The Analysis of the Structure Nash Equilibrium Solution of Two-person Two-strategy Game

The paper discusses the solution of 2-person 2strategy game in consideration that has the pure strategy equilibrium point of Nash, and adopts the underline method to get the equilibrium points of Nash considering the possibility that the gains of 2-person are equal at the first.The paper lists 81 kinds' states through the exhaustive method, and summarizes 6 kinds of independence situations: non-equilibrium point of Nash, oneequilibrium point of Nash, three-equilibrium point of Nash, fourequilibrium point of Nash for each one, and two-equilibrium point of Nash for two.In the meantime the paper gives the case of game for repairing the railway or the road for explaining the 6 kinds of equilibrium point of Nash.In the end, the paper draws a conclusion that the equilibrium points of Nash are not optimal solutions.Index Terms -equilibrium points of Nash, analytic of the structure, under line method, pure strategy Nash equilibrium, also known as a non cooperative game equilibrium, is an important term of game theory, named after John Nash.Nash balance refers to the situation that the game, for each participant, as long as the other people do not change strategy, he will not be able to improve your situation.Suppose that there are n players who participate in the game, given the strategies of the others conditions, their own optimal strategy choose each bureau (individual optimal strategy may depend on the may not be dependent on others' strategy), so as to maximize their interests.One strategy of all bureaus constitutes a strategy combination (Strategy Profile).Nash equilibrium refers to such a strategy; this strategy is composed of all persons involved in the optimal strategy.At a given others strategy case, no one has enough reason to break the balance.Nash equilibrium, in essence, is a kind of non cooperative game state.