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Emergence of Intelligence
Published in Hitoshi Iba, AI and SWARM, 2019
Evolutionarily Stable Strategy (ESS) corresponds to a situation when a strategy occupies a group and prevents other strategies from invading it. This idea was advocated in 1973 by John Maynard Smith5 and George Price6. When the strategies A and B are given, and the gain for A is assumed to be E(A, B), then the conditions of the ESS are as follows:
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
In this article, an evolutionary game is constructed, comprising of shippers, CLPs, and drivers, so as to investigate the interaction mechanism among the participants in crowd logistics. Based on the game model, a system-dynamics model is also constructed to simulate the strategies selection of participants. Static and dynamic scenarios are considered in both game and system dynamic model. Through the analysis of results, the article draws the following conclusions: Firstly, the model with static scenario cannot converge to the stable state, and if changing the initial value, the article will obtain multiple evolutionary stable strategies. Secondly, the dynamic scenario has a better performance in restraining the strategy fluctuations among participants. Under the dynamic scenario, the strategy combination of participants eventually converges to that is the evolutionarily stable strategy. Thirdly, the probability that shippers adopt “price-exploitation” strategy is positively correlated with extra profits while negatively correlated with the upper bond of the penalties. What’s more, the profit is the key factor affecting the willingness of drivers joining CLP.
Evolutionary game theoretical approach for equilibrium of cross-border traffic
Published in Transportmetrica B: Transport Dynamics, 2019
Mehmmood A. Abd, Sarab F. Al Rubeaai, Saeideh Salimpour, Ahmed Azab
In order to prove that is an evolutionary stable strategy (ESS), the system of equations in (18) must be linearized around and the Eigenvalues of the Jacobian Matrix must have negative real parts. The linearization of equation (18) is given by: which can be simplified as: Where is the Jacobin matrix that can be defined as: It is clear that the summation of the column elements are all zeros in and it has Eigenvalues of zeros. Furthermore, the diagonal values of are negative because and are diagonally dominated in a way such that Since all Eigenvalues of the matrix have a negative real part, this implies that is an evolutionarily stable strategy (Berkey 1975). It is clear that the stability of the game is proven, which signifies that the traffic distribution over finite checkpoints is ESS.
Selection of government supervision mode of PPP projects during the operation stage
Published in Construction Management and Economics, 2019
Evolutionary game theory stems from biological evolutionism (Smith 1974). Similar to the behaviour of animals, human beings generally make decisions with gut instinct or by imitating successful strategies when faced with a dilemma. An evolutionary game involves players from one or more populations, who interact with each other as a repeated game over finite or infinite time horizon (Babu and Mohan 2018). In order to maximize their payoffs, each player continuously adjusts their strategies over time through learning, imitation, mutation or even random choice (Eguíluz et al. 2005). In this game process, errors are important for equilibrium selection, and conflicts are modelled typically with a small number of pure strategies, thereby allowing them to obtain analytical solutions whenever possible (Bulò and Bomze 2011). Therefore, the new solution concept of evolutionarily stable strategy (ESS) was proposed to understand the strategies that are likely to persist in such a population (Smith and Price 1973, Taylor and Jonker 1978). ESS is a distribution of strategies in a population such that all sufficiently small deviations from the equilibrium proportions are self-correcting. This strategy will not be invaded by any small mutant strategy (Young 2011). Informally, if each individual in the entire population adopts this strategy, the population could resist any invasion of mutation strategy under the action of natural selection.