arXiv subjects

Mark Broom

Publications and source records attributed to Mark Broom.

At least 19 recordsLinked to original sources

arXiv2026

Nullclines, Subnullclines and the Asymptotic and Transient Attractors in Eco-Evolutionary Dynamics

In the demographic framework, mortality payoff function describes the cost of an interaction and fertility payoff function describes its reward. So while mortality cost depends on opponent's strategy, fertility reward can be affected by the density-dependent juvenile recruitment survival. This motivates an analysis of the eco-evolutionary dynamics of the classical Hawk-Dove game. It is shown that the stable and unstable equilibria (determined by the intersections of frequency and density nullclines) are connected by heteroclinic orbits, which attract nearby trajectories. The resulting bundle of trajectories leads to the discovery of the so-called subnullcines (manifolds placed between frequency and density nullcline) before they converge to the stable rest point. The initial isolated system is then extended by adding environmental seasonality (periodic background mortality), which acts as an external factor. This leads to complex cycling behavior and the subnullclines act as barriers to the propagation of the perturbation (resilience/resistance threshold). Thus, in a way, this paper completes, yet extends, previous works on the eco-evolutionary dynamics of games with demographic payoffs.

q-bio.PE↗

arXiv2026

Competitive Search with a Faulty Satnav (GPS): When Probability Matching is Rational

A divisible treasure is located at a node $H$ of a network. From a given start node a group of $n$ Searchers each seek to reach $H$ first, dividing the treasure equally with the other first arrivers. This type of search game is called competitive search, where the conflict is not between hider and searcher but between searchers. Examples are search for oil deposits or for a pilot downed over enemy territory. In our model, the Searchers have a common Satnav (GPS) which points to $H$ at each branch node with a known probability $p<1$ and each Searcher chooses the probability $q$ with which they follow the pointer. We consider a family of star graphs where the Searchers start at the center and $H$ lies at one of the $k$ leaf nodes. We show that for all parameter values $n,k,p,$ there is a unique trust probability $q$ which forms a symmetric equilibrium. The equilibrium $q$ is increasing in $p,$ decreasing in $n$ and increasing in $k$. Furthemore for fixed $k$ and $p$ we have $q$ equal to $p$ in the limit of $n$ tending to infinity. This last fact is a new example where what is known in behavioural science as probability matching is in fact rational.

cs.GT↗

arXiv2026

Measuring Bell non-locality in the presence of signaling

Scientific inquiry seeks causal explanations of observed phenomena. The Bell experiment provides a paradigmatic case, revealing correlations between spatially separated systems that no local model can reproduce. Such correlations, known as Bell non-locality, are typically analyzed under the non-signaling assumption, which requires that local statistics be independent of distant measurement choices. Yet real experiments, as well as applications beyond physics, often involve signaling, raising the question of how non-locality should be characterized without this constraint. We introduce a general method for quantifying Bell non-locality in the presence of signaling, designed to relax locality as little as necessary. Our approach is guided by the question: how often can locality be preserved across repeated trials in explaining the observed correlations? The task reduces to finding the optimal convex decomposition of the observed correlations into local and genuinely non-local components. We solve this problem within the linear-programming framework, obtaining a closed-form solution valid for arbitrary correlations. We further evaluate a corresponding measure of signaling, demonstrating the generality of the method and the non-trivial character of the results. By extending the notion of non-locality beyond the non-signaling regime, our framework reshapes the basis for experimental analysis in physics and offers tools applicable outside physics.

quant-ph↗

arXiv2025

The Vaccination Game on Networks

Vaccinations are an important tool in the prevention of disease. Vaccinations are generally voluntary for each member of a population and vaccination decisions are influenced by individual risk perceptions and contact structures within populations. In this study, we model vaccination uptake as an evolutionary game where individuals weigh perceived morbidity risks from both vaccination and infection. We incorporate epidemiological dynamics using an SIR model structured on networks, allowing us to determine the evolutionarily stable vaccination level for any given network topology. Our analysis shows that vaccination coverage varies across networks depending on their structure and the relative cost of vaccination (the ratio of vaccine morbidity risk to infection morbidity risk). As this cost increases, vaccination uptake decreases universally, leading to a dominant non-vaccinator strategy when the cost is high. We find that networks with low to moderate degree variability have a relatively low evolutionarily stable vaccination level when this cost is low, as in such populations lower vaccination levels are necessary to achieve equivalent levels of disease prevalence to more heterogeneous networks with high degree variability, which thus show higher vaccination levels at lower relative costs. However, for heterogeneous networks, vaccination levels decline faster as costs rise, eventually falling below the level for the more homogeneous networks. Our findings align with previous studies on vaccination thresholds in structured populations and highlight how network heterogeneity influences vaccination dynamics.

physics.soc-ph↗

arXiv2024

Fairness in Multi-Proposer-Multi-Responder Ultimatum Game

The Ultimatum Game is conventionally formulated in the context of two players. Nonetheless, real-life scenarios often entail community interactions among numerous individuals. To address this, we introduce an extended version of the Ultimatum Game, called the Multi-Proposer-Multi-Responder Ultimatum Game. In this model, multiple responders and proposers simultaneously interact in a one-shot game, introducing competition both within proposers and within responders. We derive subgame-perfect Nash equilibria for all scenarios and explore how these non-trivial values might provide insight into proposal and rejection behavior experimentally observed in the context of one vs. one Ultimatum Game scenarios. Additionally, by considering the asymptotic numbers of players, we propose two potential estimates for a "fair" threshold: either 31.8% or 36.8% of the pie (share) for the responder.

math.OC↗

arXiv2024

Mutation-Bias Learning in Games

We present two variants of a multi-agent reinforcement learning algorithm based on evolutionary game theoretic considerations. The intentional simplicity of one variant enables us to prove results on its relationship to a system of ordinary differential equations of replicator-mutator dynamics type, allowing us to present proofs on the algorithm's convergence conditions in various settings via its ODE counterpart. The more complicated variant enables comparisons to Q-learning based algorithms. We compare both variants experimentally to WoLF-PHC and frequency-adjusted Q-learning on a range of settings, illustrating cases of increasing dimensionality where our variants preserve convergence in contrast to more complicated algorithms. The availability of analytic results provides a degree of transferability of results as compared to purely empirical case studies, illustrating the general utility of a dynamical systems perspective on multi-agent reinforcement learning when addressing questions of convergence and reliable generalisation.

cs.LG↗

arXiv2024

The rules of multiplayer cooperation in networks of communities

Community organization permeates both social and biological complex systems. To study its interplay with behavior emergence, we model mobile structured populations with multiplayer interactions. We derive general analytical methods for evolutionary dynamics under high home fidelity when populations self-organize into networks of asymptotically isolated communities. In this limit, community organization dominates over the network structure and emerging behavior is independent of network topology. We obtain the rules of multiplayer cooperation in networks of communities for different types of social dilemmas. The success of cooperation is a result of the benefits shared amongst communal cooperators outperforming the benefits reaped by defectors in mixed communities. Under weak selection, cooperation can evolve and be stable for any size (Q) and number (M) of communities if the reward-to-cost ratio (V/K) of public goods is higher than a critical value. Community organization is a solid mechanism for sustaining the evolution of cooperation under public goods dilemmas, particularly when populations are organized into a higher number of smaller communities. Contrary to public goods dilemmas relating to production, the multiplayer Hawk-Dove (HD) dilemma is a commons dilemma focusing on the fair consumption of preexisting resources. This game holds mixed results but tends to favour cooperation under larger communities, highlighting that the two types of social dilemmas might lead to solid differences in the behaviour adopted under community structure.

q-bio.PE↗

arXiv2024

The Impact of Time Delay on Mutant Fixation in Evolutionary Games

Evolutionary game theory examines how strategies spread and persist in populations through reproduction and imitation based on their fitness. Traditionally, models assume instantaneous dynamics where fitness depends on the current population state. However, some real-world processes unfold over time, with outcomes emerging from history. This motivates incorporating time delays into evolutionary game models, where fitness relies on the past. We study the impact of time delays on mutant fixation in a Moran Birth-death process with two strategies in a well-mixed population. At each time step of the process, an individual reproduces proportionally to fitness coming from the past. We model this as an absorbing Markov chain, allowing computational calculation of the fixation probability and time. We focus on three important games: the Stag-Hunt, Snowdrift, and Prisoner's Dilemma. We will show time delays reduce the fixation probability in the Stag-Hunt and the Prisoner's Dilemma but increase it in the Snowdrift. For the Stag-Hunt and the Prisoner's Dilemma, time delays lengthen the fixation time until a critical point, then reduce it. The Snowdrift exhibits the opposite trend.

q-bio.PE↗

arXiv2023

The evolution of cooperation in a mobile population on random networks: Network topology matters only for low-degree networks

We consider a finite structured population of mobile individuals that strategically explore a network using a Markov movement model and interact with each other via a public goods game. We extend the model of Erovenko et al. (2019) from complete, circle, and star graphs to various random networks to further investigate the effect of network topology on the evolution of cooperation. We discover that the network topology affects the outcomes of the evolutionary process only for networks of small average degree. Once the degree becomes sufficiently high, the outcomes match those for the complete graph. The actual value of the degree when this happens is much smaller than that of the complete graph, and the threshold value depends on other network characteristics.

physics.soc-ph↗

arXiv2023

Impact of misinformation in the evolution of collective cooperation

Human societies are organized and developed through collective cooperative behaviors, in which interactions between individuals are governed by the underlying social connections. It is well known that, based on the information in their environment, individuals can form collective cooperation by strategically imitating superior behaviors and changing unfavorable surroundings in self-organizing ways. However, facing the tough situation that some humans and social bots keep spreading misinformation, we still lack the systematic investigation on the impact of such proliferation of misinformation on the evolution of social cooperation. Here we study this problem by virtue of classical evolutionary game theory. We find that misinformation generally impedes the emergence of collective cooperation compared to scenarios with completely true information, although the level of cooperation is slightly higher when the benefits provided by cooperators are reduced below a proven threshold. We further show that this possible advantage shrinks as social connections become denser, suggesting that misinformation is more detrimental to the formation of collective cooperation when 'social viscosity' is low. Our results uncover the quantitative effect of misinformation on the social cooperative behavior in the complex networked society, and pave the way for designing possible interventions to improve collective cooperation.

physics.soc-ph↗

arXiv2023

Network topology and movement cost, not updating mechanism, determine the evolution of cooperation in mobile structured populations

Evolutionary models are used to study the self-organisation of collective action, often incorporating population structure due to its ubiquitous presence and long-known impact on emerging phenomena. We investigate the evolution of multiplayer cooperation in mobile structured populations, where individuals move strategically on networks and interact with those they meet in groups of variable size. We find that the evolution of multiplayer cooperation primarily depends on the network topology and movement cost while using different stochastic update rules seldom influences evolutionary outcomes. Cooperation robustly co-evolves with movement on complete networks and structure has a partially detrimental effect on it. These findings contrast an established wisdom in evolutionary graph theory that cooperation can only emerge under some update rules and if the average degree is low. We find that group-dependent movement erases the locality of interactions, suppresses the impact of evolutionary structural viscosity on the fitness of individuals, and leads to assortative behaviour that is much more powerful than viscosity in promoting cooperation. We analyse the differences remaining between update rules through a comparison of evolutionary outcomes and fixation probabilities.

q-bio.PE↗

arXiv2023

Eco-evolutionary dynamics in finite network-structured populations with migration

We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and distribution can change through birth, death and migration, all of which are separate processes. This allows complex interaction and migration behaviours that are dependent on competition. For migration, we assume that the response of individuals to competition is governed by tolerance to their group members, such that less tolerant individuals are more likely to move away due to competition. We looked at the success of a mutant in the rare mutation limit for the complete, cycle and star networks. Unlike models with fixed population size and distribution, the distribution of the individuals per site is explicitly modelled by considering the dynamics of the population. This in turn determines the mutant appearance distribution for each network. Where a mutant appears impacts its success as it determines the competition it faces. For low and high migration rates the complete and cycle networks have similar mutant appearance distributions resulting in similar success levels for an invading mutant. A higher migration rate in the star network is detrimental for mutant success because migration results in a crowded central site where a mutant is more likely to appear.

q-bio.PE↗

arXiv2022

More can be better: An analysis of single-mutant fixation probability functions under $2\times2$ games

Evolutionary game theory has proved to be a powerful tool to probe the self-organisation of collective behaviour by considering frequency-dependent fitness in evolutionary processes. It has shown that the stability of a strategy depends not only on the payoffs received after each encounter but also on the population's size. Here, we study $2\times2$ games in well-mixed finite populations by analysing the fixation probabilities of single mutants as functions of population size. We proved that 9 out of the 24 possible games always lead to monotonically decreasing functions, similarly to fixed fitness scenarios. However, fixation functions showed increasing regions under 12 distinct anti-coordination, coordination, and dominance games. Perhaps counter-intuitively, this establishes that single-mutant strategies often benefit from being in larger populations. Fixation functions that increase from a global minimum to a positive asymptotic value are pervasive but may have been easily concealed by the weak selection limit. We obtained sufficient conditions to observe fixation increasing for small populations and three distinct ways this can occur. Finally, we describe fixation functions with increasing regions bounded by two extremes under intermediate population sizes. We associate their occurrence with transitions from having one global extreme to other shapes.

q-bio.PE↗

arXiv2019

The Stabilisation of Equilibria in Evolutionary Game Dynamics through Mutation: Mutation Limits in Evolutionary Games

The multi-population replicator dynamics (RD) can be considered a dynamic approach to the study of multi-player games, where it was shown to be related to Cross' learning, as well as of systems of coevolving populations. However, not all of its equilibria are Nash equilibria (NE) of the underlying game, and neither convergence to an NE nor convergence in general are guaranteed. Although interior equilibria are guaranteed to be NE, no interior equilibrium can be asymptotically stable in the multi-population RD, resulting, e.g., in cyclic orbits around a single interior NE. We introduce a new notion of equilibria of RD, called mutation limits, which is based on the inclusion of a naturally arising, simple form of mutation, but is invariant under the specific choice of mutation parameters. We prove the existence of such mutation limits for a large range of games, and consider a subclass of particular interest, that of attracting mutation limits. Attracting mutation limits are approximated by asymptotically stable equilibria of the (mutation-)perturbed RD, and hence, offer an approximate dynamic solution of the underlying game, especially if the original dynamic has no asymptotically stable equilibria. In this sense, mutation stabilises the system in certain cases and makes attracting mutation limits near-attainable. Furthermore, the relevance of attracting mutation limits as a game theoretic equilibrium concept is emphasised by a similarity of (mutation-)perturbed RD to the Q-learning algorithm in the context of multi-agent reinforcement learning. In contrast to the guaranteed existence of mutation limits, attracting mutation limits do not exist in all games, raising the question of their characterization.

q-bio.PE↗

arXiv2019

Methods for approximating stochastic evolutionary dynamics on graphs

Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the evolutionary process. However, for more complicated heterogeneous structures, computationally intensive methods are required such as individual-based stochastic simulations. By adapting methods from statistical physics, including moment closure techniques, we first show how to derive existing homogenised pair approximation models and the exact neutral drift model. We then develop node-level approximations to stochastic evolutionary processes on arbitrarily complex structured populations represented by finite graphs, which can capture the different dynamics for individual nodes in the population. Using these approximations, we evaluate the fixation probability of invading mutants for given initial conditions, where the dynamics follow standard evolutionary processes such as the invasion process. Comparisons with the output of stochastic simulations reveal the effectiveness of our approximations in describing the stochastic processes and in predicting the probability of fixation of mutants on a wide range of graphs. Construction of these models facilitates a systematic analysis and is valuable for a greater understanding of the influence of population structure on evolutionary processes.

q-bio.PE↗

arXiv2015

Evolutionary graph theory revisited: general dynamics and the Moran process

Evolution in finite populations is often modelled using the classical Moran process. Over the last ten years this methodology has been extended to structured populations using evolutionary graph theory. An important question in any such population, is whether a rare mutant has a higher or lower chance of fixating (the fixation probability) than the Moran probability, i.e. that from the original Moran model, which represents an unstructured population. As evolutionary graph theory has developed, different ways of considering the interactions between individuals through a graph and an associated matrix of weights have been considered, as have a number of important dynamics. In this paper we revisit the original paper on evolutionary graph theory in light of these extensions to consider these developments in an integrated way. In particular we find general criteria for when an evolutionary graph with general weights satisfies the Moran probability for the set of six common evolutionary dynamics.

q-bio.PE↗

arXiv2014

The nest site lottery: how selectively neutral density dependent growth suppression induces frequency dependent selection

Modern developments in population dynamics emphasize the role of the turnover of individuals. In the new approaches stable population size is a dynamic equilibrium between different mortality and fecundity factors instead of an arbitrary fixed carrying capacity. The latest replicator dynamics models assume that regulation of the population size acts through feedback driven by density dependent juvenile mortality. Here, we consider a simplified model to extract the properties of this approach. We show that at the stable population size, the structure of the frequency dependent evolutionary game emerges. Turnover of individuals induces a lottery mechanism where for each nest site released by a dead adult individual a single newborn is drawn from the pool of newborn candidates. This frequency dependent selection leads toward the strategy maximizing the number of newborns per adult death. However, multiple strategies can maximize this value. Among them, the strategy with the greatest mortality (which implies greater instantaneous growth rate) is selected. This result is important for the discussion about universal fitness measures and which parameters are maximized by natural selection. This is related to the fitness measures R0 and r, because the number of newborns per single dead individual equals lifetime production of newborn R0 in models without ageing. Our model suggests the existence of another fitness measure which is the combination of R0 and r. According to the nest site lottery mechanism, at stable population size, selection favours strategies with the greatest r from those with the greatest R0.

q-bio.PE↗

arXiv2014

Background fitness, eco-evolutionary feedbacks and the Hawk-Dove game

This paper further develops work from a previous article which introduced a new way of modelling evolutionary game models with an emphasis on ecological realism, concerned with how ecological factors determine payoffs in evolutionary games. The current paper is focused on the impact of selectively neutral factors (i.e. those that are the same for all strategies), such as background fitness and a neutral density dependence on game dynamics. In the previous paper background mortality was modelled by post-reproductive mortality describing aggregated mortality between game interactions. In this paper a novel approach to the modelling of background fitness, based on different occurrence rates (intensities) of game interactions and background events is presented. It is shown that the new method is more realistic and natural for dynamic models than the method used in the previous paper. The previous method in effect produces biased trajectories, but it is compatible with the new approach at the restpoints. Also in this paper a rigorous stability analysis of the restpoints of the dynamics is presented. It is shown that the stability or instability of the restpoints, can be explained by a mechanism of eco-evolutionary feedback. The results obtained are illustrated by a Hawk-Dove game example.

q-bio.PE↗