Classical Evolutionary Game Theory Research Articles

Stability, period and chaos of the evolutionary game strategy induced by time-delay and mutation feedback

In the classical evolutionary game theory, mutation is usually considered as a constant, however strategy mutation is affected by strategies in the real game process. Therefore, the main purpose of this paper is to study the effects of mutation feedback and time delays on strategy dynamics, where mutation is a linear feedback related to strategy. First, we construct a co-evolutionary game model with two time delays induced by mutation feedback and analyze the existence and stability of the equilibria of the non-time delay system. The conditions for the coexistence of the two strategies and the mutation rate are obtained. Second, Sotomayor’s theorem is used to explore the transcritical bifurcation of the system. Then, the existence of Hopf bifurcation is investigated by using feedback delay and payoff delay as bifurcation parameters in the time-delay system. Furthermore, we discuss the direction of the Hopf bifurcation, stability and periodic change of the periodic solution in detail. Finally, a series of numerical simulations are used to describe the theoretical analysis. The main results are as follows: (i) Mutation causes negative feedback to cooperative strategy. (ii) As the time delay increases, the stable equilibrium point becomes unstable, and which branches a stable limit cycle. When the time delay continues to increase sufficiently, the stable limit cycle becomes unstable and produces irregular oscillation and chaos. (iii) When the two time delays are large enough, the coexistence of the two strategies becomes that defective strategy is dominant, and the mutation rate also reaches the maximum.

Impact of misinformation in the evolution of collective cooperation on networks.

Human societies are organized and developed through collective cooperative behaviours. Based on the information in their environment, individuals can form collective cooperation by strategically changing unfavourable surroundings and imitating superior behaviours. However, facing the rampant proliferation and spreading of misinformation, we still lack systematic investigations into the impact of misinformation on the evolution of collective cooperation. Here, we study this problem by classical evolutionary game theory. We find that the existence of misinformation generally impedes the emergence of collective cooperation on networks, although the level of cooperation is slightly higher for weak social cooperative dilemma below a proven threshold. We further show that this possible advantage diminishes as social connections become denser, suggesting that the detrimental effect of misinformation further increases when 'social viscosity' is low. Our results uncover the quantitative effect of misinformation on suppressing collective cooperation, and pave the way for designing possible mechanisms to improve collective cooperation.

Half a century of evolutionary games: a synthesis of theory, application and future directions.

Half a century of evolutionary games: a synthesis of theory, application and future directions.

Evolutionary Game Theory: Darwinian Dynamics and the G Function Approach

Classical evolutionary game theory allows one to analyze the population dynamics of interacting individuals playing different strategies (broadly defined) in a population. To expand the scope of this framework to allow us to examine the evolution of these individuals’ strategies over time, we present the idea of a fitness-generating (G) function. Under this model, we can simultaneously consider population (ecological) and strategy (evolutionary) dynamics. In this paper, we briefly outline the differences between game theory and classical evolutionary game theory. We then introduce the G function framework, deriving the model from fundamental biological principles. We introduce the concept of a G-function species, explain the process of modeling with G functions, and define the conditions for evolutionary stable strategies (ESS). We conclude by presenting expository examples of G function model construction and simulations in the context of predator–prey dynamics and the evolution of drug resistance in cancer.

Replicator dynamics for the game theoretic selection models based on state

The paper presents an attempt to integrate the classical evolutionary game theory based on replicator dynamics and the state-based approach of Houston and McNamara. In the new approach, individuals have different heritable strategies; however, individuals carrying the same strategy can differ in terms of state, role or the situation in which they act. Thus, the classical replicator dynamics is completed by the additional subsystem of differential equations describing the dynamics of transitions between different states. In effect, the interactions described by game structure, in addition to the demographic payoffs (constituted by births and deaths), can lead to the change in state of the competing individuals. Special cases of reversible and irreversible incremental stage-structured models, where the state changes can describeenergy accumulation, developmental steps or aging, are derived for discrete and continuous versions. The new approach is illustrated using the example of the Owner-Intruder game with explicit dynamics of the role changes. The new model presents a generalization of the demographic version of the Hawk-Dove game,with the difference being that the opponents in the game are drawn from two separate subpopulations consisting of Owners and Intruders. Here, the Intruders check random nest sites and play the Hawk-Dove game with the Owner if they are occupied. Meanwhile, the Owners produce newborns that become Intruders, since they must find a free nest site to reproduce. An interesting feedback mechanism is produced via the fluxes of individuals between the different subpopulations. In addition, the population growth suppression mechanism resulting from the fixation Bourgeois strategy is analyzed.

Dynamic Game and Pricing for Data Sponsored 5G Systems With Memory Effect

By enabling revenue sharing between the network operators and the sponsors, the sponsored data has been proven to be a promising solution and is becoming a ubiquitous trend in the fifth generation (5G) networks for improving data connectivity for the users, increasing mobile engagement for the sponsors, and ensuring revenue for the network operators. In this paper, we investigate the data sponsored 5G system on a long-run basis. Compared with the conventional dynamic, i.e., long-run, model, the users in the system are memory-affecting, i.e., the users' decision-making is affected by their past service experience. In the system under our consideration, the users decide on the communication service access by jointly taking into account their instantaneous achievable utility and the history of their service experience, e.g., the past improved utility corresponding to the data sponsorship. The 5G system works as the utility provider for managing the communication service. Specifically, by using the concept of the power-law fading memory and the classical evolutionary game theory, we formulate a population game to model and study the dynamic behaviors of the players in the data sponsored 5G system. In the game, the interaction among the memory-affecting rational users is formulated as a fractional evolutionary game, and the communication service management of the 5G system is formulated as a classical evolutionary game. We analytically prove the existence and uniqueness of the solution to the population game. We both analytically and numerically verify the stability of the solution. The performance evaluation shows some insightful results. For example, the data sponsorship can significantly increase the data consumption for the users when they are heavily memory-affecting. Following this, we study a data sponsorship pricing problem with the objective to maximize the data consumption at the expense of the minimal data sponsorship.

Polymorphic Evolutionary Games and Non-Mendelian Genetics.

Classical evolutionary game theory (EGT) focuses on competition among phenotypes while assuming asexual transmission of these phenotypes to the next generation. However, phenotypic selection and sexual recombination are not necessarily mutually reinforcing in populations with sexual reproduction. In particular, it has been long known that some of the evolutionarily stable strategies derived by EGT methods cannot be achieved by sexually reproducing, real-world, populations. Thus, the recently formulated polymorphic evolutionary game theory (PEGT), which adds underlying genetics and sexual reproduction to evolutionary games, has the potential to revolutionize game theoretical modeling of coevolutionary processes. To illustrate the advantages of PEGT over classical EGT, I analyze two of the best known EGT models: Hawk/Retaliator/Dove and Defector/Tit-for-Tat/Altruist, by PEGT methods. I show that if one admits non-Mendelian genetics-common in heritable behavior, both of these games exhibit the properties of moderated aggression and conditional cooperation as components of population-level polymorphisms.

Dynamic Model for Network Selection in Next Generation HetNets With Memory-Affecting Rational Users

Recently, due to the staggering growth of wireless data traffic, heterogeneous networks have drawn tremendous attention due to the capabilities of enhancing the capacity/coverage and reducing energy consumption for the next generation wireless networks. In this paper, we study a long-run user-centric network selection problem in the 5G heterogeneous network, where the network selection strategies of the users can be investigated dynamically. Unlike the conventional studies on the long-run model, we incorporate the memory effect and consider the fact that the decision-making of the users is affected by their memory, i.e., their past service experience. Namely, the users select the network based on not only their instantaneous achievable service experience but also their past service experience within their memory. Specifically, we model and study the interaction among the users in the framework of fractional evolutionary game based on the classical evolutionary game theory and the concept of the power-law memory. We analytically prove that the equilibrium of the fractional evolutionary game exists, is unique and uniformly stable. We also numerically demonstrate the stability of the fractional evolutionary equilibrium. Extensive simulations have been conducted to evaluate the performance of the fractional evolutionary game. The numerical results have revealed some insightful findings. For example, the user in the fractional evolutionary game with positive memory effect can achieve a higher cumulative utility compared with the user in the fractional evolutionary game with negative memory effect. Moreover, the fractional evolutionary game with positive memory effect can reduce the loss in the user's cumulative utility caused by the small-scale fading.

Fixation probabilities in populations under demographic fluctuations

We study the fixation probability of a mutant type when introduced into a resident population. We implement a stochastic competitive Lotka–Volterra model with two types and intra- and interspecific competition. The model further allows for stochastically varying population sizes. The competition coefficients are interpreted in terms of inverse payoffs emerging from an evolutionary game. Since our study focuses on the impact of the competition values, we assume the same net growth rate for both types. In this general framework, we derive a formula for the fixation probability varphi of the mutant type under weak selection. We find that the most important parameter deciding over the invasion success of the mutant is its death rate due to competition with the resident. Furthermore, we compare our approximation to results obtained by implementing population size changes deterministically in order to explore the parameter regime of validity of our method. Finally, we put our formula in the context of classical evolutionary game theory and observe similarities and differences to the results obtained in that constant population size setting.

The Iterated Hawk–Dove Game Revisited: The Effect of Ownership Uncertainty on Bourgeois as a Pure Convention

Classical evolutionary game theory shows that respect for ownership (“Bourgeois” behavior) can arise as an arbitrary convention to avoid costly disputes, but the same theory also predicts that a paradoxical disrespect for ownership (“anti-Bourgeois” behavior) can evolve under the same conditions. Given the rarity of the latter strategy in the natural world, it is clear that the classical model is lacking in some important biological details. For instance, the classical model assumes that roles of owner and intruder can be recognized unambiguously. However, in the natural world there is often confusion over ownership, mediated for example by the temporary absence of the owner. We show that if intruders sometimes believe themselves to be owners, then the resulting confusion over ownership can broaden the conditions under which Bourgeois behavior is evolutionarily stable in the one-shot Hawk–Dove game. Likewise, introducing mistakes over ownership into a more realistic game with repeated interactions facilitates the evolution of Bourgeois behavior where previously such a result could arise only if owners are intrinsically more likely to win fights than intruders. Collectively, therefore, we find that mistakes over ownership facilitate the evolution of Bourgeois behavior. Nevertheless, relaxing the assumption that ownership is unambiguously recognized does not appear to completely explain the extreme rarity of anti-Bourgeois behavior in nature.

A New Stationary Game Equilibrium Induced by Stochastic Group Evolution and Rational Individual Choice

In the present paper, a new approach to equilibrium selection for very general normal form games has been constructed by introducing stochastic optimal stopping theory into classical evolutionary game theory. That is, the new game equilibrium is induced by both stochastic group evolution and decentralized rational individual choice. Moreover, stability of the game equilibrium is confirmed from both time and space dimensions.

Doves and hawks in economics revisited: An evolutionary quantum game theory based analysis of financial crises

The last financial and economic crisis demonstrated the dysfunctional long-term effects of aggressive behaviour in financial markets. Yet, evolutionary game theory predicts that under the condition of strategic dependence a certain degree of aggressive behaviour remains within a given population of agents. However, as a consequence of the financial crisis, it would be desirable to change the “rules of the game” in a way that prevents the occurrence of any aggressive behaviour and thereby also the danger of market crashes. The paper picks up this aspect. Through the extension of the well-known hawk–dove game by a quantum approach, we can show that dependent on entanglement, evolutionary stable strategies also can emerge, which are not predicted by the classical evolutionary game theory and where the total economic population uses a non-aggressive quantum strategy.

Doves and Hawks in Economics Revisited: An Evolutionary Quantum Game Theory-Based Analysis of Financial Crises

The last financial and economic crisis demonstrated the dysfunctional long-term effects of aggressive behaviour in financial markets. Yet, evolutionary game theory predicts that under the condition of strategic dependence a certain degree of aggressive behaviour remains within a given population of agents. However, as the consequences of the financial crisis exhibit, it would be desirable to change the ''rules of the game'' in a way that prevents the occurrence of any aggressive behaviour and thereby also the danger of market crashes. The paper picks up this aspect. Through the extension of the in literature well-known Hawk-Dove game by a quantum approach, we can show that dependent on entanglement, also evolutionary stable strategies can emerge, which are not predicted by classical evolutionary game theory and where the total economic population uses a non-aggressive quantum strategy.

Statistical Mechanics of Games

(Resume is available at http://kikkawa.cyber-ninja.jp/index.htm ) Abstract This paper formulates evolutionary game theory with a new concept using statistical mechanics. This study analyzes the following situations: each player on the lattice plays a game with its nearest neighbor or with a randomly matched player. These situations are formulated using an analogy with the Ising model and the Sherrington-Kirkpatrick model, the simplest models in statistical mechanics. As a result, theoretical calculations agree with classical evolutionary game theory in terms of the parameter (γ) size1. This study analyzes the action's probability of distribution on the lattice with percolation in details. If γ is sufficiently small, then we know the kind of patterns the distribution of actions makes on the lattice. These patterns are either a concentric circle or a chess pattern. If γ meets certain conditions, then infinite (*)-clusters coexist in a chess pattern. In particular, this study shows that bifurcations occur in a quenched system with externalities, hence, this system has multiple equilibria. This study discusses the simplified Cont and Bouchaud model through our models. We can understand the player's behavior in Cont and Bouchaud model.

Stability of Mixed Nash Equilibria in Symmetric Quantum Games

In bimatrix games the Bishop–Cannings theorem of the classical evolutionary game theory does not permit pure evolutionarily stable strategies (ESSs) when a mixed ESS exists. We find the necessary form of two-qubit initial quantum states when a switch-over to a quantum version of the game also changes the evolutionary stability of a mixed symmetric Nash equilibrium.

Spatial evolutionary game theory: Hawks and Doves revisited

We consider a spatial generalization of evolutionary game theory in which strategies are distributed over a spatial array of sites. We assume that the strategy corresponding to a given site has local interactions with the strategies sitting on neighbouring sites, and that the strategies change if neighbouring strategies are doing better. After briefly setting the stage with a formal definition of spatial evolutionary game theory, we consider the spatial extension of the Hawk-Dove game, and we show that the results are qualitatively different from those obtained from classical evolutionary game theory. For example, the proportion of Hawks in the population is in general lower in the spatial game than in the classical one. We also consider spatial generalizations of the extensions of the Hawk-Dove game obtained by including strategies such as Retaliator and Bully. Here, too, the results from the spatial game are very different from the classical results. In particular, with space Retaliator is a much more successful strategy than one would expect from classical considerations. This suggests that, in general, spatial structure may facilitate the evolution of strategies such as Retaliator, which do not necessarily prosper classically, and which are reminiscent of the \`nice', \`provokable' and `forgiving' strategies which seem to play a central role in the evolution of cooperation. The results indicate that including spatial structure in evolutionary game theory is a fruitful extension.