Abstract
A differential evolution algorithm for solving Nash equilibrium in nonlinear continuous games is presented in this paper, called NIDE (Nikaido-Isoda differential evolution). At each generation, parent and child strategy profiles are compared one by one pairwisely, adapting Nikaido-Isoda function as fitness function. In practice, the NE of nonlinear game model with cubic cost function and quadratic demand function is solved, and this method could also be applied to non-concave payoff functions. Moreover, the NIDE is compared with the existing Nash Domination Evolutionary Multiplayer Optimization (NDEMO), the result showed that NIDE was significantly better than NDEMO with less iterations and shorter running time. These numerical examples suggested that the NIDE method is potentially useful.
Highlights
Nash equilibrium(NE) is one of the most important concepts in game theory, since it reveals the intrinsic link between the game equilibrium and economic equilibrium
The nonlinear demand functions and cost functions made the model more consistent with the real market competition, this will inevitably lead to the payoff functions become extremely complex, making the NE difficult to be solved
Compared with the existing Nash Domination Evolutionary Multiplayer Optimization (NDEMO), the results suggested that the NIDE was significantly better than NDEMO with less iterations and shorter runtime for solving the NE problems
Summary
Nash equilibrium(NE) is one of the most important concepts in game theory, since it reveals the intrinsic link between the game equilibrium and economic equilibrium. NE is widely used in practical applications, it is a key issue to find NE. Infinite strategies and complex payoff functions (such as non-concave, non-differentiable, multi-modal, etc.)make it difficult to solve NE. The difficulty of solving the NE has greatly limited its application in economics, management and sociology. Economists mainly studied continuous games, in which there are infinite strategies and the payoff functions are continuous. The purpose of game analysis is to predicate a result of a game, which is NE. The commonly used methods for locating NE of a continuous game are the following
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