arXiv subjects

Lucas Wardil

Publications and source records attributed to Lucas Wardil.

15 recordsLinked to original sources

arXiv2026

Fixation probabilities for multi-allele Moran dynamics with weak selection

Fixation probabilities are essential for characterizing stochastic evolutionary dynamics, but analytical results remain limited mainly to systems with two competing types. We develop a perturbative framework to compute fixation probabilities in multi-allele Moran processes under weak selection. Exploiting the general structure of the backward Fokker-Planck operator in this regime, we show that fixation probabilities admit a systematic expansion around their neutral solution. We first introduce the framework in a general case with $M$ competing alleles and arbitrary fitness functions, and then apply it to three biologically motivated examples: a simple model of three competing alleles with a constant fitness function, a coordination game in which allele fitness increases with its frequency in the population, and a model of clonal interference between mutualistic alleles. These results extend the analytical understanding of fixation probabilities beyond pairwise interactions, establishing a framework for investigating multi-strategy stochastic evolutionary dynamics.

q-bio.PE↗

arXiv2024

The evolution of pluralistic ignorance

Pluralistic ignorance is a social-psychological phenomenon that occurs when individuals privately hold beliefs that differ from perceived group norms. Traditional models, based on opinion dynamics with private and public states, fail to account for a key aspect: when nonexpression aligns with normative behavior, initial social pressure can induce pluralistic ignorance. We show that pluralistic ignorance persists under infrequent imitation and strong initial minority influence. Although individuals can overcome this ignorance by the end of interactions, it reemerges in subsequent meetings. However, excessive imitation erases pluralistic ignorance, leading to a uniform state in which internal and external states align. Furthermore, incorporating memory into the internalization process shows that pluralistic ignorance peaks at moderate imitation levels.

physics.soc-ph↗

arXiv2022

Invasion of optimal social contracts

The Stag-hunt game is a prototype for social contracts. Adopting a new and better social contract is usually challenging because the current one is already widely adopted and stable due to deviants' sanctions. Thus, how does a population shift from the current social contract to a better one? In other words, how can a social system leave a local social optimum configuration to achieve an optimum global state? Here, we investigate the effect of promoting diversity on the evolution of social contracts. We considered group-structured populations where individuals play the Stag-hunt game in all groups. We model the diversity incentive as a Snow-drift game played in a single focus group where the individual is more prone to adopt a deviant norm. We show that moderate diversity incentives can change the system dynamics, leading the whole population to move from the locally optimal social normal to the globally optimal one. Thus, an initial fraction of adopters of the new norm can drive the system toward the new social optimum norm. After the new social contract becomes the new equilibrium, it remains stable even without the incentive. The results are obtained using Monte Carlo simulations and analytical approximation methods.

physics.soc-ph↗

arXiv2022

On the synchronization of coupled random walks and applications to social systems

Some political strategies to win elections over the last years were based heavily on fomenting general distrust in information institutions and favoring distrustful sources. The misinformation pandemic has the straightforward consequence that people do not believe any information unless it is compatible with their own beliefs. We present a simple model to study the emergence of consensus in opinion pools of uncertain agents that trust (couple to) their neighbors (information sources) with strength K. We focus the studies on regular lattices and linear coupling. Depending on the coupling constant, K, and the propensity to choose an opinion (the probability to manifest a given opinion in solitude), p_0, we get regions where consensus is surely reached even in infinity systems (K greater than or equal to K_c), regions where not-consensus is the only steady state (K lesser than K_c), and a region where consensus on any opinion is transitory with each agent presenting periods of strong oscillation of opinions before changing polarization (p_0 equal to p_c and K greater than or equal K_c. The first model in this last region presents transition probabilities identical to the voter model (p_0 equal to p_c and K equal to K_c). Different upbringings, exposition to education biased to a single political view, and previous coexistence with opinion polarized people can change the opinion of agents in isolation. We model such characteristics with heterogeneous populations (p^i_0 not equal to p^j_0 for some pairs of nodes i,j). Such systems present regions where the coexistence of local consensus (bulk-stable clusters of like-minded opinions), weak consensus (bulk-unstable temporary clusters where contrary opinions emerge inside the cluster), and distrust (random orientations that do not form clusters) are possible.

physics.soc-ph↗

arXiv2021

Acculturation and the evolution of cooperation in spatial public goods games

Cooperation is one of the foundations of human society. Many solutions to cooperation problems have been developed and culturally transmitted across generations. Because immigration can play a role in nourishing or disrupting cooperation in societies, we must understand how the newcomers' culture interacts with the hosting culture. Here, we investigate the effect of different acculturation settings on the evolution of cooperation in spatial public goods games with the immigration of defectors and efficient cooperators. Here, immigrants may be socially influenced, or not, by the native culture according to four acculturation settings: integration, where immigrants imitate both immigrants and natives; marginalization, where immigrants do not imitate either natives or other immigrants; assimilation, where immigrants only imitate natives; and separation, where immigrants only imitate other immigrants. We found that cooperation is greatly facilitated and reaches a peak for moderate values of the migration rate under any acculturation setting. Most interestingly, we found that the main acculturation factor driving the highest levels of cooperation is that immigrants do not avoid social influence from their fellow immigrants. We also show that integration may not promote the highest level of native cooperation if the benefit of cooperation is low.

physics.soc-ph↗

arXiv2021

Moderate immigration may promote a peak of cooperation among natives

In a world of hardening borders, nations may deprive themselves of enjoying the benefits of cooperative immigrants. Here, we analyze the effect of efficient cooperative immigrants on a population playing public goods games. We considered a population structured on a square lattice with individuals playing public goods games with their neighbors. The demographics are determined by stochastic birth, death, and migration. The strategies spread through imitation dynamics. Our model shows that cooperation among natives can emerge due to social contagion of good role-model agents that can provide better quality public goods. Only a small fraction of efficient cooperators, among immigrants, is enough to trigger cooperation across the native population. We see that native cooperation achieves its peak at moderate values of immigration rate. Such efficient immigrant cooperators act as nucleation centers for the growth of cooperative clusters, that eventually dominate defection.

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arXiv2020

Social dilemma in traffic with heterogeneous drivers

There is a tragedy of the traffic analogous to the tragedy of the commons that can be caused by overtaking. We analyze the effect of overtaking in a minimal model of vehicular traffic, the model proposed by Nagel and Schreckenberg, with two types of drivers: drivers that overtake and drivers that do not. We show that, under certain circumstances, overtaking is good because it increases the road capacity and minimizes the mean time spent by the driver on the road. However, when these conditions are not met, overtaking is harmful to all. More specifically, we found that a social dilemma emerges in the vicinity of the transition to the congested traffic if the probability of random deceleration is low, which can also happen in more realistic single-lane models. The essential mechanism creating the social dilemma is the abrupt deceleration when the overtaking car returns to its lane. We analyze how the payoffs depend on the frequency of strategies in the population to conclude that the drivers that overtake are defectors and the ones that do not are cooperators, analogous to the strategies in tragedy of the commons class of games.

physics.soc-ph↗

arXiv2019

Moderate death rates can be beneficial for the evolution of cooperation

Spatial structure is one of the simplest and most studied ecological factors that affect the evolution of cooperation. It has been shown that spatial reciprocity promotes cooperation due to the formation of cooperative clusters, which provide mutual support against defectors. The usual assumption is that of constant population size, where no density-related effect is possible. Here, we extend the investigation of density-related effects on the evolution of cooperation. We integrate evolutionary game theory to the Lattice Lotka-Volterra Model. In our model, the birth rate depends on the local density and on the payoff accumulated in the interactions. We characterize the evolution of cooperation in terms of the coexistence and the extinction of the types. The main result is that cooperation is most favoured at moderate levels of the death rate. Interestingly, defectors are extinct at values of the death rate that are lower than that at which cooperators are extinct. When death knocks the door, defectors are the first to perish, whereas cooperators stand longer due to mutual support.

q-bio.PE↗

arXiv2017

Cooperation in public goods games: stay, but not for too long

Cooperation in repeated public goods game is hardly achieved, unless contingent behavior is present. Surely, if mechanisms promoting positive assortment between cooperators are present, then cooperators may beat defectors, because cooperators would collect greater payoffs. In the context of evolutionary game theory, individuals that always cooperate cannot win the competition against defectors in well-mixed populations. Here, we study the evolution of a population where fitness is obtained in repeated public goods games and players have a fixed probability of playing the next round. As a result, the group size decreases during the game. The population is well-mixed and there are only two available strategies: always cooperate (ALLC) or always defect (ALLD). Through numerical calculation and analytical approximations we show that cooperation can emerge if the players stay playing the game, but not for too long. The essential mechanism is the interaction between the transition from strong to weak altruism, as the group size decreases, and the existence of an upper limit to the number of rounds representing limited time availability.

physics.soc-ph↗

arXiv2017

Role-separating ordering in social dilemmas controlled by topological frustration

"Three is a crowd" is an old proverb that applies as much to social interactions, as it does to frustrated configurations in statistical physics models. Accordingly, social relations within a triangle deserve special attention. With this motivation, we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice. This topology provides an irreconcilable frustration, which prevents anti-coordination of competing strategies that would be needed for an optimal outcome of the game. By using different strategy updating protocols, we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb-like organization, which helps to minimize the negative consequence of the topological frustration. We relate the emergence of these patterns to the microscopic dynamics of the evolutionary process, both by means of mean-field approximations and Monte Carlo simulations. For comparison, we also consider the same evolutionary dynamics on the square lattice, where of course the topological frustration is absent. However, with the deletion of diagonal links of the triangular lattice, we can gradually bridge the gap to the square lattice. Interestingly, in this case the level of cooperation in the system is a direct indicator of the level of topological frustration, thus providing a method to determine frustration levels in an arbitrary interaction network.

physics.soc-ph↗

arXiv2016

Stochastic win-stay-lose-shift strategy with dynamic aspirations in evolutionary social dilemmas

In times of plenty expectations rise, just as in times of crisis they fall. This can be mathematically described as a Win-Stay-Lose-Shift strategy with dynamic aspiration levels, where individuals aspire to be as wealthy as their average neighbor. Here we investigate this model in the realm of evolutionary social dilemmas on the square lattice and scale-free networks. By using the master equation and Monte Carlo simulations, we find that cooperators coexist with defectors in the whole phase diagram, even at high temptations to defect. We study the microscopic mechanism that is responsible for the striking persistence of cooperative behavior and find that cooperation spreads through second-order neighbors, rather than by means of network reciprocity that dominates in imitation-based models. For the square lattice the master equation can be solved analytically in the large temperature limit of the Fermi function, while for other cases the resulting differential equations must be solved numerically. Either way, we find good qualitative agreement with the Monte Carlo simulation results. Our analysis also reveals that the evolutionary outcomes are to a large degree independent of the network topology, including the number of neighbors that are considered for payoff determination on lattices, which further corroborates the local character of the microscopic dynamics. Unlike large-scale spatial patterns that typically emerge due to network reciprocity, here local checkerboard-like patterns remain virtually unaffected by differences in the macroscopic properties of the interaction network.

physics.soc-ph↗

arXiv2016

Evolutionary mixed games in structured populations: Cooperation and the benefits of heterogeneity

Evolutionary games on networks traditionally involve the same game at each interaction. Here we depart from this assumption by considering mixed games, where the game played at each interaction is drawn uniformly at random from a set of two different games. While in well-mixed populations the random mixture of the two games is always equivalent to the average single game, in structured populations this is not always the case. We show that the outcome is in fact strongly dependent on the distance of separation of the two games in the parameter space. Effectively, this distance introduces payoff heterogeneity, and the average game is returned only if the heterogeneity is small. For higher levels of heterogeneity the distance to the average game grows, which often involves the promotion of cooperation. The presented results support preceding research that highlights the favorable role of heterogeneity regardless of its origin, and they also emphasize the importance of the population structure in amplifying facilitators of cooperation.

physics.soc-ph↗

arXiv2015

Cooperation in two-dimensional mixed-games

Evolutionary game theory is a common framework to study the evolution of cooperation, where it is usually assumed that the same game is played in all interactions. Here, we investigate a model where the game that is played by two individuals is uniformly drawn from a sample of two different games. Using the master equation approach we show that the random mixture of two games is equivalent to play the average game when (i) the strategies are statistically independent of the game distribution and (ii) the transition rates are linear functions of the payoffs. We also use Monte-Carlo simulations in a two dimensional lattice and mean-field techniques to investigate the scenario when the two above conditions do not hold. We find that even outside of such conditions, several quantities characterizing the mixed-games are still the same as the ones obtained in the average game when the two games are not very different.

physics.soc-ph↗

arXiv2015

Reactive Strategies: The Establishment of Cooperation

Cooperation is usually represented as a Prisoner's Dilemma game. Although individual self-interest may not favour cooperation, cooperation can evolve if, for example, players interact multiple times adjusting their behaviour accordingly to opponent's previous action. To analyze population dynamics, replicator equation has been widely used under several versions. Although it is usually stated that a strategy called Generous-tit-for-tat is the winner within the reactive strategies set, here we show that this result depends on replicator's version and on the number of available strategies, stemming from the fact that a dynamics system is also defined by the number of available strategies and not only by the model version. Using computer simulations and analytical arguments, we show that Generous-tit-for-tat victory is found only if the number of strategies available is not too large, with defection winning otherwise.

physics.soc-ph↗

arXiv2010

Distinguishing the opponents in the prisoner dilemma in well-mixed populations

Here we study the effects of adopting different strategies against different opponent instead of adopting the same strategy against all of them in the prisoner dilemma structured in well-mixed populations. We consider an evolutionary process in which strategies that provide reproductive success are imitated and players replace one of their worst interactions by the new one. We set individuals in a well-mixed population so that network reciprocity effect is excluded and we analyze both synchronous and asynchronous updates. As a consequence of the replacement rule, we show that mutual cooperation is never destroyed and the initial fraction of mutual cooperation is a lower bound for the level of cooperation. We show by simulation and mean-field analysis that for synchronous update cooperation dominates while for asynchronous update only cooperations associated to the initial mutual cooperations are maintained. As a side effect of the replacement rule, an "implicit punishment" mechanism comes up in a way that exploitations are always neutralized providing evolutionary stability for cooperation.

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