Extensive Game of Horse Race: A Research on <i>Tian Ji's Horse Race</i> Based on Static Games of Complete Information

Abstract

There are many ways to develop of the classical problem about Tian Ji's Horse Race so that this problem may be researched deeply using theory of games. Therefore, this paper designs n-order extensive game of horse race by changing a rule of traditional problem. After analysis, this paper holds a belief that this game is a kind of static games of complete information, which means theory of static games of complete information can be used to research Tian Ji's Horse Race . With showing all of the strategy profiles of third-order extensive game of horse race and calculating Nash equilibrium of this game, this paper finds some characteristics of the strategy profiles and Nash equilibrium of extensive game of horse race and give the expression of Nash equilibrium of mixed strategy of this game. A new concept of layout is introduced to reveal how strategy profiles influence the outcome of this game. Then the characteristic of the layouts of extensive game of horse race and the layout that can make Tian Ji’s payoff biggest are found and proved, which is drawn from the result of some simulations about fourth-order and fifth-rank extensive games of horse race using a Java program.