Research on game theory and algorithm for a continuous uncertain complex system
The current research on game theory in uncertain complex systems typically involves a discrete set of strategies rather than continuous and random ones.In complex economic and social systems, continuous stochastic game problems and data ownership issues are often encountered.Against such a backdrop, this paper proposes a concept of stochastic game, builds a non-cooperative stochastic game model under a continuous strategy set and presents its Nash equilibrium solution algorithm.Firstly, the concept of non-cooperative stochastic game with uncertainty under continuous strategy is proposed, and a non-cooperative stochastic game model with the objective function of maximizing the payoff of players is built.The existence theorem of equilibrium solutions is also proposed.We build the Wasserstein fuzzy set, which is then transformed into a finite convex programming model by integrating distributed robust optimization methods with portfolio optimization methods.The genetic algorithms are employed to solve the approximate mixed strategy of the players in the game.Finally, a Nash equilibrium solution algorithm is built based on regression analysis and normalized the Nash equilibrium solution for weight confirmation.Our empirical analysis shows the theory and algorithm proposed in this article are effective and feasible.
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