Solution Method for Expected Equilibrium and Strictly Pure Nash Equilibirium and Analysis of Expecte Equilibrium in an n-person 0-1 Rational Game
Jiang Dian-yu · Systems Engineering · 2010
In order to find the most probable situation in an n-person strategy game that every player has exactly two actions and that principle of maximum entropy is all players' common knowledge when every player knows nothing about decisions of other ones,the method of solving strictly pure Nash equilibria and expected equilibria and the methods of finding the most probable situation with applications are given in this paper.By using the systems of binary numbers and decimal numbers,the algorithm of solving strictly pure Nash equilibria is proven.Basic on the above-mentioned common knowledge system,an evident formula of solving expected equilibria is given.By letting players' utilities be parameters,solving inequalities,and by formula of solving expected equilibria,an analysis method of equilibria is put forward.The study results show that simplicity of the formulas and methods come from the character of this form of games.Empirical results show that strictly pure Nash equilibria and expected equilbria can be quickly obtained by our methods and the conclusion obtained through the method of expected equilibrium analysis is more consist with practice,which is unlikely to be drawn from classical game theory.