Contract, In The Limited Strategy Type Game Discussion Between The Communication System And Its Related Strategies, The Correlated Equilibrium And Nash Equilibrium

In dealing with the choice equilibria,there is inter-relation about how to make choices concentrated on the equilibrium point and how to definite the concept of equilibrium.It belongs to basic research in game theory for the definition of equilibrium and its discussion.This paper is concerned about the game of finitelg strateging form the rules to allow the player to have a certain correlation between the circumstances of action defined by the equilibrium,its main work involves:First,it describe the correlated concept of strategy and role of norms through examples,this paper gives out instandard the correlated strategy,the game in contract,the maximum value of the minimum,the allocation set of expectation pay and one which set to meet the expectations of the individual,etc.It proves some of their nature or structure,such as that the correlated set of strategies is compact convex subset;that the expected pay is continuous function set on the correlated strategy;that the collection composed of all possible expected payment configure is compact convex subset;the corresponding strategies to the allocation set of Nash equilibria equilibrium in Game set on the gather N of players on the whole is rational;Nash belong to the subset to meet the rational expectations of individual pay-configuration, etc.Second.It illustrates some of the conclusions of the paper through specific examples,and tests some corresponding conclusions obtained by other documents, especially in the above part to point out that perfect the allocation set of Nash equilibria situated in the expected pay-configuration as well as in the expected pay-configuration which meet the rational expectation of individuals.Third.It provides a comprehensive survey to the relation and their difference between sub-game perfect Nash equilibrium and Nash equilibrium,and reveals the relation and distinction between the correlated strategy and mixed strategy in the game of finitely stralegie form,discusses the link of relevant strategies to contract game,and explains the relations between contract inclusive equilibrium and Nash equilibrium, and provides not only proof in theory but also operation method.Forth.It points out the relations among the correlcted equilibrium,Nash equilibrium and their corresponding equilibrium set.It proves that the relation between relevant equilibrium and Nash equilibrium reflects that in the limited-strategy game all Nash equilibrium are corresponded to relevant equilibrium,the relevant equilibrium definitely exists in limited-strategy game,the relevant equilibrium is compact,it introduces the strategy incentive restriction,and at the same time gives the approach for relevant equilibrium which has been illustrated through examples;Finally.It introduces communication message system and communication game,proves that any of the Nash equilibrium in communications game is equivalent to a relevant equilibrium defined by strategy incentive restriction,illustrates the role of the shown principle, points out that any of the communications systems,there may be a lot of equilibrium in communications Game,and these equilibria will be equivalent to different the correlated equilibrium.