Theory Of Games With Entropy In Management Science

In this dissertation,the author adds Shannon's entropy in information theory and principle of maximum entropy in decision analysis into game theory.So a new game system is formed.On the other hand,applications of the game system to economical management science are studied as well.In chapter 1,Shannon's entropy and principle of maximum entropy is introduced into matrix games.Compactness,convexity,commutative property of set of game solutions with maximum entropy,called Neumann-Shannon game solution,and equi-average matrix game,i.e.a matrix game with unique Neumann-Shannon solution, are studied.In Chapter 2,the author improves traditional definition of continuous games.First, players' strategy spaces are defined as[0,2],instead of[0,1].Second,players' strategies are defined as density functions,instead of distribution function.Third, Shannon entropy and principle of maximum entropy are introduced the new game systems.Then,on a Banach space,the author uses measure theory,real analysis and Shannon entropy theory of continuous random variables to obtain theory of continuous game with entropy.Basis on this,he studies convexity and topology structure of set of Neumann-Shannon game solutions,which are game solutions with maximum entropy, of continuous game with entropy.In chapter 3,the author strictly confines the "static" of static games in complete information and assumes that principle of maximum entropy is all the players' common knowledge.Basic on this,the concepts of a condition game and its expected equilibria are introduced and algorithm and properties of the equilibria are studied.In chapter 4,the concept of Neumann-Morgenstern stable sets,or briefly N-M stable sets,is introduced.And existence and uniqueness theorem and algorithm of N-M stable sets are studied. In chapters 5,the author discusses maximal stable rectangle,unique represent theorem of L-games,ideally complete static games,games with Schelling point,a complete static game with entropy and its expected equilibria and so forth.From chapters 8 to 11,the author studies applications of game theory with entropy to management science.First,some examples,as condition games,relative to investments and applications for funding in management science are given.Second, some sustainable development games,as condition games,in environmental management science are studied.Third,the author discusses expected equilibrium analysis of some classical bi-matrix games in economical management science,such as thief-guard game,poor-rich men patrolling game,game between clever pigs,game of tax inquiry-tax evasion,and social welfare game.Fourth,two examples of game with entropy in logistics management science are given.