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Large ranking games with diffusion control

Abstract : We consider a symmetric stochastic differential game where each player can control the diffusion intensity of an individual dynamic state process, and the players whose states at a deterministic finite time horizon are among the best α ∈ (0, 1) of all states receive a fixed prize. Within the mean field limit version of the game we compute an explicit equilibrium, a threshold strategy that consists in choosing the maximal fluctuation intensity when the state is below a given threshold, and the minimal intensity else. We show that for large n the symmetric n-tuple of the threshold strategy provides an approximate Nash equilibrium of the n-player game. We also derive the rate at which the approximate equilibrium reward and the best response reward converge to each other, as the number of players n tends to infinity. Finally, we compare the approximate equilibrium for large games with the equilibrium of the two player case.
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https://hal.archives-ouvertes.fr/hal-03434678
Contributor : Julian Wendt Connect in order to contact the contributor
Submitted on : Thursday, November 18, 2021 - 1:44:11 PM
Last modification on : Tuesday, January 4, 2022 - 5:52:22 AM

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  • HAL Id : hal-03434678, version 1

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Stefan Ankirchner, Nabil Kazi-Tani, Julian Wendt, Chao Zhou. Large ranking games with diffusion control. 2021. ⟨hal-03434678⟩

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