Cooperation in the face of crisis: effect of demographic noise in collective-risk social dilemmas.

In deciding whether to contribute to a public good, people often face a social dilemma known as the tragedy of the commons: either bear the cost of promoting the collective welfare, or free-ride on the efforts of others. Here, we study the dynamics of cooperation in the context of the threshold public goods games, in which groups must reach a cumulative target contribution to prevent a potential disaster, such as an environmental crisis or social unrest, that could result in the loss of all private wealth. The catch is that the crisis may never materialize, and the investment in the public good is lost. Overall, higher risk of loss promotes cooperation, while larger group size tends to undermine it. For most parameter settings, free-riders (defectors) cannot be eliminated from the population, leading to a coexistence equilibrium between cooperators and defectors for infinite populations. However, this equilibrium is unstable under the effect of demographic noise (finite population), since the cooperator-only and defector-only states are the only absorbing states of the stochastic dynamics. We use simulations and finite-size scaling to show that cooperators eventually die off and derive scaling laws for the transient lifetimes or half-lives of the coexistence metastable state. We find that for high risk, the half-life of cooperators increases exponentially with population size, while for low risk, it decreases exponentially with population size. At the risk threshold, where the coexistence regime appears in a discontinuous manner, the half-life increases with a power of the population size.

Simulating pedestrian avoidance: The human-zombie game.

This study introduces a simulated active matter system, applying the pedestrian collision avoidance paradigm, which involves dynamically adjusting the desired velocity. We present a human-zombie game set within a closed geometry, combining predator-prey behavior with a one-way contagion process that transforms prey into predators. The system demonstrates varied responses in our implemented model: with agents having the same maximum speeds, a single zombie always captures a human, whereas two zombies never capture a single human agent. As the number of human agents increases, observables such as the final fraction of zombie agents and total conversion times exhibit significant changes in the system's behavior at intermediate density values. Most notably, there is evidence of a first-order phase transition when analyzing the mean population speed as an order parameter.

Ambush strategy enhances organisms' performance in rock-paper-scissors games.

We study a five-species cyclic system wherein individuals of one species strategically adapt their movements to enhance their performance in the spatial rock-paper-scissors game. Environmental cues enable the awareness of the presence of organisms targeted for elimination in the cyclic game. If the local density of target organisms is sufficiently high, individuals move towards concentrated areas for direct attack; otherwise, they employ an ambush tactic, maximising the chances of success by targeting regions likely to be dominated by opponents. Running stochastic simulations, we discover that the ambush strategy enhances the likelihood of individual success compared to direct attacks alone, leading to uneven spatial patterns characterised by spiral waves. We compute the autocorrelation function and measure how the ambush tactic unbalances the organisms' spatial organisation by calculating the characteristic length scale of typical spatial domains of each species. We demonstrate that the threshold for local species density influences the ambush strategy's effectiveness, while the neighbourhood perception range significantly impacts decision-making accuracy. The outcomes show that long-range perception improves performance by over 60%, although there is potential interference in decision-making under high attack triggers. Understanding how organisms' adaptation their environment enhances their performance may be helpful not only for ecologists, but also for data scientists, aiming to improve artificial intelligence systems.

Discipline and punishment in panoptical public goods games.

In Public Goods Games (PGG), the temptation to free-ride on others' contributions poses a significant threat to the sustainability of cooperative societies. Therefore, societies strive to mitigate this through incentive systems, employing rewards and punishments to foster cooperative behavior. Thus, peer punishment, in which cooperators sanction defectors, as well as pool punishment, where a centralized punishment institution executes the punishment, is deeply analyzed in previous works. Although the literature indicates that these methods may enhance cooperation on social dilemmas under particular contexts, there are still open questions, for instance, the structural connection between graduated punishment and the monitoring of public goods games. Our investigation proposes a compulsory PGG framework under Panoptical surveillance. Inspired by Foucault's theories on disciplinary mechanisms and biopower, we present a novel mathematical model that scrutinizes the balance between the severity and scope of punishment to catalyze cooperative behavior. By integrating perspectives from evolutionary game theory and Foucault's theories of power and discipline, this research uncovers the theoretical foundations of mathematical frameworks involved in punishment and discipline structures. We show that well-calibrated punishment and discipline schemes, leveraging the panoptical effect for universal oversight, can effectively mitigate the free-rider dilemma, fostering enhanced cooperation. This interdisciplinary approach not only elucidates the dynamics of cooperation in societal constructs but also underscores the importance of integrating diverse methodologies to address the complexities of fostering cooperative evolution.

Evolution of cooperation in a two-species system with a common resource pool.

Understanding the evolution of cooperation is a major question in Evolutionary Biology. Here, we extend a previously proposed mathematical model in Evolutionary Game Theory that investigated how resource use by a single species composed of cooperators and defectors may lead to its maintenance or extinction. We include another species in the model, so as to investigate how different intra and interspecific interactions of cooperative or competitive nature among individuals that share the same essential resource may drive the survival and evolution of the species. Several outcomes emerge from the model, depending on the configuration of the payoff matrix, the individual contribution to the resource pool, the competition intensity between species, and the initial conditions of the system dynamics. Observed results include scenarios in which species thrive due to the action of cooperators, but also scenarios in which both species collapse due to lack of cooperation and, consequently, of resources. In particular, a high initial availability of resources may be the determinant factor to the survival of both species. Interestingly, cooperation may be more favored when individuals have less incentive to cooperate with others, and the survival of their populations may depend crucially on their competitive capacities.

Emergent cooperative behavior in transient compartments.

We introduce a minimal model of multilevel selection on structured populations, considering the interplay between game theory and population dynamics. Through a bottleneck process, finite groups are formed with cooperators and defectors sampled from an infinite pool. After the fragmentation, these transient compartments grow until the maximal number of individuals per compartment is attained. Eventually, all compartments are merged and well mixed, and the whole process is repeated. We show that cooperators, even if interacting only through mean-field intragroup interactions that favor defectors, may perform well because of the intergroup competition and the size diversity among the compartments. These cycles of isolation and coalescence may therefore be important in maintaining diversity among different species or strategies and may help to understand the underlying mechanisms of the scaffolding processes in the transition to multicellularity.

A Spatial Kinetic Model of Crowd Evacuation Dynamics with Infectious Disease Contagion.

This paper proposes a kinetic theory approach coupling together the modeling of crowd evacuation from a bounded domain with exit doors and infectious disease contagion. The spatial movement of individuals in the crowd is modeled by a proper description of the interactions with people in the crowd and the environment, including walls and exits. At the same time, interactions among healthy and infectious individuals may generate disease spreading if exposure time is long enough. Immunization of the population and individual awareness to contagion is considered as well. Interactions are modeled by tools of game theory, that let us propose the so-called tables of games that are introduced in the general kinetic equations. The proposed model is qualitatively studied and, through a series of case studies, we explore different scenarios related to crowding and gathering formation within indoor venues under the spread of a respiratory infectious disease, obtaining insights on specific policies to reduce contagion that may be implemented.

Medida Decomposta de Valor Social: uma alternativa baseada na Teoria dos Jogos / Decomposed Social Value Measure: an alternative based on Game Theory / Medida Descompuesta de Valor Social: una alternativa basada en la Teoría de Juegos

Orientação de valor social (OVS) é uma característica individual que expressa o valor que se atribui aos ganhos individuais e aos gerados às outras pessoas, revelando disposição para sacrificar interesses pessoais. O presente estudo teve como objetivo adaptar e reunir evidências de validade para a Decomposed Social Value Orientation Slider Measure, como alternativa a instrumentos tradicionais de autorrelato. A amostra foi composta por 176 respondentes, que responderam à medida adaptada, à Escala de Cooperação e Competitividade e a uma versão impressa do dilema do prisioneiro. Os resultados mostraram que a medida se correlacionou negativamente com atitudes competitivas. Não houve diferenças significativas nos escores de OVS em função das escolhas no dilema dos prisioneiros. São discutidas as propriedades psicométricas do instrumento, as limitações e potenciais usos nas pesquisas sobre dilemas sociais e cooperação.(AU)

Social Value Orientation (SVO) is an individual characteristic that expresses the value one attributes to their own and other people's results, while revealing the disposition to sacrifice personal interests. The present study aimed to adapt and gather evidence of validity for the Social Value Orientation Slider Measure, as an alternative to traditional self-report instruments. Participants (N=176) answered the measure, the Cooperation-Competitiveness Scale, and a printed version of the prisoner's dilemma. The SVO was negatively correlated with competitive attitudes. There were no differences in SVO scores based on the prisoner's dilemma choices. The psychometric properties of the measure and its limitations and potential uses in social dilemma and cooperation research, are discussed.(AU)

La orientación al valor social (OVS) es una característica individual que expresa el valor atribuido a los beneficios individuales y a los beneficios generados a otras personas, revelando una disposición a sacrificar intereses personales. El presente estudio tuvo como objetivo adaptar y reunir evidencias de validez para la Decomposed Social Value Orientation Slider Measure, como alternativa a los instrumentos tradicionales de autoinforme. La muestra se conformó por 176 personas, que respondieron a la medida adaptada, a la Escala de Cooperación y Competitividad y a una versión impresa del dilema del prisionero. Los resultados mostraron que la medida se correlacionó negativamente con las actitudes competitivas. No hubo diferencias significativas en las puntuaciones de la OVS en función de las elecciones en el dilema del prisionero. Se discuten las propiedades psicométricas del instrumento, las limitaciones y los usos potenciales en la investigación sobre dilemas sociales y cooperación.(AU)

Random multi-player games.

The study of evolutionary games with pairwise local interactions has been of interest to many different disciplines. Also, local interactions with multiple opponents had been considered, although always for a fixed amount of players. In many situations, however, interactions between different numbers of players in each round could take place, and this case cannot be reduced to pairwise interactions. In this work, we formalize and generalize the definition of evolutionary stable strategy (ESS) to be able to include a scenario in which the game is played by two players with probability p and by three players with the complementary probability 1-p. We show the existence of equilibria in pure and mixed strategies depending on the probability p, on a concrete example of the duel-truel game. We find a range of p values for which the game has a mixed equilibrium and the proportion of players in each strategy depends on the particular value of p. We prove that each of these mixed equilibrium points is ESS. A more realistic way to study this dynamics with high-order interactions is to look at how it evolves in complex networks. We introduce and study an agent-based model on a network with a fixed number of nodes, which evolves as the replicator equation predicts. By studying the dynamics of this model on random networks, we find that the phase transitions between the pure and mixed equilibria depend on probability p and also on the mean degree of the network. We derive mean-field and pair approximation equations that give results in good agreement with simulations on different networks.

Self-organized division of cognitive labor.

Often members of a group benefit from dividing the group's task into separate components, where each member specializes their role so as to accomplish only one of the components. While this division of labor phenomenon has been observed with respect to both manual and cognitive labor, there is no clear understanding of the cognitive mechanisms allowing for its emergence, especially when there are multiple divisions possible and communication is limited. Indeed, maximization of expected utility often does not differentiate between alternative ways in which individuals could divide labor. We developed an iterative two-person game in which there are multiple ways of dividing labor, but in which it is not possible to explicitly negotiate a division. We implemented the game both as a human experimental task and as a computational model. Our results show that the majority of human dyads can finish the game with an efficient division of labor. Moreover, we fitted our computational model to the behavioral data, which allowed us to explain how the perceived similarity between a player's actions and the task's focal points guided the players' choices from one round to the other, thus bridging the group dynamics and its underlying cognitive process. Potential applications of this model outside cognitive science include the improvement of cooperation in human groups, multi-agent systems, as well as human-robot collaboration.

Symbiotic behaviour in the public goods game with altruistic punishment.

Finding ways to overcome the temptation to exploit one another is still a challenge in behavioural sciences. In the framework of evolutionary game theory, punishing strategies are frequently used to promote cooperation in competitive environments. Here, we introduce altruistic punishers in the spatial public goods game. This strategy acts as a cooperator in the absence of defectors, otherwise it will punish all defectors in their vicinity while bearing a cost to do so. We observe three distinct behaviours in our model: i) in the absence of punishers, cooperators (who don't punish defectors) are driven to extinction by defectors for most parameter values; ii) clusters of punishers thrive by sharing the punishment costs when these are low; iii) for higher punishment costs, punishers, when alone, are subject to exploitation but in the presence of cooperators can form a symbiotic spatial structure that benefits both. This last observation is our main finding since neither cooperation nor punishment alone can survive the defector strategy in this parameter region and the specificity of the symbiotic spatial configuration shows that lattice topology plays a central role in sustaining cooperation. Results were obtained by means of Monte Carlo simulations on a square lattice and subsequently confirmed by a pairwise comparison of different strategies' payoffs in diverse group compositions, leading to a phase diagram of the possible states.

Prelúdio para uma filosofia do jogo: a definição de Bernard Suits / Prelude for a philosophy of games: Bernard Suits's definition / Preludio para una filosofía del juego: la definición de Bernard Suits

Resumo Parte-se do pressuposto de que o filósofo americano Bernard Suits é central para a filosofia do esporte, especialmente na literatura internacional. Sua extensa obra oferece uma teoria do Jogo original e ainda não explorada na Educação Física brasileira. Suits distingue o fenômeno Jogo (game) da experiência do jogar (play), além de propor uma definição analítica de Jogo que é aqui apresentada aos modos de um prelúdio de sua teoria. Discute-se que, do ponto de vista de uma filosofia analítica, avança-se na metafísica do Jogo, ou em uma efetiva filosofia do Jogo, quando mobilizamos a definição de Suits de jogar um Jogo (game-playing). Reconhecem-se ainda subsídios analíticos distintos da definição intencionalmente vaga de famílias de jogos da herança wittgensteiniana, influente nas concepções brasileiras. Acredita-se que tais recursos fornecem renovado material para os estudos do Jogo na filosofia do esporte e Educação Física brasileiras, nos domínios da metafísica, lógica, epistemologia e axiologia.

Abstract It is assumed that the American philosopher Bernard Suits is central to the philosophy of sport, especially in the international literature. His extensive work offers an original and unexplored theory of game in Brazilian Physical Education. Suits distinguishes the phenomenon of game from the experience of playing, in addition to proposing an analytical definition of game that is presented in the ways of a prelude to his theory. It is argued that, from the point of view of an analytical philosophy, one advances into the metaphysics of games, or an effective philosophy of the game, when Suits's definition of game-playing is mobilized. One also recognizes different analytical subsidies from the intentionally vague definition of game families of Wittgensteinian heritage, influential in Brazilian conceptions. It is believed that such resources provide new material for game studies in Brazilian sport philosophy and Physical Education, in the domains of metaphysics, logic, epistemology and axiology.

Resumen Se parte del supuesto de que el filósofo estadounidense Bernard Suits es fundamental para la filosofía del deporte, especialmente en la literatura internacional. Su extensa obra ofrece una teoría de juegos original y aún inexplorada en la Educación Física brasileña. Suits distingue el fenómeno juego (game) de la experiencia de jugar (play), además de proponer una definición analítica de juego, presentada aquí como un preludio a su teoría. Se discute que, desde el punto de vista de una filosofía analítica, se avanza en la metafísica del juego, o en una efectiva filosofía del juego, cuando movilizamos la definición de Suits de jugar un juego (game-playing). Se reconocen, además, subsidios analíticos distintos a la definición intencionalmente vaga de familias de juegos de la herencia wittgensteiniana, que tiene influencia en las concepciones brasileñas. Se cree que tales recursos brindan renovado material para los estudios del juego en la filosofía del deporte y en la Educación Física brasileñas, en los dominios de la metafísica, la lógica, la epistemología y la axiología.

MECHANISMS Study: Using Game Theory to Assess the Effects of Social Norms and Social Networks on Adolescent Smoking in Schools-Study Protocol.

This proof of concept study harnesses novel transdisciplinary insights to contrast two school-based smoking prevention interventions among adolescents in the UK and Colombia. We compare schools in these locations because smoking rates and norms are different, in order to better understand social norms based mechanisms of action related to smoking. We aim to: (1) improve the measurement of social norms for smoking behaviors in adolescents and reveal how they spread in schools; (2) to better characterize the mechanisms of action of smoking prevention interventions in schools, learning lessons for future intervention research. The A Stop Smoking in Schools Trial (ASSIST) intervention harnesses peer influence, while the Dead Cool intervention uses classroom pedagogy. Both interventions were originally developed in the UK but culturally adapted for a Colombian setting. In a before and after design, we will obtain psychosocial, friendship, and behavioral data (e.g., attitudes and intentions toward smoking and vaping) from ~300 students in three schools for each intervention in the UK and the same number in Colombia (i.e., ~1,200 participants in total). Pre-intervention, participants take part in a Rule Following task, and in Coordination Games that allow us to assess their judgments about the social appropriateness of a range of smoking-related and unrelated behaviors, and elicit individual sensitivity to social norms. After the interventions, these behavioral economic experiments are repeated, so we can assess how social norms related to smoking have changed, how sensitivity to classroom and school year group norms have changed and how individual changes are related to changes among friends. This Game Theoretic approach allows us to estimate proxies for norms and norm sensitivity parameters and to test for the influence of individual student attributes and their social networks within a Markov Chain Monte Carlo modeling framework. We identify hypothesized mechanisms by triangulating results with qualitative data from participants. The MECHANISMS study is innovative in the interplay of Game Theory and longitudinal social network analytical approaches, and in its transdisciplinary research approach. This study will help us to better understand the mechanisms of smoking prevention interventions in high and middle income settings.

Fixation probabilities for the Moran process with three or more strategies: general and coupling results.

We study fixation probabilities for the Moran stochastic process for the evolution of a population with three or more types of individuals and frequency-dependent fitnesses. Contrary to the case of populations with two types of individuals, in which fixation probabilities may be calculated by an exact formula, here we must solve a large system of linear equations. We first show that this system always has a unique solution. Other results are upper and lower bounds for the fixation probabilities obtained by coupling the Moran process with three strategies with birth-death processes with only two strategies. We also apply our bounds to the problem of evolution of cooperation in a population with three types of individuals already studied in a deterministic setting by Núñez Rodríguez and Neves (J Math Biol 73:1665-1690, 2016). We argue that cooperators will be fixated in the population with probability arbitrarily close to 1 for a large region of initial conditions and large enough population sizes.

Evolutionary game inspired by Cipolla's basic laws of human stupidity.

In this work we present an evolutionary game inspired by the work of Carlo Cipolla entitled The Basic Laws of Human Stupidity. The game expands the classical scheme of two archetypical strategies, collaborators and defectors, by including two additional strategies. One of these strategies is associated with a stupid player that, according to Cipolla, is the most dangerous one as it undermines the global wealth of the population. By considering a spatial evolutionary game and imitation dynamics that go beyond the paradigm of a rational player we explore the impact of Cipolla's ideas and analyze the extent of the damage that stupid players inflict on the population.

A Game Theory-Based Model for Predicting Depression due to Frustration in Competitive Environments.

A computational model based on game theory is here proposed to forecast the prevalence of depression caused by frustration in a competitive environment. This model comprises a spatially structured game, in which the individuals are socially connected. This game, which is equivalent to the well-known prisoner's dilemma, represents the payoffs that can be received by the individuals in the labor market. These individuals may or may not have invested in a formal academic education. It is assumed that an individual becomes depressed when the difference between the average payoff earned by the neighbors in this game and the personal payoff surpasses a critical number, which can be distinct for men and women. Thus, the transition to depression depends on two thresholds, whose values are tuned for the model accurately predicting the percentage of individuals that become depressed due to a frustrating payoff. Here, this tuning is performed by using data of young adults living in the United Kingdom in 2014-2016.

Plans and plays. / Planes y juegos.

This article is structured around two concepts - planning (as the attempt to predict the future through reason) and play (as freedom in the present) - used to discuss work processes, organizational forms, institutionality and the management of public institutions in the social field, with an emphasis on the fields of health and education. Based on Nietzche's reflection regarding the mythological figures of Dionysus and Apollo, a synthesis of the development of planning in Latin America is carried out with the aid of works by Carlos Matus and Mario Testa. From this perspective, play is analyzed over the course of history, in addition to the proposal of Homo ludens and the unrecognized role of play in the day life of social institutions. However, understanding the game does not guarantee that the forms of playing it will change. Therein lie the complexity and challenges that must be considered in relation to structures that are both structuring and structured by the actions of their agents, in the framework of processes of reproduction and social domination that naturalize current institutional forms.

Este artículo se estructura sobre dos conceptos: la planificación (como intento de predicción del futuro a través de la razón) y el juego (en tanto libertad en el presente), desde los cuales se discuten los procesos de trabajo, las formas organizativas, la institucionalidad y la gestión de las instituciones públicas del campo social, con énfasis en las del campo de la salud y la educación. A partir del planteo de Nietzsche sobre las figuras mitológicas griegas Dionisio y Apolo, se realiza una síntesis del desarrollo de la planificación en América Latina a través de Carlos Matus y Mario Testa para, desde allí, analizar el juego a lo largo de la historia, la propuesta del Homo ludens y la presencia no reconocida del juego en el cotidiano de las instituciones sociales. Entender el juego no garantiza que se cambien las formas en que se lo juega. Allí reside la complejidad y el desafío que debe ser pensado en la relación de estructuras que son estructurantes pero que, a su vez, son estructuradas por la acción de sus agentes, en el marco de procesos de reproducción y dominación social que naturalizan las formas institucionales vigentes.

Long-term evidence on cooperation and cultural differences in public goods dilemmas.

It is hard to isolate human cooperation features outside the prevalent experimental laboratory context in a controlled setting. Since cooperation rates are very context-sensitive, a new setting-a public goods game in an online game-is analysed. This unique dataset addresses multiple critical issues: it is more realistic, individuals have an intrinsic motivation to play, there are no observer effects, and data are available for more than 18 000 individuals playing over 10 months. Participants come from 10 countries, which allows us to test for cultural influences on cooperation. We find small differences in cooperation rates between countries, ranging from 8.5% (Argentina) to 14.1% (Greece). Moreover, cooperation remains stable over long periods of time. Different cultural, economic and religious backgrounds do not seem to have a discernible influence on cooperation rates. Instead, individual differences seem to play a larger role. Finally, cooperation levels may be lower than suggested by experiments from the classical laboratory context.

Positive interactions may decrease cooperation in social dilemma experiments.

A social dilemma appears in the public goods problem, where the individual has to decide whether to contribute to a common resource. The total contributions to the common pool are increased by a synergy factor and evenly split among the members. The ideal outcome occurs if everyone contributes the maximum amount. However, regardless of what the others do, each individual is better off by contributing nothing. Yet, cooperation is largely observed in human society. Many mechanisms have been shown to promote cooperation in humans, alleviating, or even resolving, the social dilemma. One class of mechanisms that is under-explored is the spillover of experiences obtained from different environments. There is some evidence that positive experiences promote cooperative behaviour. Here, we address the question of how experiencing positive cooperative interactions - obtained in an environment where cooperation yields high returns - affects the level of cooperation in social dilemma interactions. In a laboratory experiment, participants played repeated public goods games (PGGs) with rounds alternating between positive interactions and social dilemma interactions. We show that, instead of promoting pro-social behaviour, the presence of positive interactions lowered the level of cooperation in the social dilemma interactions. Our analysis suggests that the high return obtained in the positive interactions sets a reference point that accentuates participants' perceptions that contributing in social dilemma interactions is a bad investment.

Fixation probabilities for the Moran process in evolutionary games with two strategies: graph shapes and large population asymptotics.

This paper is based on the complete classification of evolutionary scenarios for the Moran process with two strategies given by Taylor et al. (Bull Math Biol 66(6):1621-1644, 2004. https://doi.org/10.1016/j.bulm.2004.03.004 ). Their classification is based on whether each strategy is a Nash equilibrium and whether the fixation probability for a single individual of each strategy is larger or smaller than its value for neutral evolution. We improve on this analysis by showing that each evolutionary scenario is characterized by a definite graph shape for the fixation probability function. A second class of results deals with the behavior of the fixation probability when the population size tends to infinity. We develop asymptotic formulae that approximate the fixation probability in this limit and conclude that some of the evolutionary scenarios cannot exist when the population size is large.