Title:

Large tournament games

Abstract:

We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank dependent, the equilibrium has a surprisingly explicit characterization, which allows us to conduct comparative statics and obtain explicit solution to several optimal reward design problems. In the general case when the players are heterogenous and payoffs are not purely rank dependent, we prove the existence, uniqueness and stability of the Nash equilibrium of the associated mean field game, and the existence of an approximate Nash equilibrium of the finite-player game.

Biography:

Erhan Bayraktar, the holder of the Susan Smith Chair, is a full professor of Mathematics at the University of Michigan, where he has been since 2004. Professor Bayraktar’s research is in stochastic analysis, control, applied probability, mean field games, machine learning and mathematical finance. He has over 150 publications in top journals in these areas.

Professor Bayraktar is recognized as a leader in his areas of research: He is a corresponding editor in the SIAM Journal on Control and Optimization and also serves in the editorial boards of Applied Mathematics and Optimization, Mathematics of Operations Research, Mathematical Finance. His research has been also been continually funded by the National Science Foundation. In particular, he received a CAREER grant. He has been a plenary speaker in numerous conferences (AMAMEF, Bachlier Congress etc.) and workshops (at CIRM, BIRS, Oberwolfach, University of Chicago, etc.).

 

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