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 finiteplayer game. Our results have some potential economic implications; e.g., they lend support to government subsidies for R and D, assuming the profits to be made are substantial.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 DOI:
 10.48550/arXiv.1811.00076
 arXiv:
 arXiv:1811.00076
 Bibcode:
 2018arXiv181100076B
 Keywords:

 Mathematics  Optimization and Control;
 Mathematics  Probability;
 91A13;
 91B40;
 93E20
 EPrint:
 57 pages, 7 figures, 2 tables