Faculty in  Mathematical  Finance             Math Finance Home Conferences Seminars People Open Positions Contact Probability and Computational Finance Seminar Yuchong Zhang Columbia University Title: Large tournament games Abstract: We consider a stochastic tournament game in which each player works toward accomplishing her goal and is rewarded based on her rank in terms of the time to completion. We prove existence, uniqueness and stability of the game with infinitely many players, and existence of approximate equilibrium with finitely many players. When players are homogeneous, the equilibrium has an explicit characterization. We find that the welfare may be increasing in the cost of effort in its low range, as the cost reduces players' eagerness to work too hard. The reward function that minimizes the expected time until a given fraction $\alpha$ of the population has reached the target, as well as the aggregate welfare, only depends on whether the rank is above or below $\alpha$. However, that is no longer true when maximizing a function of the completion time. Numerical examples are also provided when players are inhomogeneous. (Based on joint work with Erhan Bayraktar and Jaksa Cvitanic)Date: Monday, March 5, 2018Time: 4:30 pmLocation: Wean Hall 8220Submitted by:  Johannes Muhle-Karbe