China
Africa
Explore chapters and articles related to this topic
∞ Evolutionary Game Strategies of a Population of Evolutionary Biological Networks
Published in Bor-Sen Chen, Stochastic Game Strategies and Their Applications, 2019
The replicator equation (20.1) could translate these mathematical terms into the elementary principle of natural selection: strategies, or individuals using a given strategy, that reproduce with more efficiently, spread, and displace those with lesser fitness. Based on the dynamic equation in (20.1), the tools of dynamical system theory can be used to derive the fundamental characteristics of an evolutionary game. Since every rest point of the replicator dynamics is a Nash equilibrium, (20.1) can provide an evolutionary mechanism for achieving an equilibrium. Note that the replicator equation can be transformed by appropriate changes in variables into the Lotka–Volterra equation [503, 505]. From (20.1), it is noted also that (i) the replicator equation contains no mutations – strategies increase or decrease only due to reproduction; (ii) variation in population size has a linear relation to payoff difference; and (iii) the influence of environmental changes is not considered in the evolutionary mechanism [506]. Since random genetic variations and environmental disturbances play an important role in real biological evolution, the omission of these factors constitutes a deficiency of the replicator equation.
Evolutionary game analysis and simulation with system dynamics for behavioral strategies of participants in crowd logistics
Published in Transportation Letters, 2021
Yi Zhang, Chuankai Xiang, Lanxin Li, Hong Jiang
According to the EGT, replicator dynamics can be used to represent the learning and evolution mechanism of individuals in the game process of crowd logistics participants. Replicator dynamics, borrowed from biology, is an important concept in EGT (Taylor and Jonker 1978; Roca, Cuesta, and Sánchez 2009; Friedman 1991). According to replicator dynamics, the players will learn and imitate the beneficial strategies from others, which changes the proportion of players choosing one strategy (Friedman 1991). According to the method of Friedman (Friedman 1991), the change rate of a selected strategy is equal to the result of its expected payoffs subtracting the average expected payoffs (Roca, Cuesta, and Sánchez 2009; Friedman 1991; Zhou et al. 2019). The equation of the change rate is also named as replicator equation, and it was first proposed by Schuster and Sigmund (Roca, Cuesta, and Sánchez 2009; Schuster and Sigmund 1983). The replicator equation reflects the speed and direction of the strategy adjustment of the players (Guo, Zhang, and Yang 2018). When the replicator equation is equal to zero, it indicates that the players will not change their strategy again and the evolutionary game system reaches a relatively stable equilibrium state (Guo, Zhang, and Yang 2018; Liu, Li, and Hassall 2015).