Evolutionary Game-theoretic Model Research Articles

Recidivism and Rehabilitation of Criminal Offenders: A Carrot and Stick Evolutionary Game

Motivated by recent efforts by the criminal justice system to treat and rehabilitate nonviolent offenders rather than focusing solely on their punishment, we introduce an evolutionary game theoretic model to study the effects of “carrot and stick” intervention programs on criminal recidivism. We use stochastic simulations to study the evolution of a population where individuals may commit crimes depending on their past history, surrounding environment and, in the case of recidivists, on any counseling, educational or training programs available to them after being punished for their previous crimes. These sociological factors are embodied by effective parameters that determine the decision making probabilities. Players may decide to permanently reform or continue engaging in criminal activity, eventually reaching a state where they are considered incorrigible. Depending on parameter choices, the outcome of the game is a society with a majority of virtuous, rehabilitated citizens or incorrigibles. Since total resources may be limited, we constrain the combined punishment and rehabilitation costs per crime to be fixed, so that increasing one effort will necessarily decrease the other. We find that the most successful strategy in reducing crime is to optimally allocate resources so that after being punished, criminals experience impactful intervention programs, especially during the first stages of their return to society. Excessively harsh or lenient punishments are less effective. We also develop a system of coupled ordinary differential equations with memory effects to give a qualitative description of our simulated societal dynamics. We discuss our findings and sociological implications.

Individual memory and the emergence of cooperation

The social brain hypothesis states that selection pressures associated with complex social relationships have driven the evolution of sophisticated cognitive processes in primates. We investigated how the size of cooperative primate communities depends on the memory of each of its members and on the pressure exerted by natural selection. To this end we devised an evolutionary game theoretical model in which social interactions are modelled in terms of a repeated Prisoner's Dilemma played by individuals who may exhibit a different memory capacity. Here, memory is greatly simplified and mapped onto a single parameter m describing the number of conspecifics whose previous action each individual can remember. We show that increasing m enables cooperation to emerge and be maintained in groups of increasing sizes. Furthermore, harsher social dilemmas lead to the need for a higher m in order to ensure high levels of cooperation. Finally, we show how the interplay between the dilemma individuals face and their memory capacity m allows us to define a critical group size below which cooperation may thrive, and how this value depends sensitively on the strength of natural selection.

EVOLUTIONARY DYNAMICS OF CLIMATE CHANGE UNDER COLLECTIVE-RISK DILEMMAS

Preventing global warming requires overall cooperation. Contributions will depend on the risk of future losses, which plays a key role in decision-making. Here, we discuss an evolutionary game theoretical model in which decisions within small groups under high risk and stringent requirements toward success significantly raise the chances of coordinating to save the planet's climate, thus escaping the tragedy of the commons. We discuss both deterministic dynamics in infinite populations, and stochastic dynamics in finite populations.

An evolutionary game-theoretic model for ethno-religious conflicts between two groups

Ethno-religious conflict in multi-cultural societies has been one of the major causes of loss of life and property in recent history. In this paper, we present and analyze a multi-agent game theoretic model for computational study of ethno-religious conflicts in multi-cultural societies. Empirical fact-based research in sociology and conflict resolution literature have identified (a) ethno-religious identity of the population, (b) spatial structure (distribution) of the population, (c) existing history of animosity, and (d) influence of leaders as some of the salient factors causing ethno-religious violence. It has also been experimentally shown by Lumsden that multi-cultural conflict can be viewed as a Prisoner's Dilemma (PD) game. Using the above observations, we model the multi-cultural conflict problem as a variant of the repeated PD game in graphs. The graph consists of labeled nodes corresponding to the different ethno-religious types and the topology of the graph encodes the spatial distribution and interaction of the population. We assume the structure of the graph to have the statistical properties of a social network with the high degree nodes representing the leaders of the society. The agents play the game with neighbors of their opponent type and they update their strategies based on neighbors of their same type. This strategy update dynamics, where the update neighborhood is different from the game playing neighborhood, distinguishes our model from conventional models of PD games in graphs. We present simulation results showing the effect of various parameters of our model to the propensity of conflict in a population consisting of two ethno-religious groups. We also compare our simulation results to real data of occurrence of ethno-religious violence in Yugoslavia.

A theory of leadership in human cooperative groups

Two types of models aim to account the origins of rank differentiation and social hierarchy in human societies. Conflict models suggest that the formation of social hierarchies is synonymous with the establishment of relationships of coercive social dominance and exploitation. Voluntary or 'integrative' models, on the other hand, suggest that rank differentiation – the differentiation of leader from follower, ruler from ruled, or state from subject – may sometimes be preferred over more egalitarian social arrangements as a solution to the challenges of life in social groups, such as conflict over resources, coordination failures, and free-riding in cooperative relationships. Little formal theoretical work, however, has established whether and under what conditions individuals would indeed prefer the establishment of more hierarchical relationships over more egalitarian alternatives. This paper provides an evolutionary game theoretical model for the acceptance of leadership in cooperative groups. We propose that the effort of a leader can reduce the likelihood that cooperation fails due to free-riding or coordination errors, and that under some circumstances, individuals would prefer to cooperate in a group under the supervision of a leader who receives a share of the group's productivity than to work in an unsupervised group. We suggest, in particular, that this becomes an optimal solution for individual decision makers when the number of group members required for collective action exceeds the maximum group size at which leaderless cooperation is viable.

Corporate virtue: Treatment of whistle blowers and the punishment of violators

An evolutionary game-theoretic model is employed to address three essential aspects of whistle blowing: ethical decision making, the duality of mutual accountability among cohorts in large organizations, and role conflict between individual and organizational values. I derive an equilibrium condition relating the treatment of whistle blowers to the punishment of violators. The model facilitates an evaluation of the whistle blowing provisions in the Sarbanes–Oxley (2002) Act.

A dynamic approach to voluntary environmental contributions in tourism

In an evolutionary game-theoretical model of tourism firms that use an endogenous natural Common Pool Resource (CPR) we show that stable equilibria with voluntary environmental initiatives may coexist with other equilibria where voluntary abatement is absent. The basins of attraction of the equilibria are identified and a bifurcation analysis is carried out producing two results with policy implications. First, there is a highly non-linear relationship between the cost of abatement required to be green and the share of green firms. Second, increases in the number of the CPR's users will ultimately dissipate the incentives to make abatement beyond regulation.

Evolutionary game-theoretic model for dynamic congestion pricing in multi-class traffic networks

This paper describes an evolutionary game-theoretic learning model for dynamic congestion pricing in urban road networks, taking into account route choice stochasticity and reliability considerations, and the heterogeneity of users, in terms of their value of travel time and real-time information acquisition. The learning model represents the dynamic adjustments of users to travel cost changes which may take place in the day-to-day as well as the within-day timescales. The implementation into a simplified and a real urban road network signifies the important implications of modeling the dynamic and stochastic learning components of users' behavior for accommodating the efficient deployment of congestion pricing schemes.

Contrasting size evolution in marine and freshwater diatoms.

Diatoms are key players in the global carbon cycle and most aquatic ecosystems. Their cell sizes impact carbon sequestration and energy transfer to higher trophic levels. We report fundamental differences in size distributions of marine and freshwater diatoms, with marine diatoms significantly larger than freshwater species. An evolutionary game theoretical model with empirical allometries of growth and nutrient uptake shows that these differences can be explained by nitrogen versus phosphorus limitation, nutrient fluctuations and mixed layer depth differences. Constant and pulsed phosphorus supply select for small sizes, as does constant nitrogen supply. In contrast, intermediate frequency nitrogen pulses common in the ocean select for large sizes or the evolutionarily stable coexistence of large and small sizes. Size-dependent sinking interacts with mixed layer depth (MLD) to further modulate optimal sizes, with smaller sizes selected for by strong sinking and shallow MLD. In freshwaters, widespread phosphorus limitation, together with strong sinking and shallow MLD produce size distributions with smaller range, means and upper values, compared with the ocean. Shifting patterns of nutrient limitation and mixing may alter diatom size distributions, affecting global carbon cycle and the structure and functioning of aquatic ecosystems.

An Agent-Based Computational Model of the Predatory State

Olson (1993) has proposed that a self-interested bandit has an incentive to become stationary and provide public goods within his domain, in particular protection of property rights, particularly against other roving bandits. The consequent increased social productivity permits the stationary bandit (dignified with the title of king) to obtain a greater personal return than is obtained by roving bandits preying on a poorer society. At the same time, increased security provides the subjects with a greater incentive to invest, thereby leading to longer term increases in social wealth. Olson`s analysis complements the property-rights view of development most closely associated with Douglass North (North & Thomas (1973), North (1981)). North argues that respect by rulers for the property rights of subjects is responsible for economic development by providing an incentive for productive investment. Olson`s theory gives an explanation of why a self-interested ruler might choose to respect property rights. This paper presents a spatial evolutionary game-theoretic agent-based computational model of the North/Olson argument.

Social preferences and private provision of public goods: A ‘double critical mass’ model

We set up an evolutionary game-theoretic model aimed at addressing the issue of local public good provision via direct commitment of voluntary forces (private donors and nonprofit providers) only. Two classes of agents are assumed to strategically interact within a ‘double critical mass’ model and we investigate the critical factors affecting the dynamic outcomes of such interaction. Further, we explore the conditions under which (what we term) ‘evolutionary crowding-out/in’ occurs, depending on agents’ degree of opportunism, social comparison and positive selective incentives (such as subsidies given by the government to ‘virtuous’ citizens or nonprofits only).

Stern-Judging: A Simple, Successful Norm Which Promotes Cooperation under Indirect Reciprocity

We study the evolution of cooperation under indirect reciprocity, believed to constitute the biological basis of morality. We employ an evolutionary game theoretical model of multilevel selection, and show that natural selection and mutation lead to the emergence of a robust and simple social norm, which we call stern-judging. Under stern-judging, helping a good individual or refusing help to a bad individual leads to a good reputation, whereas refusing help to a good individual or helping a bad one leads to a bad reputation. Similarly for tit-for-tat and win-stay-lose-shift, the simplest ubiquitous strategies in direct reciprocity, the lack of ambiguity of stern-judging, where implacable punishment is compensated by prompt forgiving, supports the idea that simplicity is often associated with evolutionary success.

An evolutionary game-theoretic approach to congestion control

This paper investigates a system where a set of users sharing a bottleneck link must choose the transmission rate at which multimedia traffic is received. Users are assumed to be self-regarding and make their decisions with the sole goal of maximizing their perceived quality. We are interested in the dynamic process by which users adapt their data rates and the convergence of this process to equilibria. We propose a novel two-layer model to represent this system: the upper layer is an evolutionary game-theoretic model that captures how users adapt their rates; the lower layer model captures the network performance and the quality perceived by the users. Using the model proposed, we demonstrate analytically and numerically several interesting properties of the system equilibria. In particular, we establish the relationship between system states that have non-negligible steady state probabilities and Nash equilibria of the induced game.

An evolutionary game-theoretic model of network revenue management in oligopolistic competition

This paper articulates a dynamic model of price-based network revenue management, where a set of service providers are involved in oligopolistic competition that is equilibrium tending. The service providers are price setters whose price setting strategies induce time lagged impacts on demand. The price setting mechanisms of these providers resemble the replicator dynamics that are common to evolutionary games. This paper shows that the resulting Cournot—Nash game takes the form of a differential variational inequality. Existence results are provided and an abstract numerical example is solved via a fixed point algorithm that may be implemented with off-the-shelf software. Suggested extensions of the model are also provided.

The ‘Art City’ as A Local Public Good: The Strategic Interplay between Private Donors and Arts Organizations

In this paper we set up a simple evolutionary game-theoretic model aimed at addressing the issue of ‘art cities’ promotion and preservation over time via simultaneous commitment of nonprofit actors such as private donors and arts organizations. Two classes of agents are assumed to interact strategically in a ‘double critical mass’ model where the provision and maintenance, on voluntary bases, of a public-type good such as an art city is concerned. Uncertainty as to equilibrium outcomes emerges in that, within both categories, a positive proportion of agents face the temptation to opportunistically free ride on others’ efforts. Further, private donors’ and arts organizations’ payoff functions are interdependent, in the sense that (a) potential donors decide to be actual donors only insofar as a ‘large enough’ proportion of arts organizations provide a high effort level – otherwise they act as free riders; (b) arts organizations prefer to exert a high productive effort only insofar as a ‘large enough’ proportion of potential donors act as actual donors – otherwise they exert a low effort level. Through this analytical framework, we are able to focus on the critical factors affecting the dynamic outcome of the local interaction under study. Under certain conditions, in a medium-long run perspective, even art cities where, initially, either a large proportion of agents behave as free riders or a large proportion of arts organizations exert a low effort level may manage to survive and flourish.

Endogenous fluctuations under evolutionary pressure in Cournot competition

An evolutionary game theoretic model of Cournot competition is investigated. Individuals choose from a finite set of different behavioral rules. Each rule specifies the quantity to be produced in the current period as a function of past quantities. Using more sophisticated rules may require extra information costs. Based upon realized payoffs, the fractions of the population choosing a certain behavioral rule are updated according to the replicator equation with noise. The long-run behavior of the evolutionary system consisting of the population dynamics coupled with the quantity dynamics of the Cournot game may be complicated and endogenous fluctuations may arise. We consider a typical example where firms can choose between two rules: the Nash rule and the best-reply rule. We show that a homoclinic tangency between the stable and unstable manifold of the equilibrium occurs as evolutionary pressure increases, implying bifurcation routes to complicated dynamics and strange attractors.

RECIPROCAL ALTRUISM UNDER CONDITIONS OF PARTNER SELECTION

This paper is a contribution to solving the problem of whether reciprocal altruism can emerge and maintain itself in a population of selfish individuals. We use an evolutionary game theoretic simulation model (the Social Evolution Model) to investigate the relative fitness of two versions of a reciprocal altruistic trait competing with a defecting trait. One main difference between the Social Evolution Model and most of the models that are known in this field is that partner selection is straightforwardly built into the strategies of the players. In most of the models in the literature, partner selection is not an option in the game. Because of this element of forced play, much attention is given to the ability of strategies to detect cheaters and to retaliate. We show that modeling partner selection points to disadvantages of a preoccupation with cheater-detection and to the importance of committing oneself to a partner.

Bertrand Price Competition in a Social Environment

We analyze the dynamic behaviour of firms that locally interact through price competition in a social environment in an evolutionary game-theoretic model. These firms update their prices according to the behavioural rule ‘Win Cooperate, Lose Defect’ (WCLD), which is often observed in experimental economics. It can be regarded as a generalized Tit-for-Tat strategy. The model can explain the simultaneous emergence of collusive behaviour, price dispersion and occasional local price wars. Price wars only last for a short period of time after which the firms start to collude again.

An Evolutionary Approach to the Climate Change Negotiation Game

We describe in this paper an evolutionary game theoretic model aiming at representing the climate change negotiation. The model is used to examine the outcome of climate change negotiations in a framework which seeks to closely represent negotiation patterns. Evolutionary setting allows us to consider a decision making structure characterised by agents with bounded knowledge practising mimics and learning from past events and strategies. We show on that framework that a third significant alternative to the binary coordination-defection strategies needs to be considered: a unilateral commitment as precautionary strategy. As a means to widen cooperation, we examine the influence of linking environmental and trade policies via the implementation of a trade penalty on non cooperative behaviours.

Generalized Replicator Dynamics as a Model of Specialization and Diversity in Societies

We consider a generalization of replicator dynamics as a non-cooperative evolutionary game-theoretic model of a community of N agents. All agents update their individual mixed strategy profiles to increase their total payoff from the rest of the community. The properties of attractors in this dynamics are studied. Evidence is presented that under certain conditions the typical attractors of the system are corners of state space where each agent has specialized to a pure strategy, and/or the community exhibits diversity, i.e., all strategies are represented in the final states. The model suggests that new pure strategies whose payoff matrix elements satisfy suitable inequalities with respect to the existing ones can destabilize existing attractors if N is sufficiently large, and be regarded as innovations that enhance the diversity of the community.