The solution of evolutionary games using the theory of Hamilton-Jacobi equations

Tarasyev AM (1995). The solution of evolutionary games using the theory of Hamilton-Jacobi equations. Applied Mathematics and Mechanics 59 (6): 921-933. DOI:10.1016/0021-8928(95)00125-5.

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Abstract

A dynamical model of a non-antagonistic evolutionary game for two coalitions is considered. The model features an infinite time span and discounted payoff functionals. A solution is presented using differential game theory. The solution is based on the construction of a value function for auxiliary antagonistic differential games and uses an approximate grid scheme from the theory of generalized solutions of the Hamilton-Jacobi equations. Together with the value functions the optimal guaranteeing procedures for control on the grid are computed and the Nash dynamic equilibrium is constructed. The behaviour of trajectories generated by the guaranteeing controls is investigated. Examples are given.

Item Type: Article
Research Programs: Dynamic Systems (DYN)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 02:05
Last Modified: 25 Aug 2016 11:24
URI: http://pure.iiasa.ac.at/4321

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