arXiv subjects

Alex McAvoy

Publications and source records attributed to Alex McAvoy.

At least 19 recordsLinked to original sources

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

Meeting times on graphs in near-cubic time

The expected meeting time of two random walkers on an undirected graph of size $N$, where at each time step one walker moves and the process stops when they collide, satisfies a system of $\binom{N}{2}$ linear equations. Na\"{i}vely, solving this system takes $O\left(N^{6}\right)$ operations. However, this system of linear equations has nice structure in that it is almost a Sylvester equation, with the obstruction being a diagonal absorption constraint. We give a simple algorithm for solving this system that exploits this structure, leading to $O\left(N^{4}\right)$ operations and $\Theta\left(N^{2}\right)$ space for exact computation of all $\binom{N}{2}$ meeting times. While this practical method uses only standard dense linear algebra, it can be improved (in theory) to $O\left(N^{3}\log^{2}N\right)$ operations by exploiting the Cauchy structure of the diagonal correction. We generalize this result slightly to cover the Poisson equation for the absorbing "lazy" pair walk with an arbitrary source, which can be solved at the same cost, with $O\left(N^{3}\right)$ per additional source on the same graph. We conclude with applications to evolutionary dynamics, giving improved algorithms for calculating fixation probabilities and mean trait frequencies.

q-bio.PE↗

arXiv2025

Expectation-enforcing strategies for repeated games

Originating in evolutionary game theory, the class of "zero-determinant" strategies enables a player to unilaterally enforce linear payoff relationships in simple repeated games. An upshot of this kind of payoff constraint is that it can shape the incentives for the opponent in a predetermined way. An example is when a player ensures that the agents get equal payoffs. While extensively studied in infinite-horizon games, extensions to discounted games, nonlinear payoff relationships, richer strategic environments, and behaviors with long memory remain incompletely understood. In this paper, we provide necessary and sufficient conditions for a player to enforce arbitrary payoff relationships (linear or nonlinear), in expectation, in discounted games. These conditions characterize precisely which payoff relationships are enforceable using strategies of arbitrary complexity. Our main result establishes that any such enforceable relationship can actually be implemented using a simple two-point reactive learning strategy, which conditions on the opponent's most recent action and the player's own previous mixed action, using information from only one round into the past. For additive payoff constraints, we show that enforcement is possible using even simpler (reactive) strategies that depend solely on the opponent's last move. In other words, this tractable class is universal within expectation-enforcing strategies. As examples, we apply these results to characterize extortionate, generous, equalizer, and fair strategies in the iterated prisoner's dilemma, asymmetric donation game, nonlinear donation game, and the hawk-dove game, identifying precisely when each class of strategy is enforceable and with what minimum discount factor.

econ.TH↗

arXiv2025

PropensityBench: Evaluating Latent Safety Risks in Large Language Models via an Agentic Approach

Recent advances in Large Language Models (LLMs) have sparked concerns over their potential to acquire and misuse dangerous or high-risk capabilities, posing frontier risks. Current safety evaluations primarily test for what a model \textit{can} do - its capabilities - without assessing what it $\textit{would}$ do if endowed with high-risk capabilities. This leaves a critical blind spot: models may strategically conceal capabilities or rapidly acquire them, while harboring latent inclinations toward misuse. We argue that $\textbf{propensity}$ - the likelihood of a model to pursue harmful actions if empowered - is a critical, yet underexplored, axis of safety evaluation. We present $\textbf{PropensityBench}$, a novel benchmark framework that assesses the proclivity of models to engage in risky behaviors when equipped with simulated dangerous capabilities using proxy tools. Our framework includes 5,874 scenarios with 6,648 tools spanning four high-risk domains: cybersecurity, self-proliferation, biosecurity, and chemical security. We simulate access to powerful capabilities via a controlled agentic environment and evaluate the models' choices under varying operational pressures that reflect real-world constraints or incentives models may encounter, such as resource scarcity or gaining more autonomy. Across open-source and proprietary frontier models, we uncover 9 alarming signs of propensity: models frequently choose high-risk tools when under pressure, despite lacking the capability to execute such actions unaided. These findings call for a shift from static capability audits toward dynamic propensity assessments as a prerequisite for deploying frontier AI systems safely. Our code is available at https://github.com/scaleapi/propensity-evaluation.

cs.CY↗

arXiv2025

Behavioral alignment in social networks

The orderly behaviors observed in large-scale groups, such as fish schooling and the organized movement of crowds, are both ubiquitous and essential for the survival and stability of these systems. Understanding how such complex collective behaviors emerge from simple local interactions and behavioral adjustments is a significant scientific challenge. Historically, research has predominantly focused on imitation and social learning, where individuals adopt the strategies of more successful peers to refine their behavior. However, in recent years, an alternative learning approach based on self-exploration and introspective learning has garnered increasing attention. In this paradigm, individuals assess their own circumstances and select strategies that best align with their specific conditions. Two examples are coordination and anti-coordination, where individuals align with and diverge from the local majority, respectively. In this study, we analyze networked systems of coordinating and anti-coordinating individuals, exploring the combined effects of system dynamics, network structure, and behavioral patterns. We address several practical questions, including the number of equilibria, their characteristics, the equilibrium time, and the resilience of the system. We find that the number of equilibrium states can be extremely large, even increasing exponentially with minor alterations to the network structure. Moreover, the network structure has a significant impact on the average equilibrium time. Despite the complexity of these findings, we find that variations can be captured by a single, simple network characteristic (the average path length), which we illustrate in both synthetic and empirical networks.

physics.soc-ph↗

arXiv2024

Frequency-dependent returns in nonlinear public goods games

When individuals interact in groups, the evolution of cooperation is traditionally modeled using the framework of public goods games. These models often assume that the return of the public good depends linearly on the fraction of contributors. In contrast, in real life public goods interactions, the return can depend on the size of the investor pool as well. Here, we consider a model in which the multiplication factor (marginal per capita return) for the public good depends linearly on how many contribute, which results in a nonlinear model of public goods. This simple model breaks the curse of dominant defection found in linear public goods interactions and gives rise to richer dynamical outcomes in evolutionary settings. We provide an in-depth analysis of the more varied decisions by the classical rational player in nonlinear public goods interactions as well as a mechanistic, microscopic derivation of the evolutionary outcomes for the stochastic dynamics in finite populations and in the deterministic limit of infinite populations. This kind of nonlinearity provides a natural way to model public goods with diminishing returns as well as economies of scale.

q-bio.PE↗

arXiv2024

Promoting collective cooperation through temporal interactions

Collective cooperation drives the dynamics of many natural, social, and economic phenomena, making understanding the evolution of cooperation with evolutionary game theory a central question of modern science. Although human interactions are best described as complex networks, current explorations are limited to static networks where interactions represented by network links are permanent and do not change over time. In reality, human activities often involve temporal interactions, where links are impermanent, and understanding the evolution of cooperation on such ubiquitous temporal networks is an open question. Here, we present a general framework for systematically analyzing how collective cooperation evolves on any temporal network, which unifies the study of evolutionary game dynamics with dynamic and static interactions. We show that the emergence of cooperation is facilitated by a simple rule of thumb: hubs (individuals with many social ties) should be temporally deprioritized in interactions. We further provide a quantitative metric capturing the priority of hubs, which we utilize to orchestrate the ordering of interactions to best promote cooperation on empirical temporal networks. Our findings unveil the fundamental advantages conferred by temporal interactions for promoting collective cooperation, which transcends the specific insights gleaned from studying traditional static snapshots.

physics.soc-ph↗

arXiv2023

Imitation dynamics on networks with incomplete information

Imitation is an important learning heuristic in animal and human societies. Previous explorations report that the fate of individuals with cooperative strategies is sensitive to the protocol of imitation, leading to a conundrum about how different styles of imitation quantitatively impact the evolution of cooperation. Here, we take a different perspective on the personal and external social information required by imitation. We develop a general model of imitation dynamics with incomplete information in networked systems, which unifies classical update rules including the death-birth and pairwise-comparison rule on complex networks. Under pairwise interactions, we find that collective cooperation is most promoted if individuals neglect personal information. If personal information is considered, cooperators evolve more readily with more external information. Intriguingly, when interactions take place in groups on networks with low degrees of clustering, using more personal and less external information better facilitates cooperation. Our unifying perspective uncovers intuition by examining the rate and range of competition induced by different information situations.

physics.soc-ph↗

arXiv2023

Evolution of reciprocity with limited payoff memory

Direct reciprocity is a mechanism for the evolution of cooperation in repeated social interactions. According to this literature, individuals naturally learn to adopt conditionally cooperative strategies if they have multiple encounters with their partner. Corresponding models have greatly facilitated our understanding of cooperation, yet they often make strong assumptions on how individuals remember and process payoff information. For example, when strategies are updated through social learning, it is commonly assumed that individuals compare their average payoffs. This would require them to compute (or remember) their payoffs against everyone else in the population. To understand how more realistic constraints influence direct reciprocity, we consider the evolution of conditional behaviors when individuals learn based on more recent experiences. Even in the most extreme case that they only take into account their very last interaction, we find that cooperation can still evolve. However, such individuals adopt less generous strategies, and they tend to cooperate less often than in the classical setup with average payoffs. Interestingly, once individuals remember the payoffs of two or three recent interactions, cooperation rates quickly approach the classical limit. These findings contribute to a literature that explores which kind of cognitive capabilities are required for reciprocal cooperation. While our results suggest that some rudimentary form of payoff memory is necessary, it already suffices to remember a few interactions.

physics.soc-ph↗

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

Strategy evolution on temporal hypergraphs

Individuals interact and cooperate in structured systems. Many studies represent this structure using static networks, where each link represents a permanent connection between two nodes. However, real interactions are generally not time-invariant and are often not pairwise. Recently, progress has been made in modeling higher-order interactions using hypergraphs, where a link may connect more than two individuals. Here, we study cooperation on temporal hypergraphs, capturing the time-varying, higher-order interactions seen in empirical systems. We find that temporal hypergraphs can promote cooperation compared with static networks, and the latter may even underestimate the cooperation-boosting effects of constrained, local interactions. We further show that cooperation can be facilitated by temporal hypergraphs with sparse components and higher-order interactions. Importantly, when the size of group interactions (hyperedges) is comparable to the population size, relatively small hyperedge sizes best facilitate cooperation. Synthetic and empirical hypergraphs alike affirm our findings, illuminating how temporal, higher-order interactions profoundly shape the evolution of cooperation.

physics.soc-ph↗

arXiv2022

Evolutionary instability of selfish learning in repeated games

Across many domains of interaction, both natural and artificial, individuals use past experience to shape future behaviors. The results of such learning processes depend on what individuals wish to maximize. A natural objective is one's own success. However, when two such "selfish" learners interact with each other, the outcome can be detrimental to both, especially when there are conflicts of interest. Here, we explore how a learner can align incentives with a selfish opponent. Moreover, we consider the dynamics that arise when learning rules themselves are subject to evolutionary pressure. By combining extensive simulations and analytical techniques, we demonstrate that selfish learning is unstable in most classical two-player repeated games. If evolution operates on the level of long-run payoffs, selection instead favors learning rules that incorporate social (other-regarding) preferences. To further corroborate these results, we analyze data from a repeated prisoner's dilemma experiment. We find that selfish learning is insufficient to explain human behavior when there is a trade-off between payoff maximization and fairness.

q-bio.PE↗

arXiv2022

Selfish optimization and collective learning in populations

A selfish learner seeks to maximize their own success, disregarding others. When success is measured as payoff in a game played against another learner, mutual selfishness typically fails to produce the optimal outcome for a pair of individuals. However, learners often operate in populations, and each learner may have a limited duration of interaction with any other individual. Here, we compare selfish learning in stable pairs to selfish learning with stochastic encounters in a population. We study gradient-based optimization in repeated games like the prisoner's dilemma, which feature multiple Nash equilibria, many of which are suboptimal. We find that myopic, selfish learning, when distributed in a population via ephemeral encounters, can reverse the dynamics that occur in stable pairs. In particular, when there is flexibility in partner choice, selfish learning in large populations can produce optimal payoffs in repeated social dilemmas. This result holds for the entire population, not just for a small subset of individuals. Furthermore, as the population size grows, the timescale to reach the optimal population payoff remains finite in the number of learning steps per individual. While it is not universally true that interacting with many partners in a population improves outcomes, this form of collective learning achieves optimality for several important classes of social dilemmas. We conclude that naïve learning can be surprisingly effective in populations of individuals navigating conflicts of interest.

q-bio.PE↗

arXiv2022

The coalescent in finite populations with arbitrary, fixed structure

The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial, age, and class structure, along with other features of real-world populations. To further extend the range of population structures to which coalescent theory applies, we formulate a coalescent process for a broad class of neutral drift models with arbitrary -- but fixed -- spatial, age, sex, and class structure, haploid or diploid genetics, and any fixed mating pattern. Here, the coalescent is represented as a random sequence of mappings $\mathcal{C} = \left(C_t\right)_{t=0}^\infty$ from a finite set $G$ to itself. The set $G$ represents the ``sites'' (in individuals, in particular locations and/or classes) at which these alleles can live. The state of the coalescent, $C_t:G \to G$, maps each site $g \in G$ to the site containing $g$'s ancestor, $t$ time-steps into the past. Using this representation, we define and analyze coalescence time, coalescence branch length, mutations prior to coalescence, and stationary probabilities of identity-by-descent and identity-by-state. For low mutation, we provide a recipe for computing identity-by-descent and identity-by-state probabilities via the coalescent. Applying our results to a diploid population with arbitrary sex ratio $r$, we find that measures of genetic dissimilarity, among any set of sites, are scaled by $4r(1-r)$ relative to the even sex ratio case.

q-bio.PE↗

arXiv2022

Evaluating the structure-coefficient theorem of evolutionary game theory

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 frequency with which mutations arise.

q-bio.PE↗

arXiv2022

Payoff landscapes and the robustness of selfish optimization in iterated games

In iterated games, a player can unilaterally exert influence over the outcome through a careful choice of strategy. A powerful class of such "payoff control" strategies was discovered by Press and Dyson (2012). Their so-called "zero-determinant" (ZD) strategies allow a player to unilaterally enforce a linear relationship between both players' payoffs. It was subsequently shown by Chen and Zinger (2014) that when the slope of this linear relationship is positive, ZD strategies are robustly effective against a selfishly optimizing co-player, in that all adapting paths of the selfish player lead to the maximal payoffs for both players (at least when there are certain restrictions on the game parameters). In this paper, we investigate the efficacy of selfish learning against a fixed player in more general settings, for both ZD and non-ZD strategies. We first prove that in any symmetric $2\times 2$ game, the selfish player's final strategy must be of a certain form and cannot be fully stochastic. We then show that there are prisoner's dilemma interactions for which selfish optimization does not always lead to maximal payoffs against fixed ZD strategies with positive slope. We give examples of selfish adapting paths that lead to locally but not globally optimal payoffs, undermining the robustness of payoff control strategies. For non-ZD strategies, these pathologies arise regardless of the original restrictions on the game parameters. Our results illuminate the difficulty of implementing robust payoff control and selfish optimization, even in the simplest context of playing against a fixed strategy.

cs.GT↗

arXiv2021

Evolution of prosocial behavior in multilayer populations

Human societies include diverse social relationships. Friends, family, business colleagues, and online contacts can all contribute to one's social life. Individuals may behave differently in different domains, but success in one domain may engender success in another. Here, we study this problem using multilayer networks to model multiple domains of social interactions, in which individuals experience different environments and may express different behaviors. We provide a mathematical analysis and find that coupling between layers tends to promote prosocial behavior. Even if prosociality is disfavored in each layer alone, multilayer coupling can promote its proliferation in all layers simultaneously. We apply this analysis to six real-world multilayer networks, ranging from the socio-emotional and professional relationships in a Zambian community, to the online and offline relationships within an academic University. We discuss the implications of our results, which suggest that small modifications to interactions in one domain may catalyze prosociality in a different domain.

physics.soc-ph↗

arXiv2021

Fixation probabilities in evolutionary dynamics under weak selection

In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutant-appearance distribution. This "fixation probability" is difficult to compute in general, as it depends on the mutation's effect on the organism as well as the population's spatial structure, mating patterns, and other factors. In this study, we consider weak selection, which means that the mutation's effect on the organism is small. We obtain a weak-selection perturbation expansion of a mutant's fixation probability, from an arbitrary initial configuration of mutant and resident types. Our results apply to a broad class of stochastic evolutionary models, in which the size and spatial structure are arbitrary (but fixed). The problem of whether selection favors a given trait is thereby reduced from exponential to polynomial complexity in the population size, when selection is weak. We conclude by applying these methods to obtain new results for evolutionary dynamics on graphs.

q-bio.PE↗