Static Continuous Game Econometric Model

The game theory is the effective instrument to analyze the action of player when the one player's action affects others. The game of econometric is a main analysis instrument in the empirical analysis of this problem.This paper wound study the econometric of continuous game, which is the expanding of the research in game-econometric.The main contribution of this paper is to give a simple frame:write the payment function as integration function; estimate the payment function indirectly by estimate the function in the integration. In this frame the econometrician can apply the robust econometrics method.The main objection of this paper to resolve three problems:estimating the payment and reaction function of player under complete information;the estimation of payment and reaction function under incomplete information.Chapter 2 introduce the main achievement in research of game-econometric,and give the thought of estimate continuous game in this paper.Chapter 3 focus on the estimate of continuous game under complete information. This paper give a estimate frame of continuous game:analyze the condition of uniqueness equilibrium firstly; then study the identification of the parameter; and then study the estimation of payment function and reaction function. Chapter 4 focus the estimation payment function under incomplete information. We study the condition to the uniqueness of BNE,and the identification of parameter. This paper put forward four information structure based on the information set of econometrician,and thought estimate method and step in the five information structure.Chapter 5 focus on the estimate reaction function of player under the incomplete game.The main innovation of this paper embody in the four aspect.First, this paper gives a theoretic frame about the estimate continuous game systematically, including estimate of continuous game under complete and incomplete information. We put forward the thought of game under the complete information firstly. Then we thought about the information structure of econometrician,and study the estimate step in the five information. In the contrary of estimate discrete game,which apply some new econometric method,but the result is not robust. This paper give a simple frame:write the payment function as integration function; estimate the payment function indirectly by estimate the function in the integration. In this frame the econometrician can apply the robust econometrics method.This paper study the condition to the uniqueness of equilibrium in the continuous game. The characteristic root of derivative matrix of player's reaction function is less than one under the complete information. Similarly this paper gives the condition of uniqueness equilibrium under incomplete information. The identification condition of player's payment function is same under complete and incomplete information.In order to estimate the player' payment function, this paper apply the specific FIML method, the coefficient of endogenous variable is unrestraint. We prove the consistent and converge distribution of FIML estimate.In order to estimate the payment and reaction function under incomplete information, this paper put forward two stage nonparametric method, and prove the converge rate of nonparametric instrument.