Research Model Discrete Sequential Games

In game theory, we study the decision-making problems of interests influence eachother. Game theory has broadened the research field of economics, deepened the economicanalysis. Econometrics reveals the objective number relationships in economic activity, hasoccupied a very important position in economics. Game theory and econometrics havebecome the two most powerful approaches of analyzing economic problems now, andrepeatedly won the Nobel Prize in economics. Game-theoretic econometric models are thecombination of game theory and econometrics, are econometric analysis of game models,integrate the advantages of game theory and econometrics, and will make the analysis ofproblems in a more realistic way to reveal the inherent laws of economic activities.The role of game-theoretic econometric models in economic research is increasing,also has attracted more and more attentions. Many scholars have made contributions in thisfield. But the existing studies on sequential game are rarely. In this dissertation we willsystematically discuss the estimations of discrete sequential game-theoretic econometricmodels in various information cases, including the estimations of discrete sequentialgame-theoretic econometric models of complete and perfect information, the estimationsof discrete sequential game-theoretic econometric models of complete and imperfectinformation, and the estimations of discrete sequential game-theoretic econometric modelsof incomplete and perfect information. For the estimations of each type models, thisdissertation is begun with a simple model, further extended to the general model, andfinally given an example. Then based on the assumptions of the specific models, wecompute the appearing probabilities of all game equilibria, and estimate the modelparameters by observed data. Because in estimating of game-theoretic econometric models,the researchers can only observe actions, and cannot observe strategies, in the estimation ofgame-theoretic econometric models in various information cases of this dissertation, weanalyze the game equilibria based on actions but not strategies, give the conditions ofequilibrium action combinations, compute the ranges of random disturbancescorresponding game equilibria after ensuring equilibrium uniqueness. Then, we can get theappearing probabilities of corresponding equilibrium action combinations by calculatingthe products of the integrations of random disturbances in certain ranges and the appearing probabilities of equilibrium action combinations in these ranges, and these probabilities arerepresented with multiple integrals of random disturbances. When the number of players ingames is small, the dimension of the multiple integrals is low. The multiple integralsgenerally can be directly calculated, and the model parameters can be estimated directly bymaximum likelihood method. When the number of players in games is large, the dimensionof the multiple integrals is high. The direct calculation of the multiple integrals is difficult,so we simplify the calculation using the methods of GHK (Geweke-Hajivassiliou-Keane)simulation and estimate the model parameters by maximum simulation likelihood method.Study on game-theoretic econometric models has important theoretical and practicalsignificance. Sequential games are ubiquitous in real games. The methods of theestimations of discrete sequential game-theoretic econometric models in this dissertationimprove the theoretical system of game-theoretic econometric models, and expand itsapplication scopes.