustains cooperation.

physics.soc-ph↗

arXiv2026

Hyperedge approximation for stochastic processes on higher-order networks

Graphs are a standard framework for describing dynamical processes shaped by pairwise interactions among agents. But many systems involve interactions in groups of three or more agents. Here, we develop a method of "$\ell$-hyperedge approximation", a framework to analyze stochastic population processes on regular hypergraphs, in which each individual belongs to $k$ groups of size $\ell$. The framework accommodates both higher-order interactions that determine payoffs and higher-order processes for updating states in response to payoffs. Applied to evolutionary game dynamics, the framework generalizes the classical pairwise result on benefits and costs, $b/c>k$, that favors the spread of cooperation; and it provides critical benefit-to-cost ratios for nonlinear $\ell$-player public goods games that cannot be reduced to pairwise interactions. Applied to complex contagions, where inheritance of states occurs within hyperedges rather than along parent-offspring edges, the framework gives a closed-form result for the fixation probability, which shows how a complexity parameter governs the spread of rare types. Coupling the two processes produces a single stochastic model of payoff-biased complex contagion in structured populations. These results extend pair approximation from graphs to hypergraphs, accommodating multi-way interactions and inheritance structures with no pairwise analog.

physics.soc-ph↗

arXiv2026

Generative artificial intelligence reduces social welfare through model collapse

Generative artificial intelligence (genAI) is rapidly reshaping how knowledge and culture are produced and consumed. Yet generative models are vulnerable to model collapse: when trained on data generated by earlier versions of themselves, their outputs can lose diversity and accuracy. This creates a social dilemma, because delegating tasks to genAI can be individually beneficial in the short term even as widespread adoption degrades future model performance. Here we develop a parsimonious model of behavior in collaborative interactions in which individuals can either exert human effort, rely on genAI, or refrain from work altogether. The welfare consequences of genAI are organized by a simple two-dimensional taxonomy: the strength of the incentive to perform the task without AI, and the severity of model collapse. Within this framework, the introduction of genAI -- while initially beneficial at the individual level -- will reduce social welfare for the most important types of tasks. In addition, habit formation around genAI use can couple otherwise separate domains, so that adoption in low-stakes tasks spills over into high-value tasks and amplifies welfare losses. Together, these results identify a general pathway by which, in the absence of intervention, individually rational adoption of genAI will assuredly and profoundly reduce collective welfare.

physics.soc-ph↗

arXiv2025

The Evolution of Trust under Institutional Moral Hazard

We study the behavior of for-profit institutions that broadcast reputations to foster trust among market participants. We develop a theoretical model in which buyers and sellers are matched on a platform to engage in transactions involving a moral hazard: sellers can either faithfully deliver goods after receiving payment, or not. Although the buyer does not know a seller's true type, the platform maintains a reputation system that probabilistically assigns binary reputation signals. Buyers make purchase decisions based on reputation signals, which influence the payoffs to sellers who then adapt their type over time. These market dynamics ultimately shape the platform's profit from commissions on sales. Our analysis reveals that platforms inherently have an incentive for rating inflation, driven by the desire to increase commission. This introduces a second layer of moral hazard: the platform's incentive to distort reputations for its own profit. Such distortion is self-limited by the platform's need to maintain enough accuracy that trustworthy sellers remain in the market, without which rational buyers would refrain from purchases altogether. Nonetheless, the optimal strategy for the platform can be to invest in order to reduce signal accuracy. When the platform can freely set commission fees, however, maximum profit may be achieved by costly investment in an accurate reputation system. These findings highlight the intricate tensions between platform incentives and resulting social utility for marketplace participants.

cs.GT↗

arXiv2025

Evolution of social behaviors in noisy environments

Evolutionary game theory offers a general framework to study how behaviors evolve by social learning in a population. This body of theory can accommodate a range of social dilemmas, or games, as well as real-world complexities such as spatial structure or behaviors conditioned on reputations. Nonetheless, this approach typically assumes a deterministic payoff structure for social interactions. Here, we extend evolutionary game theory to account for random changes in the social environment, so that mutual cooperation may bring different rewards today than it brings tomorrow, for example. Even when such environmental noise is unbiased, we find it can have a qualitative impact on the behaviors that evolve in a population. Noisy payoffs can permit the stable co-existence of cooperators and defectors in the prisoner's dilemma, for example, as well as bistability in snowdrift games and stable limit cycles in rock-paper-scissors games -- dynamical phenomena that cannot occur in the absence of noise. We conclude by discussing the relevance of our framework to scenarios where the nature of social interactions is subject to external perturbations.

physics.soc-ph↗

arXiv2025

When it pays to teach: a population threshold for dedicated teaching

Teachers hold a prominent place in modern societies, particularly where education is compulsory and widely institutionalized. This ubiquity obscures an underlying question: why do societies designate certain individuals exclusively for the instruction of others? This question is especially enigmatic for dedicated teachers, who invest their labor in cultivating others' skills but do not directly participate in the productive activities for which their students are being trained. To address this puzzle, we develop a simple, mathematically tractable model of teaching and learning in a population with a shared goal. We identify a tradeoff between the size of the workforce and its collective level of expertise; and we analyze the optimal proportion of a population that should serve as teachers across a wide range of scenarios. We show that a population must exceed a critical size before it is beneficial to allocate anyone as a dedicated teacher at all. Subsequently, the peak demand for teachers is achieved at an intermediate population size, and it never surpasses one half of the population. For more complicated tasks, our analysis predicts the optimal allocation of teachers across different levels of expertise. The structure of this teacher allocation is more complex when the population size is large, in agreement with the general size-complexity hypothesis. Our account lays a foundation for understanding the adaptive advantage of dedicated teachers in both human and non-human societies.

q-bio.PE↗

arXiv2024

Institutions of public judgment established by social contract and taxation

Indirect reciprocity is a plausible mechanism for sustaining cooperation: people cooperate with those who have a good reputation, which can be acquired by helping others. However, this mechanism requires the population to agree on who has good or bad moral standing. Consensus can be provided by a central institution that monitors and broadcasts reputations. But how might such an institution be maintained, and how can a population ensure that it is effective and incorruptible? Here we explore a simple mechanism to sustain an institution of reputational judgment: a compulsory contribution from each member of the population, i.e., a tax. We analyze the maximum possible tax rate that individuals will rationally pay to sustain an institution of judgment, which provides a public good in the form of information, and we derive necessary conditions for individuals to resist the temptation to evade their tax payment. We also consider the possibility that institution members may be corrupt and subject to bribery, and we analyze how often an institution must be audited to prevent bribery. Our analysis has implications for the establishment of robust public institutions that provide social information to support cooperation in large populations--and the potential negative consequences associated with wealth or income inequality.

econ.TH↗

arXiv2024

Social learning with complex contagion

We introduce a mathematical model that combines the concepts of complex contagion with payoff-biased imitation, to describe how social behaviors spread through a population. 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. Our framework generalizes this process to incorporate complex contagion, which requires multiple exposures before an individual considers adopting a different behavior. We formulate this 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, the most widely used dynamical model in evolutionary game theory. When applied to linear frequency-dependent games, our 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 towards more successful types. Our analysis intercalates the fields of evolutionary game theory with complex contagions, and it provides a synthetic framework that describes more realistic forms of behavioral change in social systems.

physics.soc-ph↗

arXiv2024

Convergence of reputations under indirect reciprocity

Previous research has shown how indirect reciprocity can promote cooperation through evolutionary game theoretic models. Most work in this field assumes a separation of time-scales: individuals' reputations equilibrate at a fast time scale for given frequencies of strategies while the strategies change slowly according to the replicator dynamics. Much of the previous research has focused on the behaviour and stability of equilibria for the replicator dynamics. Here we focus on the underlying reputational dynamics that occur on a fast time scale. We describe reputational dynamics as systems of differential equations and conduct stability analyses on their equilibria. We prove that reputations converge to a unique equilibrium for each of the five standard norms whether assessments are public or private. These results confirm a crucial but previously unconfirmed assumption underlying the theory of indirect reciprocity for the most studied set of norms.

q-bio.PE↗

arXiv2023

A mechanistic model of gossip, reputations, and cooperation

Social reputations facilitate cooperation: those who help others gain a good reputation, making them more likely to receive help themselves. But when people hold private views of one another, this cycle of indirect reciprocity breaks down, as disagreements lead to the perception of unjustified behavior that ultimately undermines cooperation. Theoretical studies often assume population-wide agreement about reputations, invoking rapid gossip as an endogenous mechanism for reaching consensus. However, the theory of indirect reciprocity lacks a mechanistic description of how gossip actually generates consensus. Here we develop a mechanistic model of gossip-based indirect reciprocity that incorporates two alternative forms of gossip: exchanging information with randomly selected peers or consulting a single gossip source. We show that these two forms of gossip are mathematically equivalent under an appropriate transformation of parameters. We derive an analytical expression for the minimum amount of gossip required to reach sufficient consensus and stabilize cooperation. We analyze how the amount of gossip necessary for cooperation depends on the benefits and costs of cooperation, the assessment rule (social norm), and errors in reputation assessment, strategy execution, and gossip transmission. Finally, we show that biased gossip can either facilitate or hinder cooperation, depending on the direction and magnitude of the bias. Our results contribute to the growing literature on cooperation facilitated by communication, and they highlight the need to study strategic interactions coupled with the spread of social information.

physics.soc-ph↗

arXiv2023

The Game Theory of Fake News

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.

econ.TH↗

arXiv2023

Strategy evolution on dynamic networks

Models of strategy evolution on static networks help us understand how population structure can promote the spread of traits like cooperation. One key mechanism is the formation of altruistic spatial clusters, where neighbors of a cooperative individual are likely to reciprocate, which protects prosocial traits from exploitation. But most real-world interactions are ephemeral and subject to exogenous restructuring, so that social networks change over time. Strategic behavior on dynamic networks is difficult to study, and much less is known about the resulting evolutionary dynamics. Here, we provide an analytical treatment of cooperation on dynamic networks, allowing for arbitrary spatial and temporal heterogeneity. We show that transitions among a large class of network structures can favor the spread of cooperation, even if each individual social network would inhibit cooperation when static. Furthermore, we show that spatial heterogeneity tends to inhibit cooperation, whereas temporal heterogeneity tends to promote it. Dynamic networks can have profound effects on the evolution of prosocial traits, even when individuals have no agency over network structures.

physics.soc-ph↗

arXiv2023

Quantifying the evolution of harmony and novelty in western classical music

Music is a complex socio-cultural construct, which fascinates researchers in diverse fields, as well as the general public. Understanding the historical development of music may help us understand perceptual and cognition, while also yielding insight in the processes of cultural transmission, creativity, and innovation. Here, we present a study of musical features related to harmony, and we document how they evolved over 400 years in western classical music. We developed a variant of the center of effect algorithm to call the most likely for a given set of notes, to represent a musical piece as a sequence of local keys computed measure by measure. We develop measures to quantify key uncertainty, and diversity and novelty in key transitions. We provide specific examples to demonstrate the features represented by these concepts, and we argue how they are related to harmonic complexity and can be used to study the evolution of harmony. We confirm several observations and trends previously reported by musicologists and scientists, with some discrepancies during the Classical period. We report a decline in innovation in harmonic transitions in the early classical period followed by a steep increase in the late classical; and we give an explanation for this finding that is consistent with accounts by music theorists. Finally, we discuss the limitations of this approach for cross-cultural studies and the need for more expressive but still tractable representations of musical scores, as well as a large and reliable musical corpus, for future study.

physics.soc-ph↗

arXiv2023

Historical constraints on the evolution of efficient color naming

Color naming in natural languages is not arbitrary: it reflects efficient partitions of perceptual color space modulated by the relative needs to communicate about different colors. These psychophysical and communicative constraints help explain why languages around the world have remarkably similar, but not identical, mappings of colors to color terms. Languages converge on a small set of efficient representations. But languages also evolve, and the number of terms in a color vocabulary may change over time. Here we show that history, i.e. the existence of an antecedent color vocabulary, acts as a non-adaptive constraint that biases the choice of efficient solution as a language transitions from a vocabulary of size n to n+1 terms. Moreover, as vocabularies evolve to include more terms they explore a smaller fraction of all possible efficient vocabularies compared to equally-sized vocabularies constructed de novo. This path dependence on the cultural evolution of color naming presents an opportunity. Historical constraints can be used to reconstruct ancestral color vocabularies, allowing us to answer long-standing questions about the evolutionary sequences of color words, and enabling us to draw inferences from phylogenetic patterns of language change.

q-bio.PE↗

arXiv2023

The emergence of burstiness in temporal networks

Human social interactions tend to vary in intensity over time, whether they are in person or online. Variable rates of interaction in structured populations can be described by networks with the time-varying activity of links and nodes. One of the key statistics to summarize temporal patterns is the inter-event time (IET), namely the duration between successive pairwise interactions. Empirical studies have found IET distributions that are heavy-tailed (or "bursty"), for temporally varying interaction, both physical and digital. But it is difficult to construct theoretical models of time-varying activity on a network that reproduces the burstiness seen in empirical data. Here we develop a spanning-tree method to construct temporal networks and activity patterns with bursty behavior. Our method ensures a desired target IET distribution of single nodes/links, provided the distribution fulfills a consistency condition, regardless of whether the underlying topology is static or time-varying. We show that this model can reproduce burstiness found in empirical datasets, and so it may serve as a basis for studying dynamic processes in real-world bursty interactions.

physics.soc-ph↗

arXiv2022

Evolution of social norms for moral judgment

Reputations provide a powerful mechanism to sustain cooperation, as individuals cooperate with those of good social standing. But how should moral reputations be updated as we observe social behavior, and when will a population converge on a common norm of moral assessment? Here we develop a mathematical model of cooperation conditioned on reputations, for a population that is stratified into groups. Each group may subscribe to a different social norm for assessing reputations, and so norms compete as individuals choose to move from one group to another. We show that a group initially comprising a minority of the population may nonetheless overtake the entire population--especially if it adopts the Stern Judging norm, which assigns a bad reputation to individuals who cooperate with those of bad standing. When individuals do not change group membership, stratifying reputation information into groups tends to destabilize cooperation, unless individuals are strongly insular and favor in-group social interactions. We discuss the implications of our results for the structure of information flow in a population and the evolution of social norms of moral judgment.

q-bio.PE↗

arXiv2022

Optimality of intercellular signaling: direct transport versus diffusion

Intercellular signaling has an important role in organism development, but not all communication occurs using the same mechanism. Here, we analyze the energy efficiency of intercellular signaling by two canonical mechanisms: diffusion of signaling molecules and direct transport mediated by signaling cellular protrusions. We show that efficient contact formation for direct transport can be established by an optimal rate of projecting protrusions, which depends on the availability of information about the location of the target cell. The optimal projection rate also depends on how signaling molecules are transported along the protrusion, in particular the ratio of the energy cost for contact formation and molecule synthesis. Also, we compare the efficiency of the two signaling mechanisms, under various model parameters. We find that the direct transport is favored over the diffusion when transporting a large amount of signaling molecules. There is a critical number of signaling molecules at which the efficiency of the two mechanisms are the same. The critical number is small when the distance between cells is far, which helps explain why protrusion-based mechanisms are observed in long-range cellular communications.

q-bio.QM↗

arXiv2022

The arrow of evolution when the offspring variance is large

The concept of fitness is central to evolution, but it quantifies only the expected number of offspring an individual will produce. The actual number of offspring is also subject to noise, arising from environmental or demographic stochasticity. In nature, individuals who are more fecund tend to have greater variance in their offspring number -- sometimes far greater than the Poisson variance assumed in classical models of population genetics. Here, we develop a model for the evolution of two types reproducing in a population of non-constant size. The frequency-dependent fitness of each type is determined by pairwise interactions in a prisoner's dilemma game, but the offspring number is subject to an exogenously controlled variance that may depend upon the mean. Whereas defectors are preferred by natural selection in classical well-mixed populations, since they always have greater fitness than cooperators, we show that large offspring variance can reverse the direction of evolution and favor cooperation. Reproductive over-dispersion produces qualitatively new dynamics for other types of social interactions, as well, which cannot arise in populations with a fixed size or Poisson offspring variance.

q-bio.PE↗