The Repeated Game Theory And Its Applications

The repeated game theory plays an important role in non-cooperative games.It constitutes a very practical platform for studying dynamic games of strategic interactions.In the traditional literature,most of the researches on repeated games are all about some specific cases.The general mathematical expression model is rarely given.The existed folk theorems are mostly established under certain circumstances or assumptions,lack consistency.In order to better adapt to the needs of practical problems and further expand the scope of application of the model,a more general model of repeated game is established and a description of the folk theorem is given.Combining the repeated game with Cournot Model and Prisoner's Dilemma Model,the condition of complete information and incomplete information games are discussed in this paper.Firstly,the basic theoretical knowledge of the game theory is introduced briefly,including development history,basic concepts,specific classification,as well as equilibrium and solving methods of complete information game theory and incomplete information game theory.It provides theoretical support for the establishment of this model and the balanced solution.Secondly,a more general model for the research of repeated games is established.The strategies for repeated games and the returns under different circumstances are expressed,respectively.Further the folk theorems of repeated games are discussed.Thirdly,the Cournot Model under the complete information repeated game is studied.On the one hand,a consistent result is drawn by different methods to solve the static game model with certain two participants when the costs are not the same.And the two participants are generalized to multiple participants,a dynamic game model with multiple participants is constructed,the model is solved by optimization theory and matrix theory,presents a general mathematical expression of equilibrium output.On theother hand,the finite and infinite repeated games between two participants and multiple participants are discussed when the costs are the same.By constructing different trigger strategy,the conditions of the discount factor would satisfy under monopoly production situation is given.Finally,the Prisoner's Dilemma Model under repeated games with incomplete information is discussed.The classic Prisoner's Dilemma Model was improved by establishing a game model in which only one participant has incomplete information and two participants have incomplete information.And in the case of finite Prisoner's Dilemma repeated games,the generating condition of the cooperative equilibrium and equilibrium solution are obtained,when the participants adopt the“TFT ”and“TS ”strategies respectively.In other words,it is proved that there exists a perfect Bayesian equilibrium on the finite Prisoner's Dilemma repeated games,where participants have incomplete information with certain types.Now,applying the model to the concrete examples,which show that in the case of incomplete information,cooperation equilibrium can be achieved.Consequently,the validity of the model is proved.