  We analyze a mean field tournament: a mean field game in which the agents
receive rewards according to the ranking of the terminal value of their
projects and are subject to cost of effort. Using Schr\"{o}dinger bridges we
are able to explicitly calculate the equilibrium. This allows us to identify
the reward functions which would yield a desired equilibrium and solve several
related mechanism design problems. We are also able to identify the effect of
reward inequality on the players' welfare as well as calculate the price of
anarchy.
