scholarly journals Evolution of populations with strategy-dependent time delays

2019 ◽  
Author(s):  
Jacek Miȩkisz ◽  
Marek Bodnar
Keyword(s):  
Stationary State ◽  
Time Delays ◽  
Replicator Dynamics ◽  
Evolutionarily Stable Strategy ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Small Time ◽  
Stochastic Perturbations ◽  
New Type ◽  
Novel Behavior

AbstractWe address the issue of stability of coexistence of two strategies with respect to time delays in evolving populations. It is well known that time delays may cause oscillations. Here we report a novel behavior. We show that a microscopic model of evolutionary games with a unique mixed evolutionarily stable strategy (a globally asymptotically stable interior stationary state in the standard replicator dynamics) and with strategy-dependent time delays leads to a new type of replicator dynamics. It describes the time evolution of fractions of the population playing given strategies and the size of the population. Unlike in all previous models, an interior stationary state of such dynamics depends continuously on time delays and at some point it might disappear, no cycles are present. In particular, this means that an arbitrarily small time delay changes an interior stationary state. Moreover, at certain time delays, there may appear another interior stationary state.Author summarySocial and biological processes are usually described by ordinary or partial differential equations, or by Markov processes if we take into account stochastic perturbations. However, interactions between individuals, players or molecules, naturally take time. Results of biological interactions between individuals may appear in the future, and in social models, individuals or players may act, that is choose appropriate strategies, on the basis of the information concerning events in the past. It is natural therefore to introduce time delays into evolutionary game models. It was usually observed, and expected, that small time delays do not change the behavior of the system and large time delays may cause oscillations. Here we report a novel behavior. We show that microscopic models of evolutionary games with strategy-dependent time delays, in which payoffs appear some time after interactions of individuals, lead to a new type of replicator dynamics. Unlike in all previous models, interior stationary states of such dynamics depend continuously on time delays. This shows that effects of time delays are much more complex than it was previously thought.

scholarly journals The stabilization of equilibria in evolutionary game dynamics through mutation: mutation limits in evolutionary games

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190355 ◽  
Author(s):  
Johann Bauer ◽  
Mark Broom ◽  
Eduardo Alonso
Keyword(s):  
Nash Equilibrium ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Solution Concept ◽  
Evolutionary Games ◽  
Dynamic Approach ◽  
Q Learning ◽  
Interior Equilibrium ◽  
Dynamic Solution ◽  
Multi Agent

The multi-population replicator dynamics is a dynamic approach to coevolving populations and multi-player games and is related to Cross learning. In general, not every equilibrium is a Nash equilibrium of the underlying game, and the convergence is not guaranteed. In particular, no interior equilibrium can be asymptotically stable in the multi-population replicator dynamics, e.g. resulting in cyclic orbits around a single interior Nash equilibrium. We introduce a new notion of equilibria of replicator dynamics, called mutation limits, based on a naturally arising, simple form of mutation, which is invariant under the specific choice of mutation parameters. We prove the existence of mutation limits for a large class of games, and consider a particularly interesting subclass called attracting mutation limits. Attracting mutation limits are approximated in every (mutation-)perturbed replicator dynamics, hence they offer an approximate dynamic solution to the underlying game even if the original dynamic is not convergent. Thus, mutation stabilizes the system in certain cases and makes attracting mutation limits near attainable. Hence, attracting mutation limits are relevant as a dynamic solution concept of games. We observe that they have some similarity to Q-learning in multi-agent reinforcement learning. Attracting mutation limits do not exist in all games, however, raising the question of their characterization.

DYNAMICS OF DETERMINISTIC AND STOCHASTIC EVOLUTIONARY GAMES WITH MULTIPLE DELAYS

2013 ◽  
Vol 23 (07) ◽  
pp. 1350122
Author(s):  
NICOLETA SÎRGHI ◽  
MIHAELA NEAMŢU
Keyword(s):  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Multiple Delays ◽  
Differential Delay Equation ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Differential Delay ◽  
Stochastic Differential Delay Equation ◽  
White And Colored Noise

In the present paper, we study the effect of time delays in evolutionary games with one population of users and two strategies. The case where the delays, corresponding to different strategies, are not the same is considered. The local stability of the stationary state for the replicator dynamics is analyzed. We show that there is Hopf bifurcation. The stability of the bifurcating periodic solutions is determined by using the center manifold theorem and normal form theory. The stochastic evolutionary game with delay is taken into consideration. We also study the behavior of the first and second solution moments for linear stochastic differential delay equation in the presence of white and colored noise. The last part of the paper includes numerical simulations and conclusions.

scholarly journals Evolutionary games and population dynamics: maintenance of cooperation in public goods games

2006 ◽  
Vol 273 (1600) ◽  
pp. 2565-2571 ◽  
Author(s):  
Christoph Hauert ◽  
Miranda Holmes ◽  
Michael Doebeli
Keyword(s):  
Public Goods ◽  
Prisoner's Dilemma ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Natural Extension ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Darwinian Evolution ◽  
Ecological Dynamics ◽  
Public Goods Games

The emergence and abundance of cooperation in nature poses a tenacious and challenging puzzle to evolutionary biology. Cooperative behaviour seems to contradict Darwinian evolution because altruistic individuals increase the fitness of other members of the population at a cost to themselves. Thus, in the absence of supporting mechanisms, cooperation should decrease and vanish, as predicted by classical models for cooperation in evolutionary game theory, such as the Prisoner's Dilemma and public goods games. Traditional approaches to studying the problem of cooperation assume constant population sizes and thus neglect the ecology of the interacting individuals. Here, we incorporate ecological dynamics into evolutionary games and reveal a new mechanism for maintaining cooperation. In public goods games, cooperation can gain a foothold if the population density depends on the average population payoff. Decreasing population densities, due to defection leading to small payoffs, results in smaller interaction group sizes in which cooperation can be favoured. This feedback between ecological dynamics and game dynamics can generate stable coexistence of cooperators and defectors in public goods games. However, this mechanism fails for pairwise Prisoner's Dilemma interactions and the population is driven to extinction. Our model represents natural extension of replicator dynamics to populations of varying densities.

scholarly journals The Stability of Two-Community Replicator Dynamics with Discrete Multi-Delays

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2120
Author(s):  
Jinxiu Pi ◽  
Hui Yang ◽  
Yadong Shu ◽  
Chongyi Zhong ◽  
Guanghui Yang
Keyword(s):  
Time Delays ◽  
Replicator Dynamics ◽  
Evolutionarily Stable Strategy ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stable Strategy ◽  
Two Delays ◽  
The Stability ◽  
Delay Dependent ◽  
Evolutionarily Stable

This article investigates the stability of evolutionarily stable strategy in replicator dynamics of two-community with multi-delays. In the real environment, players interact simultaneously while the return of their choices may not be observed immediately, which implies one or more time-delays exists. In addition to using the method of classic characteristic equations, we also apply linear matrix inequality (i.e., LMI) to discuss the stability of the mixed evolutionarily stable strategy in replicator dynamics of two-community with multi-delays. We derive a delay-dependent stability and a delay-independent stability sufficient conditions of the evolutionarily stable strategy in the two-community replicator dynamics with two delays, and manage to extend the sufficient condition to n time delays. Lastly, numerical trials of the Hawk–Dove game are given to verify the effectiveness of the theoretical consequences.

scholarly journals USING EVOLUTIONARY GAMES THEORY FOR PLAYERS BEHAVIOR ANALYSIS IN COMPETITIVE SHOOTING GAMES: A LITERATURE REVIEW

2021 ◽  
pp. 101-103
Author(s):  
Luka Baryshych ◽  
Igor Baklan
Keyword(s):  
Game Theory ◽  
Behavior Analysis ◽  
Evolutionary Biology ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Fuzzy Algorithms ◽  
Evolutionary Games Theory ◽  
Games Theory ◽  
Competitive Shooting

The paper is dedicated to the overview of current state of the evolutionary games approach to the building of environments to analyze players behavior. The evolutionary game theory applications differ from the orthodox game theory. Initially, it was used to address problems in evolutionary biology and later was suited for broader range of problems.We will oversee the development of the evolutionary games theory in finance and its applications in behavior analysis in competitive gaming. The paper is focused on replicator dynamics, learning model based on it and its possible application to behavior analysis based on fuzzy algorithms and approaches used in economics to be applied to the new emerging field of cybersports.

scholarly journals Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 431
Author(s):  
Chongyi Zhong ◽  
Hui Yang ◽  
Zixin Liu ◽  
Juanyong Wu
Keyword(s):  
Time Delay ◽  
Replicator Dynamics ◽  
Evolutionarily Stable Strategy ◽  
Evolutionary Games ◽  
Stability Conditions ◽  
Stable Strategy ◽  
Distributed Time Delay ◽  
Player Game ◽  
The Stability ◽  
Evolutionarily Stable

In this paper, we consider evolutionary games and construct a model of replicator dynamics with bounded continuously distributed time delay. In many circumstances, players interact simultaneously while impacts of their choices take place after some time, which implies a time delay exists. We consider the time delay as bounded continuously distributed other than some given constant. Then, we investigate the stability of the evolutionarily stable strategy in the replicator dynamics with bounded continuously distributed time delay in two-player game contexts. Some stability conditions of the unique interior Nash equilibrium are obtained. Finally, the simple but important Hawk–Dove game is used to verify our results.

scholarly journals Research on Optimization of Array Honeypot Defense Strategies Based on Evolutionary Game Theory

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 805
Author(s):  
Leyi Shi ◽  
Xiran Wang ◽  
Huiwen Hou
Keyword(s):  
Replicator Dynamics ◽  
Evolutionarily Stable Strategy ◽  
Evolutionary Game ◽  
Game Model ◽  
Evolutionarily Stable Strategies ◽  
Defense Strategies ◽  
Active Defense ◽  
Defense Technology ◽  
The Stability ◽  
Evolutionarily Stable

Honeypot has been regarded as an active defense technology that can deceive attackers by simulating real systems. However, honeypot is actually a static network trap with fixed disposition, which is easily identified by anti-honeypot technology. Thus, honeypot is a “passive” active defense technology. Dynamic honeypot makes up for the shortcomings of honeypot, which dynamically adjusts defense strategies with the attack of hackers. Therefore, the confrontation between defenders and attackers is a strategic game. This paper focuses on the non-cooperative evolutionary game mechanism of bounded rationality, aiming to improve the security of the array honeypot system through the evolutionarily stable strategies derived from the evolutionary game model. First, we construct a three-party evolutionary game model of array honeypot, which is composed of defenders, attackers and legitimate users. Secondly, we formally describe the strategies and revenues of players in the game, and build the three-party game payoff matrices. Then the evolutionarily stable strategy is obtained by analyzing the Replicator Dynamics of various parties. In addition, we discuss the equilibrium condition to get the influence of the number of servers N on the stability of strategy evolution. MATLAB and Gambit simulation experiment results show that deduced evolutionarily stable strategies are valid in resisting attackers.

scholarly journals SATO–CRUTCHFIELD FORMULATION FOR SOME EVOLUTIONARY GAMES

2003 ◽  
Vol 14 (07) ◽  
pp. 963-971 ◽  
Author(s):  
E. AHMED ◽  
A. S. HEGAZI ◽  
A. S. ELGAZZAR
Keyword(s):  
Prisoner's Dilemma ◽  
Initial Conditions ◽  
Evolutionarily Stable Strategy ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Theoretical Explanation ◽  
Battle Of The Sexes ◽  
Different Types ◽  
Evolutionarily Stable ◽  
Rules Of The Game

The Sato–Crutchfield equations are analytically and numerically studied. The Sato–Crutchfield formulation corresponds to losing memory. Then the Sato–Crutchfield formulation is applied for some different types of games including hawk–dove, prisoner's dilemma and the battle of the sexes games. The Sato–Crutchfield formulation is found not to affect the evolutionarily stable strategy of the ordinary games. But choosing a strategy becomes purely random, independent of the previous experiences, initial conditions, and the rules of the game itself. The Sato–Crutchfield formulation for the prisoner's dilemma game can be considered as a theoretical explanation for the existence of cooperation in a population of defectors.

scholarly journals System Dynamics Model for the Evolutionary Behaviour of Government Enterprises and Consumers in China’s New Energy Vehicle Market

2020 ◽  
Vol 12 (4) ◽  
pp. 1578 ◽  
Author(s):  
Hongxia Sun ◽  
Yao Wan ◽  
Huirong Lv
Keyword(s):  
System Dynamics ◽  
Motor Vehicle ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Practical Significance ◽  
Subsidy Policy ◽  
New Energy ◽  
New Energy Vehicle ◽  
The Impact ◽  
Vehicle Market

Exhaust pollution and energy crises are worsening worldwide. China has become the largest motor vehicle producer; thus, promoting the use of new energy vehicles (NEVs) in China has important practical significance. In this paper, considering the limited rationality of governments, NEV enterprises and consumers, we study the subsidy policy of the China NEV market using the evolutionary game and system dynamics (SD) methods. First, a tripartite evolutionary game model is developed and the replicator dynamics equations and Jacobian matrix are obtained. A SD simulation of the model was conducted to further clarify the impact of the initial market proportion and three variables used in the model. The results show that the initial market proportion affects the evolution speed but does not affect the evolution result when the three group players all choose a mixed strategy. For governments, they should not hastily cancel price subsidies provided to consumers; rather, they should dynamically adjust the rate of the subsidy decrease and increase the consumers’ extra cost for purchasing fuel vehicles (FVs). NEV enterprises should appropriately increase their investments in the research and development (R&D) of NEVs.

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