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Large tournament games. (English) Zbl 1443.91035
The authors formulate large population tournament games as mean field games, i.e., stochastic games with infinitely many small players interacting through their aggregate distribution.
The rewards of the players depend on how their completion times are ranked. The completion time is the hitting time of the player’s own diffusion process, whose drift is controlled by the player by costly effort. Two cases are studied. The first one is concerned with the homogeneous players. In this set-up the semi-explicit formula for the equilibrium is found. It enables to analyse comparative statics and to tackle the problem of mechanism design. The second approach deals with heterogeneous players or rewards that are not purely rank-based. By the Schauder fixed point theorem the existence of equilibrium is proved and under additional monotonicity assumptions its uniqueness is shown.

MSC:
91A15 Stochastic games, stochastic differential games
91A16 Mean field games (aspects of game theory)
91A07 Games with infinitely many players
91A06 \(n\)-person games, \(n>2\)
91B03 Mechanism design theory
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References:
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