Evolutionary Game Theoretic Models Research Articles

Convergence of reputations under indirect reciprocity

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

Gaps in modelling animal migration with evolutionary game theory: infection can favour the loss of migration.

Ongoing environmental changes alter how natural selection shapes animal migration. Understanding how these changes play out theoretically can be done using evolutionary game theoretic (EGT) approaches, such as looking for evolutionarily stable strategies. Here, we first describe historical patterns of how EGT models have explored different drivers of migration. We find that there are substantial gaps in both the taxa (mammals, amphibians, reptiles, insects) and mechanisms (mutualism, interspecific competition) included in past EGT models of migration. Although enemy interactions, including parasites, are increasingly considered in models of animal migration, they remain the least studied of factors for migration considered to date. Furthermore, few papers look at changes in migration in response to perturbations (e.g. climate change, new species interactions). To address this gap, we present a new EGT model to understand how infection with a novel parasite changes host migration. We find three possible outcomes when migrants encounter novel parasites: maintenance of migration (despite the added infection cost), loss of migration (evolutionary shift to residency) or population collapse, depending on the risk and cost of getting infected, and the cost currency. Our work demonstrates how emerging infection can alter animal behaviour such as migration. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

Game Modeling of the Political Space: Analysis of Foreign Literature

Purpose is to identify the main trends and gaps in the research of foreign scientists on the topic “Game modeling of political space”.Methods. In this review, the authors used a semi-systematic method of researching the literature, in which at the first stage they used quantitative methods, and then the selected array of publications was investigated by the integrative method, revealing theoretical studies and practical results of the application of game political components.Results. Based on the selected foreign publication stream on the topic “game modeling of political space” by the method of semi-systematic analysis, six main trends in the study and application of game theory and game modeling in political discourse have been identified:considering the value of game modeling through the prism of interaction, not collision of actors;application of game modeling in the development and adoption of political decisions;development of new approaches to the analysis of the very methodology of game modeling in politics;game as a form of effective political communication;study of game theory on the basis of fundamental classical monographs of the mid-20th century as applied to the solution of pressing political problems;application of game modeling in predicting election results, especially in those political systems that are based on the theory of rational choice during voting.A lacuna in the studies of recent decades has identified the issue of using political game modeling in electoral processes. Despite the continuing relevance of the topic of elections around the world, no significant volume of publications was selected.Conclusions. Foreign researchers use the potential of game modeling in politics more often and more multifaceted than in domestic political science. Evolutionary game-theoretic models are used not only to model political and international processes themselves, but also to related social spheres, such as economics, religious and ethnic relations. Game theory is used to study a wide range of social and political problems and social phenomena: voting, fundamentalism, religious and ethnic conflicts, civil violence.

Integrating evolutionary game theory and cross-cultural psychology to understand cultural dynamics.

In this article, we show that an evolutionary game theoretic (EGT) modeling approach can be fruitfully integrated with research in cross-cultural psychology to provide insight into cultural dynamics. EGT was initially developed to model biological evolution, but has been increasingly used to study the evolution of human behavior. Through "virtual experimentation," EGT models can be used to test the effects of various factors on the trajectories of behavioral change at the population level. We illustrate how EGT models can provide new insights into processes of cultural adaptation, transmission, maintenance, and change. We conclude with the strengths and limitations of using EGT to study cultural dynamics and new frontiers that await investigation. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Chaotic dynamics in the presence of medical malpractice litigation: A topological proof via linked twist maps for two evolutionary game theoretic contexts

In the present work we reconsider the evolutionary game theoretic models by Antoci et al. (2016, 2018) describing the dynamic outcomes arising from the interactions between patients and physicians, whose behavior is subject to clinical and legal risks. In particular, Antoci et al. (2016) analyzed the case of positive defensive medicine, while Antoci et al. (2018) dealt with the case of negative defensive medicine. We show that, when the models admit a nonisochronous center, it is possible to prove the existence of chaotic dynamics for the Poincaré map associated with those systems via the method of Linked Twist Maps (LTMs). To such aim we exploit in both frameworks, using a similar rationale, the periodic dependence on time of a model parameter influencing the position of the center and describing some risk associated with certain medical interventions, whose seasonal variation is empirically grounded. We also recall the ecological interpretation of the same model proposed by Harvie et al. (2007) and connected with intraspecific competition and environmental carrying capacity in predator-prey settings. In this case, it is sensible to assume a seasonal variation both for the carrying capacities and for the intrinsic growth rates of the two populations. Although such parameters influence the shape of the orbits, but do not affect the center position, we show that it is still possible to prove the existence of chaotic dynamics for the associated Poincaré map via the LTMs technique dealing with a different geometrical configuration for orbits in the phase plane.

Foresight in a Game of Leadership

Leadership can be effective in promoting cooperation within a group, but as the saying goes “heavy is the head that wears the crown”. A lot of debate still surrounds exactly what motivates individuals to expend the effort necessary to lead their groupmates. Evolutionary game theoretic models represent individual’s thought processes by strategy update protocols. The most common of these are random mutation, individual learning, selective imitation, and myopic optimization. Recently we introduced a new strategy update protocol - foresight - which takes into account future payoffs, and how groupmates respond to one’s own strategies. Here we apply our approach to a new 2 × 2 game, where one player, a leader, ensures via inspection and punishment that the other player, a subordinate, produces collective good. We compare the levels of inspection and production predicted by Nash Equilibrium, Quantal Response Equilibrium, level-k cognition, fictitious play, reinforcement learning, selective payoff-biased imitation, and foresight. We show that only foresight and selective imitation are effective at promoting contribution by the subordinate and inspection and punishment by the leader. The role of selective imitation in cultural and social evolution is well appreciated. In line with our prior findings, foresight is a viable alternative route to cooperation.

Violations of monotonicity in evolutionary models with sample-based beliefs

This paper considers a class of evolutionary game-theoretic models, namely those in which agents form beliefs about the behavior of others on the basis of random samples from the population. It shows that the dynamics of these models violate the property of monotonicity, which many authors have argued any well-specified evolutionary model should possess.

Simulated robots and the evolution of reciprocity

The relative rarity of reciprocity in nature, contrary to theoretical predictions that it should be widespread, is currently one of the major puzzles in social evolution theory. Here we use evolutionary robotics to solve this puzzle. We show that models based on game theory are misleading because they neglect the mechanics of behavior. In a series of experiments with simulated robots controlled by artificial neural networks, we find that reciprocity does not evolve, and show that this results from a general constraint that likely also prevents it from evolving in the wild. Reciprocity can evolve if it requires very few mutations, as is usually assumed in evolutionary game theoretic models, but not if, more realistically, it requires the accumulation of many adaptive mutations.

Evolutionary robotics simulations help explain why reciprocity is rare in nature.

The relative rarity of reciprocity in nature, contrary to theoretical predictions that it should be widespread, is currently one of the major puzzles in social evolution theory. Here we use evolutionary robotics to solve this puzzle. We show that models based on game theory are misleading because they neglect the mechanics of behavior. In a series of experiments with simulated robots controlled by artificial neural networks, we find that reciprocity does not evolve, and show that this results from a general constraint that likely also prevents it from evolving in the wild. Reciprocity can evolve if it requires very few mutations, as is usually assumed in evolutionary game theoretic models, but not if, more realistically, it requires the accumulation of many adaptive mutations.

The Inevitability of Ethnocentrism Revisited: Ethnocentrism Diminishes As Mobility Increases.

Nearly all major conflicts across the globe, both current and historical, are characterized by individuals defining themselves and others by group membership. This existence of group-biased behavior (in-group favoring and out-group hostile) has been well established empirically, and has been shown to be an inevitable outcome in many evolutionary studies. Thus it is puzzling that statistics show violence and out-group conflict declining dramatically over the past few centuries of human civilization. Using evolutionary game-theoretic models, we solve this puzzle by showing for the first time that out-group hostility is dramatically reduced by mobility. Technological and societal advances over the past centuries have greatly increased the degree to which humans change physical locations, and our results show that in highly mobile societies, one’s choice of action is more likely to depend on what individual one is interacting with, rather than the group to which the individual belongs. Our empirical analysis of archival data verifies that contexts with high residential mobility indeed have less out-group hostility than those with low mobility. This work suggests that, in fact, group-biased behavior that discriminates against out-groups is not inevitable after all.

Evolving to Generalize: Trading Precision for Speed

Biologists and philosophers of biology have argued that learning rules that do not lead organisms to play evolutionarily stable strategies (ESSes) in games will not be stable and thus not evolutionarily successful. This claim, however, stands at odds with the fact that learning generalization---a behavior that cannot lead to ESSes when modeled in games---is observed throughout the animal kingdom. In this paper, I use learning generalization to illustrate how previous analyses of the evolution of learning have gone wrong. It has been widely argued that the function of learning generalization is to allow for swift learning about novel stimuli. I show that in evolutionary game theoretic models learning generalization, despite leading to suboptimal behavior, can indeed speed learning. I further observe that previous analyses of the evolution of learning ignored the short term success of learning rules. If one drops this assumption, I argue, it can be shown that learning generalization will be expected to evolve in these models. I also use this analysis to show how ESS methodology can be misleading, and to reject previous justifications about ESS play derived from analyses of learning.

Bribe and Punishment: An Evolutionary Game-Theoretic Analysis of Bribery.

Harassment bribes, paid by citizens to corrupt officers for services the former are legally entitled to, constitute one of the most widespread forms of corruption in many countries. Nation states have adopted different policies to address this form of corruption. While some countries make both the bribe giver and the bribe taker equally liable for the crime, others impose a larger penalty on corrupt officers. We examine the consequences of asymmetric and symmetric penalties by developing deterministic and stochastic evolutionary game-theoretic models of bribery. We find that the asymmetric penalty scheme can lead to a reduction in incidents of bribery. However, the extent of reduction depends on how the players update their strategies over time. If the interacting members change their strategies with a probability proportional to the payoff of the alternative strategy option, the reduction in incidents of bribery is less pronounced. Our results indicate that changing from a symmetric to an asymmetric penalty scheme may not suffice in achieving significant reductions in incidents of harassment bribery.

Fairness and Trust in Structured Populations

Classical economic theory assumes that people are rational and selfish, but behavioral experiments often point to inconsistent behavior, typically attributed to “other regarding preferences.” The Ultimatum Game, used to study fairness, and the Trust Game, used to study trust and trustworthiness, have been two of the most influential and well-studied examples of inconsistent behavior. Recently, evolutionary biologists have attempted to explain the evolution of such preferences using evolutionary game theoretic models. While deterministic evolutionary game theoretic models agree with the classical economics predictions, recent stochastic approaches that include uncertainty and the possibility of mistakes have been successful in accounting for both the evolution of fairness and the evolution of trust. Here I explore the role of population structure by generalizing and expanding these existing results to the case of non-random interactions. This is a natural extension since such interactions do not occur randomly in the daily lives of individuals. I find that, in the limit of weak selection, population structure increases the space of fair strategies that are selected for but it has little-to-no effect on the optimum strategy played in the Ultimatum Game. In the Trust Game, in the limit of weak selection, I find that some amount of trust and trustworthiness can evolve even in a well-mixed population; however, the optimal strategy, although trusting if the return on investment is sufficiently high, is never trustworthy. Population structure biases selection towards strategies that are both trusting and trustworthy trustworthy and reduces the critical return threshold, but, much like in the case of fairness, it does not affect the winning strategy. Further considering the effects of reputation and structure, I find that they act synergistically to promote the evolution of trustworthiness.

Societal threat and cultural variation in the strength of social norms: An evolutionary basis

The strengths of social norms vary considerably across cultures, yet little research has shown whether such differences have an evolutionary basis. Integrating research in cross-cultural psychology with evolutionary game theory, we show that groups that face a high degree of threat develop stronger norms for organizing social interaction, with a higher degree of norm–adherence and higher punishment for deviant behavior. Conversely, groups that have little threat can afford to have weaker norms with less punishment for deviance. Our results apply to two kinds of norms: norms of cooperation, in which individuals must choose whether to cooperate (thereby benefitting everyone) or enrich themselves at the expense of others; and norms of coordination, in which there are several equally good ways for individuals to coordinate their actions, but individuals need to agree on which way to coordinate. This is the first work to show that different degrees of norm strength are evolutionarily adaptive to societal threat. Evolutionary game theoretic models of cultural adaptation may prove fruitful for exploring the causes of many other cultural differences that may be adaptive to particular ecological and historical contexts.

Evolutionary game theory on measure spaces: Well-posedness

An attempt is made to find a comprehensive mathematical framework in which to investigate the problems of well-posedness and asymptotic analysis for fully nonlinear evolutionary game theoretic models. The model should be rich enough to include all classical nonlinearities, e.g., Beverton–Holt or Ricker type. For several such models formulated on the space of integrable functions, it is known that as the variance of the payoff kernel becomes small the solution converges in the long term to a Dirac measure centered at the fittest strategy; thus the limit of the solution is not in the state space of integrable functions. Starting with the replicator–mutator equation and a generalized logistic equation as bases, a general model is formulated as a dynamical system on the state space of finite signed measures. Well-posedness is established, and then it is shown that by choosing appropriate payoff kernels this model includes all classical density models, both selection and mutation, and discrete and continuous strategy (trait) spaces.

Individual variation and the resolution of conflict over parental care in penduline tits

Eurasian penduline tits (Remiz pendulinus) have an unusually diverse breeding system consisting of frequent male and female polygamy, and uniparental care by the male or the female. Intriguingly, 30 to 40 per cent of all nests are deserted by both parents. To understand the evolution of this diverse breeding system and frequent clutch desertion, we use 6 years of field data to derive fitness expectations for males and females depending on whether or not they care for their offspring. The resulting payoff matrix corresponds to an asymmetric Snowdrift Game with two alternative evolutionarily stable strategies (ESSs): female-only and male-only care. This, however, does not explain the polymorphism in care strategies and frequent biparental desertion, because theory predicts that one of the two ESSs should have spread to fixation. Using a bootstrapping approach, we demonstrate that taking account of individual variation in payoffs explains the patterns of care better than a model based on the average population payoff matrix. In particular, a model incorporating differences in male attractiveness closely predicts the observed frequencies of male and female desertion. Our work highlights the need for a new generation of individual-based evolutionary game-theoretic models.

Dynamic social networks promote cooperation in experiments with humans

Human populations are both highly cooperative and highly organized. Human interactions are not random but rather are structured in social networks. Importantly, ties in these networks often are dynamic, changing in response to the behavior of one's social partners. This dynamic structure permits an important form of conditional action that has been explored theoretically but has received little empirical attention: People can respond to the cooperation and defection of those around them by making or breaking network links. Here, we present experimental evidence of the power of using strategic link formation and dissolution, and the network modification it entails, to stabilize cooperation in sizable groups. Our experiments explore large-scale cooperation, where subjects' cooperative actions are equally beneficial to all those with whom they interact. Consistent with previous research, we find that cooperation decays over time when social networks are shuffled randomly every round or are fixed across all rounds. We also find that, when networks are dynamic but are updated only infrequently, cooperation again fails. However, when subjects can update their network connections frequently, we see a qualitatively different outcome: Cooperation is maintained at a high level through network rewiring. Subjects preferentially break links with defectors and form new links with cooperators, creating an incentive to cooperate and leading to substantial changes in network structure. Our experiments confirm the predictions of a set of evolutionary game theoretic models and demonstrate the important role that dynamic social networks can play in supporting large-scale human cooperation.

Game Theory, Indirect Modeling, and the Origin of Morality

The idea that the origin of moral norms can be explained in Darwinian terms has been with us since Darwin himself. But recently it has taken a more promising form with the advent of evolutionary game theory. Combining concepts and formal tools from evolutionary biology and economics, current evolutionary game theoretic models embody a distinct picture of the origin of morality. On this picture morality is the product of cultural evolution. That is, the evolution of norms happens within culture as the aggregate product of individual-level behavioral learning. The circumstances in which moral norms come into play are represented as strategic interactions such as bargaining and cooperation/defection scenarios. A basic assumption is that social agents generally seek to improve their lot in such interactions and that they do so by learning from peers. Strategies that have secured higher payoffs will tend to spread, because social learners will tend to adopt them more readily. The result is a Darwinian process operating on top of the basic

A note on frequency dependence and the levels/units of selection

On the basis of distinctions between those properties of entities that can be defined without reference to other entities and those that (in different ways) cannot, this note argues that non-trivial forms of frequency-dependent selection of entities should be interpreted as selection occurring at a level higher than that of those entities. It points out that, except in degenerately simple cases, evolutionary game-theoretic models of selection are not models of individual selection. Similarly, models of genotypic selection such as heterosis cannot be legitimately interpreted as models of genic selection. The analysis presented here supports the views that: (i) selection should be viewed as a multi-level process; (ii) upper-level selection is ubiquitous; (iii) kin selection should be viewed as a type of group selection rather than individual selection; and (iv) inclusive fitness is not an individual property.

Payoff-Monotonic Game Dynamics and the Maximum Clique Problem

Evolutionary game-theoretic models and, in particular, the so-called replicator equations have recently proven to be remarkably effective at approximately solving the maximum clique and related problems. The approach is centered around a classic result from graph theory that formulates the maximum clique problem as a standard (continuous) quadratic program and exploits the dynamical properties of these models, which, under a certain symmetry assumption, possess a Lyapunov function. In this letter, we generalize previous work along these lines in several respects. We introduce a wide family of game-dynamic equations known as payoff-monotonic dynamics, of which replicator dynamics are a special instance, and show that they enjoy precisely the same dynamical properties as standard replicator equations. These properties make any member of this family a potential heuristic for solving standard quadratic programs and, in particular, the maximum clique problem. Extensive simulations, performed on random as well as DIMACS benchmark graphs, show that this class contains dynamics that are considerably faster than and at least as accurate as replicator equations. One problem associated with these models, however, relates to their inability to escape from poor local solutions. To overcome this drawback, we focus on a particular subclass of payoff-monotonic dynamics used to model the evolution of behavior via imitation processes and study the stability of their equilibria when a regularization parameter is allowed to take on negative values. A detailed analysis of these properties suggests a whole class of annealed imitation heuristics for the maximum clique problem, which are based on the idea of varying the parameter during the imitation optimization process in a principled way, so as to avoid unwanted inefficient solutions. Experiments show that the proposed annealing procedure does help to avoid poor local optima by initially driving the dynamics toward promising regions in state space. Furthermore, the models outperform state-of-the-art neural network algorithms for maximum clique, such as mean field annealing, and compare well with powerful continuous-based heuristics.