scholarly journals Stability of evolutionarily stable strategies in discrete replicator dynamics with time delay

2004 ◽  
Vol 231 (2) ◽  
pp. 175-179 ◽  
Author(s):  
Jan Alboszta ◽  
Jacek Mie¸kisz
Keyword(s):  
Time Delay ◽  
Replicator Dynamics ◽  
Evolutionarily Stable Strategies ◽  
Evolutionarily Stable

scholarly journals Evolutionary Game Theory: A Generalization of the ESS Definition

2019 ◽  
Vol 21 (04) ◽  
pp. 1950005
Author(s):  
Elvio Accinelli ◽  
Filipe Martins ◽  
Jorge Oviedo
Keyword(s):  
Game Theory ◽  
Strategic Planning ◽  
Evolutionary Game Theory ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Previous Literature ◽  
Evolutionarily Stable Strategies ◽  
Symmetric Games ◽  
Two Populations ◽  
Evolutionarily Stable

In this paper, we study the concept of Evolutionarily Stable Strategies (ESSs) for symmetric games with [Formula: see text] players. The main properties of these games and strategies are analyzed and several examples are provided. We relate the concept of ESS with previous literature and provide a proof of finiteness of ESS in the context of symmetric games with [Formula: see text] players. We show that unlike the case of [Formula: see text], when there are more than two populations an ESS does not have a uniform invasion barrier, or equivalently, it is not equivalent to the strategy performing better against all strategies in a neighborhood. We also construct the extended replicator dynamics for these games and we study an application to a model of strategic planning of investment.

scholarly journals Discrete Dynamics in Evolutionary Games

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Orlando Gomes
Keyword(s):  
Discrete Time ◽  
Replicator Dynamics ◽  
Evolutionary Games ◽  
Strategic Interaction ◽  
Discrete Dynamics ◽  
Evolutionarily Stable Strategies ◽  
Evolutionarily Stable

This paper furnishes a guide for the study of 2-dimensional evolutionary games in discrete time. Evolutionarily stable strategies are identified and nonlinear outcomes are explored. Besides the baseline payoffs of the established strategic interaction, the following elements are also vital to determine the dynamic outcome of a game: the initial fitness of each agent and the rule of motion that describes how individuals switch between strategies. In addition to the dynamic rule commonly used in evolutionary games, the replicator dynamics, we propose another rule, which acknowledges the role of expectations and sophisticates the replicator mechanism.

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 Evolutionary Stability for Interactions among Kin under Quantitative Inheritance.

Genetics ◽  
1989 ◽  
Vol 121 (4) ◽  
pp. 877-889
Author(s):  
A B Harper
Keyword(s):  
Inclusive Fitness ◽  
Fitness Function ◽  
Quantitative Inheritance ◽  
Evolutionarily Stable Strategies ◽  
Environmental Variance ◽  
Pairwise Interactions ◽  
Simplifying Assumptions ◽  
Multilocus Model ◽  
Evolutionarily Stable

Abstract The theory of evolutionarily stable strategies (ESS) predicts the long-term evolutionary outcome of frequency-dependent selection by making a number of simplifying assumptions about the genetic basis of inheritance. I use a symmetrized multilocus model of quantitative inheritance without mutation to analyze the results of interactions between pairs of related individuals and compare the equilibria to those found by ESS analysis. It is assumed that the fitness changes due to interactions can be approximated by the exponential of a quadratic surface. The major results are the following. (1) The evolutionarily stable phenotypes found by ESS analysis are always equilibria of the model studied here. (2) When relatives interact, one of the two conditions for stability of equilibria differs between the two models; this can be accounted for by positing that the inclusive fitness function for quantitative characters is slightly different from the inclusive fitness function for characters determined by a single locus. (3) The inclusion of environmental variance will in general change the equilibrium phenotype, but the equilibria of ESS analysis are changed to the same extent by environmental variance. (4) A class of genetically polymorphic equilibria occur, which in the present model are always unstable. These results expand the range of conditions under which one can validly predict the evolution of pairwise interactions using ESS analysis.

Conditions for evolutionarily stable strategies

1980 ◽  
Vol 17 (2) ◽  
pp. 559-562 ◽  
Author(s):  
Andris Abakuks
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Evolutionarily Stable Strategies ◽  
Necessary And Sufficient ◽  
Evolutionarily Stable

It is pointed out that the conditions given by Haigh (1975) for finding evolutionarily stable strategies corresponding to a given matrix are sufficient, but not always necessary. An example is given, and an amended version of the necessary and sufficient conditions is stated.

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