Asymmetric Evolutionary Games

Study on the interior equilibrium point of a special class of 2 × 2 × 2 asymmetric evolutionary games

Many behavioural interactions in real life involve three individuals. When each individual has two alternative strategies, they can be abstracted into mathematical models by means of2 × 2 × 2 asymmetric games. In this paper, we explore a special class of2 × 2 × 2 asymmetric games satisfying fixed conditions. Firstly, we analyse two solitary interior equilibrium points and provide the judgement condition for their instability based on the Jacobi matrix local stability analysis method. Secondly, we analyse the interior equilibrium points that are continuously distributed within a line and probe into their stability conditions based on generalized Hamiltonian systems theory. Under the circumstances, the stable interior equilibrium point is surrounded by closed orbits in phase space, which presents an observable stable state where two strategies coexist and fluctuate in each of the three game populations. This work enriches the study of2 × 2 × 2 asymmetric games' evolutionary dynamics.

The Unification of Evolutionary Dynamics through the Bayesian Decay Factor in a Game on a Graph

We unify evolutionary dynamics on graphs in strategic uncertainty through a decaying Bayesian update. Our analysis focuses on the Price theorem of selection, which governs replicator(-mutator) dynamics, based on a stratified interaction mechanism and a composite strategy update rule. Our findings suggest that the replication of a certain mutation in a strategy, leading to a shift from competition to cooperation in a well-mixed population, is equivalent to the replication of a strategy in a Bayesian-structured population without any mutation. Likewise, the replication of a strategy in a Bayesian-structured population with a certain mutation, resulting in a move from competition to cooperation, is equivalent to the replication of a strategy in a well-mixed population without any mutation. This equivalence holds when the transition rate from competition to cooperation is equal to the relative strength of selection acting on either competition or cooperation in relation to the selection differential between cooperators and competitors. Our research allows us to identify situations where cooperation is more likely, irrespective of the specific payoff levels. This approach provides new perspectives into the intended purpose of Price's equation, which was initially not designed for this type of analysis.

Strategy evolution on higher-order networks

Cooperation is key to prosperity in human societies. Population structure is well understood as a catalyst for cooperation, where research has focused on pairwise interactions. But cooperative behaviors are not simply dyadic, and they often involve coordinated behavior in larger groups. Here we develop a framework to study the evolution of behavioral strategies in higher-order population structures, which include pairwise and multi-way interactions. We provide an analytical treatment of when cooperation will be favored by higher-order interactions, accounting for arbitrary spatial heterogeneity and nonlinear rewards for cooperation in larger groups. Our results indicate that higher-order interactions can act to promote the evolution of cooperation across a broad range of networks, in public goods games. Higher-order interactions consistently provide an advantage for cooperation when interaction hyper-networks feature multiple conjoined communities. Our analysis provides a systematic account of how higher-order interactions modulate the evolution of prosocial traits.

Co-evolution of heterogeneous cognition in spatial snowdrift game with asymmetric cost

The emergence of the evolutionary game on complex networks provides a fresh framework for studying cooperation behavior between complex populations. Numerous recent progress has been achieved in studying asymmetric games. However, there is still a substantial need to address how to flexibly express the individual asymmetric nature. In this paper, we employ mutual cognition among individuals to elucidate the asymmetry inherent in their interactions. Cognition arises from individuals' subjective assessments and significantly influences their decision-making processes. In social networks, mutual cognition among individuals is a persistent phenomenon and frequently displays heterogeneity as the influence of their interactions. This unequal cognitive dynamic will, in turn, influence the interactions, culminating in asymmetric outcomes. To better illustrate the inter-individual cognition in asymmetric snowdrift games, the concept of favor value is introduced here. On this basis, the evolution of cognition and its relationship with asymmetry degree are defined. In our simulation, we investigate how game cost and the intensity of individual cognitive changes impact the cooperation frequency. Furthermore, the temporal evolution of individual cognition and its variation under different parameters was also examined. The simulation results reveal that the emergence of heterogeneous cognition effectively addresses social dilemmas, with asymmetric interactions among individuals enhancing the propensity for cooperative choices. It is noteworthy that distinctions exist in the rules governing cooperation and cognitive evolution between regular networks and Watts-Strogatz small-world networks. In light of this, we deduce the relationship between cognition evolution and cooperative behavior in co-evolution and explore potential factors influencing cooperation within the system.

Complex pathways to cooperation emergent from asymmetry in heterogeneous populations

Cooperation within asymmetric populations has garnered significant attention in evolutionary games. This paper explores cooperation evolution in populations with weak and strong players, using a game model where players choose between cooperation and defection. Asymmetry stems from different benefits for strong and weak cooperators, with their benefit ratio indicating the degree of asymmetry. Varied rankings of parameters including the asymmetry degree, cooperation costs, and benefits brought by weak players give rise to scenarios including the prisoner's dilemma (PDG) for both player types, the snowdrift game (SDG), and mixed PDG-SDG interactions. Our results indicate that in an infinite well-mixed population, defection remains the dominant strategy when strong players engage in the prisoner's dilemma game. However, if strong players play snowdrift games, global cooperation increases with the proportion of strong players. In this scenario, strong cooperators can prevail over strong defectors when the proportion of strong players is low, but the prevalence of cooperation among strong players decreases as their proportion increases. In contrast, within a square lattice, the optimum global cooperation emerges at intermediate proportions of strong players with moderate degrees of asymmetry. Additionally, weak players protect cooperative clusters from exploitation by strong defectors. This study highlights the complex dynamics of cooperation in asymmetric interactions, contributing to the theory of cooperation in asymmetric games.

The evolution and social cost of herding mentality promote cooperation

Herding behavior has a social cost for individuals not following the herd, influencing human decision-making. This work proposes including a social cost derived from herding mentality into the payoffs of pairwise game interactions. We introduce a co-evolutionary asymmetric model with four individual strategies (cooperation vs. defection and herding vs. non-herding) to understand the co-emergence of herding behavior and cooperation. Computational experiments show how including herding costs promotes cooperation by increasing the parameter space under which cooperation persists. Results demonstrate a synergistic relationship between the emergence of cooperation and herding mentality: the highest cooperation is achieved when the herding mentality also achieves its highest level. Finally, we study different herding social costs and its relationship to cooperation and herding evolution. This study points to new social mechanisms, related to conformity-driven imitation behavior, that help to understand how and why cooperation prevails in human groups.

Evolutionary dynamics on sequential temporal networks

Population structure is a well-known catalyst for the evolution of cooperation and has traditionally been considered to be static in the course of evolution. Conversely, real-world populations, such as microbiome communities and online social networks, frequently show a progression from tiny, active groups to huge, stable communities, which is insufficient to be captured by constant structures. Here, we propose sequential temporal networks to characterize growing networked populations, and we extend the theory of evolutionary games to these temporal networks with arbitrary structures and growth rules. We derive analytical rules under which a sequential temporal network has a higher fixation probability for cooperation than its static counterpart. Under neutral drift, the rule is simply a function of the increment of nodes and edges in each time step. But if the selection is weak, the rule is related to coalescence times on networks. In this case, we propose a mean-field approximation to calculate fixation probabilities and critical benefit-to-cost ratios with lower calculation complexity. Numerical simulations in empirical datasets also prove the cooperation-promoting effect of population growth. Our research stresses the significance of population growth in the real world and provides a high-accuracy approximation approach for analyzing the evolution in real-life systems.

Zero-determinant strategy in stochastic Stackelberg asymmetric security game

In a stochastic Stackelberg asymmetric security game, the strong Stackelberg equilibrium (SSE) strategy is a popular option for the defender to get the highest utility against an attacker with the best response (BR) strategy. However, the attacker may be a boundedly rational player, who adopts a combination of the BR strategy and a fixed stubborn one. In such a condition, the SSE strategy may not maintain the defensive performance due to the stubbornness. In this paper, we focus on how the defender can adopt the unilateral-control zero-determinate (ZD) strategy to confront the boundedly rational attacker. At first, we verify the existence of ZD strategies for the defender. We then investigate the performance of the defender's ZD strategy against a boundedly rational attacker, with a comparison of the SSE strategy. Specifically, when the attacker's strategy is close to the BR strategy, the ZD strategy admits a bounded loss for the defender compared with the SSE strategy. Conversely, when the attacker's strategy is close to the stubborn strategy, the ZD strategy can bring higher defensive performance for the defender than the SSE strategy does.

Generalized Lotka-Volterra Equations with Random, Nonreciprocal Interactions: The Typical Number of Equilibria

We compute the typical number of equilibria of the generalized Lotka-Volterra equations describing species-rich ecosystems with random, nonreciprocal interactions using the replicated Kac-Rice method. We characterize the multiple-equilibria phase by determining the average abundance and similarity between equilibria as a function of their diversity (i.e., of the number of coexisting species) and of the variability of the interactions. We show that linearly unstable equilibria are dominant, and that the typical number of equilibria differs with respect to the average number.

Complex evolutionary interactions in multiple populations

In competitive settings that entail several populations, individuals often engage in intra- and interpopulation interactions that determine their fitness and evolutionary success. With this simple motivation, we here study a multipopulation model where individuals engage in group interactions within their own population and in pairwise interactions with individuals from different populations. We use the evolutionary public goods game and the prisoner's dilemma game to describe these group and pairwise interactions, respectively. We also take into account asymmetry in the extent to which group and pairwise interactions determine the fitness of individuals. We find that interactions across multiple populations reveal new mechanisms through which the evolution of cooperation can be promoted, but this depends on the level of interaction asymmetry. If inter- and intrapopulation interactions are symmetric, the sole presence of multiple populations promotes the evolution of cooperation. Asymmetry in the interactions can further promote cooperation at the expense of the coexistence of the competing strategies. An in-depth analysis of the spatiotemporal dynamics reveals loop-dominated structures and pattern formation that can explain the various evolutionary outcomes. Thus, complex evolutionary interactions in multiple populations reveal an intricate interplay between cooperation and coexistence, and they also open up the path toward further explorations of multipopulation games and biodiversity.

The evolution of cooperation in the unidirectional linear division of labour of finite roles

Evolution of cooperation is a puzzle in evolutionary biology and social sciences. Previous studies assumed that players are equal and have symmetric relationships. In our society, players are in different roles, have an asymmetric relationship and cooperate together. We focused on the linear division of labour in a unidirectional chain that has finite roles, each of which is assigned to one group with cooperators and defectors. A cooperator in an upstream group produces and modifies a product, paying a cost of cooperation, and hands it to a player in a downstream group who obtains the benefit from the product. If players in all roles cooperate, a final product can be completed. However, if a player in a group chooses defection, the division of labour stops, the final product cannot be completed and all players in all roles suffer damage. By using the replicator equations of the asymmetric game, we investigate which sanction system promotes the evolution of cooperation in the division of labour. We find that not the benefit of the product but the cost of cooperation matters to the evolutionary dynamics and that the probability of finding a defector determines which sanction system promotes the evolution of cooperation.

Social relationship adjustments within the same sex promote marital bliss

Parental care is essential for biological systems. Marital bliss is one of the ideal paradigms for parental care, in which males contribute in raising offspring and females require a courtship time. Yet marital bliss state is neither Nash equilibrium nor Pareto optimum for the classic Battle of the Sexes. It thus leads to a gap between evolutionary theory and marital bliss. Previous works concentrate on the pairwise interactions between the two sexes to fill this gap, such as the courtship time and encounter rate. The social relationships within the same sex, however, receives much less attention. Here we investigate how social relationships within the same sex change marital bliss by introducing the coevolution of strategy and social network. Based on the time scale separation, it is found that a symmetric game is emergent via social adjustments within each sex, and the evolutionary outcome is determined by the interplay between the emergent symmetric game and the Battle of the Sexes. We find that marital bliss can be promoted when males are rational (strong selection limit) and females are irrational (weak selection limit); the stable Coy-Coy social relationships both stabilize and speed up marital bliss; the general criterion of stabilising marital bliss for arbitrary imitation function are found, which are verified by simulations. Furthermore, the emergent symmetric games are insightful for determining whether the stable marital bliss is global stable. Our work provides an alternative avenue to facilitate marital bliss, which can be applied for general asymmetric games on dynamical networks.

Multi-Agent Evolutionary Game in the Recycling Utilization of Sulfate-Rich Wastewater

Current industrial development has led to an increase in sulfate-rich industrial sewage, threatening industrial ecology and the environment. Incorrectly treating high-concentration sulfate wastewater can cause serious environmental problems and even harm human health. Water with high sulfate levels can be treated as a resource and treated harmlessly to meet the needs of the circular economy. Today, governments worldwide are working hard to encourage the safe disposal and reuse of industrial salt-rich wastewater by recycling sulfate-rich wastewater (SRW) resources. However, the conflict of interests between the SRW production department, the SRW recycling department, and the governments often make it challenging to effectively manage sulfate-rich wastewater resources. This study aims to use the mechanism of evolutionary game theory (EGT) to conduct theoretical modelling and simulation analysis on the interaction of the behaviour of the above three participants. This paper focuses on the impact of government intervention and the ecological behaviour of wastewater producers on the behavioural decisions of recyclers. The results suggest that the government should play a leading role in developing the SRW resource recovery industry. SRW producers protect the environment in the mature stage, and recyclers actively collect and recover compliant sulfate wastewater resources. Governments should gradually deregulate and eventually withdraw from the market. Qualified recyclers and environmentally friendly wastewater producers can benefit from a mature SRW resources recovery industry.

Evolution of cooperation with contextualized behavior

How do networks of social interaction govern the emergence and stability of prosocial behavior? Theoretical studies of this question typically assume unconditional behavior, meaning that an individual either cooperates with all opponents or defects against all opponents-an assumption that produces a pessimistic outlook for the evolution of cooperation, especially in highly connected populations. Although these models may be appropriate for simple organisms, humans have sophisticated cognitive abilities that allow them to distinguish between opponents and social contexts, so they can condition their behavior on the identity of opponents. Here, we study the evolution of cooperation when behavior is conditioned by social context, but behaviors can spill over between contexts. Our mathematical analysis shows that contextualized behavior rescues cooperation across a broad range of population structures, even when the number of social contexts is small. Increasing the number of social contexts further promotes cooperation by orders of magnitude.

Evolution of state-dependent strategies in stochastic games

In a population of interacting individuals, the environment for interactions often changes due to individuals' behaviors, which in turn drive the evolution of individuals' behaviors. The interplay between the environment and individuals' behaviors has been demonstrated to remarkably influence the evolutionary outcomes. In reality, in highly cognitive species such as social primates and human beings, individuals are often capable of perceiving the environment change and then differentiate their strategies across different environment states. We propose a model of environmental feedback with state-dependent strategies: individuals have perceptions of distinct environment states and therefore take distinct sub-strategies under each of them; based on the sub-strategy, individuals then decide their behaviors; their behaviors subsequently modify the environment state. We use the theory of stochastic games and evolutionary dynamics to analyze this idea. We find that when environment changes slower than behaviors, state-dependent strategies (i.e. taking different sub-strategies under different environment states) can outperform state-independent strategies (i.e. taking an identical sub-strategy under all environment states), such as Win-Stay, Lose-Shift, the most leading strategy among state-independent strategies. The intuition is that delayed environmental feedback provides chances for individuals with state-dependent strategies to exploit those with state-independent strategies. Our results hold (1) in both well-mixed and structured populations; (2) when the environment switches between two or more states. Furthermore, the environment changing rate decides if state-dependent strategies benefit global cooperation. The evolution sees the rise of the cooperation level for fast environment switching and the decrease otherwise. Our work stresses that individuals' perceptions of different environment states are beneficial to their survival and social prosperity in a changing world.

Natural selection between two games with environmental feedback

Evolutionary game theory has extensively investigated situations in which several games are competing against each other at the same time, but the model only assumes symmetric interactions in homogeneous environments. Now, the population is considered in heterogeneous environments, individuals in the population occupy a different quality of patches, and individual fitness depends not only on the interaction between individuals, but also on the quality of the environment. Here, by establishing a mathematical framework, we analyze the natural selection between two strategies and two games in heterogeneous environments. Furthermore, we analyze the natural selection of Prisoner’s Dilemma and Hawk–Dove games theoretically to demonstrate the dynamics of cooperators and defectors in their choice of environment and their respective games. As expected, the distribution of games and strategies changes with time. Based on different initial population compositions, we also discuss the invasion problem of games from different perspectives. To one’s surprise, we can find that good quality patches attract all individuals; the long-term dynamics in invariant rich environments is the same as the dynamics of symmetric interactions in homogeneous environments.

Effect of asymmetry on cooperation in spatial evolution

Asymmetry is omnipresent in human society and nature and the reasons causing asymmetry are multiple. To think about the impact of asymmetries on the cooperation systems, we focus on a typical model of great asymmetric traits-the boxed pigs game-and extended the one-to-one interaction to the interaction in population. We consider the asymmetry of payoff and the spatial structure of the two populations in space. Our results have shown that the almost equal abundance and strength of two populations kills cooperative behavior. The single increase of either strength-asymmetry or abundance-asymmetry promotes cooperation. But high levels of both asymmetries would inhibit cooperative behavior, making the powerful mechanism of cooperation broken.

Avoiding the bullies: The resilience of cooperation among unequals

Can egalitarian norms or conventions survive the presence of dominant individuals who are ensured of victory in conflicts? We investigate the interaction of power asymmetry and partner choice in games of conflict over a contested resource. Previous models of cooperation do not include both power inequality and partner choice. Furthermore, models that do include power inequalities assume a static game where a bully's advantage does not change. They have therefore not attempted to model complex and realistic properties of social interaction. Here, we introduce three models to study the emergence and resilience of cooperation among unequals when interaction is random, when individuals can choose their partners, and where power asymmetries dynamically depend on accumulated payoffs. We find that the ability to avoid bullies with higher competitive ability afforded by partner choice mostly restores cooperative conventions and that the competitive hierarchy never forms. Partner choice counteracts the hyper dominance of bullies who are isolated in the network and eliminates the need for others to coordinate in a coalition. When competitive ability dynamically depends on cumulative payoffs, complex cycles of coupled network-strategy-rank changes emerge. Effective collaborators gain popularity (and thus power), adopt aggressive behavior, get isolated, and ultimately lose power. Neither the network nor behavior converge to a stable equilibrium. Despite the instability of power dynamics, the cooperative convention in the population remains stable overall and long-term inequality is completely eliminated. The interaction between partner choice and dynamic power asymmetry is crucial for these results: without partner choice, bullies cannot be isolated, and without dynamic power asymmetry, bullies do not lose their power even when isolated. We analytically identify a single critical point that marks a phase transition in all three iterations of our models. This critical point is where the first individual breaks from the convention and cycles start to emerge.

Replicator equations induced by microscopic processes in nonoverlapping population playing bimatrix games

This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection-as a result of competition fashioned by game-theoretic consideration-into the Wright-Fisher process, a stochastic birth-death process. The process is further considered to be active in a generation-wise nonoverlapping finite population where individuals play a two-strategy bimatrix population game. Subsequently, connections among the corresponding master equation, the Fokker-Planck equation, and the Langevin equation are exploited to arrive at the deterministic discrete replicator maps in the limit of infinite population size.

Cooperation in a generalized age-structured spatial game

The emergence and prevalence of cooperative behavior within a group of selfish individuals remains a puzzle for evolutionary game theory precisely because it conflicts directly with the central idea of natural selection. Accordingly, in recent years, the search for an understanding of how cooperation can be stimulated, even when it conflicts with individual interest, has intensified. We investigate the emergence of cooperation in an age-structured evolutionary spatial game. In it, players age with time and the payoff that they receive after each round depends on their age. We find that the outcome of the game is strongly influenced by the type of distribution used to modify the payoffs according to the age of each player. The results show that, under certain circumstances, cooperators may not only survive but dominate the population.

Evolutionary dynamics with game transitions

The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a model of evolutionary dynamics with game transitions, where individuals' behaviors together with the games that they play in one time step influence the games to be played in the next time step. Within this model, we study the evolution of cooperation in structured populations and find a simple rule: Weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b, to the corresponding cost, c, exceeds [Formula: see text], where k is the average number of neighbors of an individual and [Formula: see text] captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game, allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly connected populations.

Adversity and cooperation in heterogeneous pairs

This paper provides a game-theoretic model of the effect of higher adversity on the evolution of cooperation. The focus lies on how this effect of higher adversity is impacted when there is transient, non-genetic heterogeneity in the form of differences in the players' capabilities of contributing to the public good, in the benefits they obtain from the public good, or in their cooperation costs. A framework is provided that identifies the common mechanisms that are at work across two models of cooperation (jointly producing a public good, and jointly defending an existing public good), and across the mentioned types of heterogeneity. With relatively small heterogeneity, higher adversity generates a common-enemy effect for large cooperation costs and a deterrence effect for small cooperation costs. Yet, these results on the effect of higher adversity are completely reversed for relatively large heterogeneity.

Evolutionary dynamics of complex multiple games

Evolutionary game theory has been successful in describing phenomena from bacterial population dynamics to the evolution of social behaviour. However, it has typically focused on a single game describing the interactions between individuals. Organisms are simultaneously involved in many intraspecies and interspecies interactions. Therefore, there is a need to move from single games to multiple games. However, these interactions in nature involve many players. Shifting from 2-player games to multiple multiplayer games yield richer dynamics closer to natural settings. Such a complete picture of multiple game dynamics (MGD), where multiple players are involved, was lacking. For multiple multiplayer games—where each game could have an arbitrary finite number of players and strategies, we provide a replicator equation for MGD having many players and strategies. We show that if the individual games involved have more than two strategies, then the combined dynamics cannot be understood by looking only at individual games. Expected dynamics from single games is no longer valid, and trajectories can possess different limiting behaviour. In the case of finite populations, we formulate and calculate an essential and useful stochastic property, fixation probability. Our results highlight that studying a set of interactions defined by a single game can be misleading if we do not take the broader setting of the interactions into account. Through our results and analysis, we thus discuss and advocate the development of evolutionary game(s) theory, which will help us disentangle the complexity of multiple interactions.

Cooperation dynamics in networked geometric Brownian motion

Recent works suggest that pooling and sharing may constitute a fundamental mechanism for the evolution of cooperation in well-mixed fluctuating environments. The rationale is that, by reducing the amplitude of fluctuations, pooling and sharing increases the steady-state growth rate at which individuals self-reproduce. However, in reality interactions are seldom realized in a well-mixed structure, and the underlying topology is in general described by a complex network. Motivated by this observation, we investigate the role of the network structure on the cooperative dynamics in fluctuating environments, by developing a model for networked pooling and sharing of resources undergoing a geometric Brownian motion. The study reveals that, while in general cooperation increases the individual steady state growth rates (i.e., is evolutionary advantageous), the interplay with the network structure may yield large discrepancies in the observed individual resource endowments. We comment possible biological and social implications and discuss relations to econophysics.

Evolutionary multiplayer games on graphs with edge diversity

Evolutionary game dynamics in structured populations has been extensively explored in past decades. However, most previous studies assume that payoffs of individuals are fully determined by the strategic behaviors of interacting parties, and social ties between them only serve as the indicator of the existence of interactions. This assumption neglects important information carried by inter-personal social ties such as genetic similarity, geographic proximity, and social closeness, which may crucially affect the outcome of interactions. To model these situations, we present a framework of evolutionary multiplayer games on graphs with edge diversity, where different types of edges describe diverse social ties. Strategic behaviors together with social ties determine the resulting payoffs of interactants. Under weak selection, we provide a general formula to predict the success of one behavior over the other. We apply this formula to various examples which cannot be dealt with using previous models, including the division of labor and relationship- or edge-dependent games. We find that labor division can promote collective cooperation markedly. The evolutionary process based on relationship-dependent games can be approximated by interactions under a transformed and unified game. Our work stresses the importance of social ties and provides effective methods to reduce the calculating complexity in analyzing the evolution of realistic systems.

Bribery games on interdependent complex networks

Bribe demands present a social conflict scenario where decisions have wide-ranging economic and ethical consequences. Nevertheless, such incidents occur daily in many countries across the globe. Harassment bribery constitute a significant sub-set of such bribery incidents where a government official demands a bribe for providing a service to a citizen legally entitled to it. We employ an evolutionary game-theoretic framework to analyse the evolution of corrupt and honest strategies in structured populations characterized by an interdependent complex network. The effects of changing network topology, average number of links and asymmetry in size of the citizen and officer population on the proliferation of incidents of bribery are explored. A complex network topology is found to be beneficial for the dominance of corrupt strategies over a larger region of phase space when compared with the outcome for a regular network, for equal citizen and officer population sizes. However, the extent of the advantage depends critically on the network degree and topology. A different trend is observed when there is a difference between the citizen and officer population sizes. Under those circumstances, increasing randomness of the underlying citizen network can be beneficial to the fixation of honest officers up to a certain value of the network degree. Our analysis reveals how the interplay between network topology, connectivity and strategy update rules can affect population level outcomes in such asymmetric games.

Symmetric Decomposition of Asymmetric Games

We introduce new theoretical insights into two-population asymmetric games allowing for an elegant symmetric decomposition into two single population symmetric games. Specifically, we show how an asymmetric bimatrix game (A,B) can be decomposed into its symmetric counterparts by envisioning and investigating the payoff tables (A and B) that constitute the asymmetric game, as two independent, single population, symmetric games. We reveal several surprising formal relationships between an asymmetric two-population game and its symmetric single population counterparts, which facilitate a convenient analysis of the original asymmetric game due to the dimensionality reduction of the decomposition. The main finding reveals that if (x,y) is a Nash equilibrium of an asymmetric game (A,B), this implies that y is a Nash equilibrium of the symmetric counterpart game determined by payoff table A, and x is a Nash equilibrium of the symmetric counterpart game determined by payoff table B. Also the reverse holds and combinations of Nash equilibria of the counterpart games form Nash equilibria of the asymmetric game. We illustrate how these formal relationships aid in identifying and analysing the Nash structure of asymmetric games, by examining the evolutionary dynamics of the simpler counterpart games in several canonical examples.

Bribery games on inter-dependent regular networks

We examine a scenario of social conflict that is manifest during an interaction between government servants providing a service and citizens who are legally entitled to the service, using evolutionary game-theory in structured populations characterized by an inter-dependent network. Bribe-demands by government servants during such transactions, called harassment bribes, constitute a widespread form of corruption in many countries. We investigate the effect of varying bribe demand made by corrupt officials and the cost of complaining incurred by harassed citizens, on the proliferation of corrupt strategies in the population. We also examine how the connectivity of the various constituent networks affects the spread of corrupt officials in the population. We find that incidents of bribery can be considerably reduced in a network-structured populations compared to mixed populations. Interestingly, we also find that an optimal range for the connectivity of nodes in the citizen's network (signifying the degree of influence a citizen has in affecting the strategy of other citizens in the network) as well as the interaction network aids in the fixation of honest officers. Our results reveal the important role of network structure and connectivity in asymmetric games.

Structural symmetry in evolutionary games

In evolutionary game theory, an important measure of a mutant trait (strategy) is its ability to invade and take over an otherwise-monomorphic population. Typically, one quantifies the success of a mutant strategy via the probability that a randomly occurring mutant will fixate in the population. However, in a structured population, this fixation probability may depend on where the mutant arises. Moreover, the fixation probability is just one quantity by which one can measure the success of a mutant; fixation time, for instance, is another. We define a notion of homogeneity for evolutionary games that captures what it means for two single-mutant states, i.e. two configurations of a single mutant in an otherwise-monomorphic population, to be 'evolutionarily equivalent' in the sense that all measures of evolutionary success are the same for both configurations. Using asymmetric games, we argue that the term 'homogeneous' should apply to the evolutionary process as a whole rather than to just the population structure. For evolutionary matrix games in graph-structured populations, we give precise conditions under which the resulting process is homogeneous. Finally, we show that asymmetric matrix games can be reduced to symmetric games if the population structure possesses a sufficient degree of symmetry.

The dynamics of human behavior in the public goods game with institutional incentives

The empirical research on the public goods game (PGG) indicates that both institutional rewards and institutional punishment can curb free-riding and that the punishment effect is stronger than the reward effect. Self-regarding models that are based on Nash equilibrium (NE) strategies or evolutionary game dynamics correctly predict which incentives are best at promoting cooperation, but individuals do not play these rational strategies overall. The goal of our study is to investigate the dynamics of human decision making in the repeated PGG with institutional incentives. We consider that an individual's contribution is affected by four factors, which are self-interest, the behavior of others, the reaction to rewards, and the reaction to punishment. We find that people on average do not react to rewards and punishment, and that self-interest and the behavior of others sufficiently explain the dynamics of human behavior. Further analysis suggests that institutional incentives promote cooperation by affecting the self-regarding preference and that the other-regarding preference seems to be independent of incentive schemes. Because individuals do not change their behavioral patterns even if they were not rewarded or punished, the mere potential to punish defectors and reward cooperators can lead to considerable increases in the level of cooperation.