Large Ranking Games with Diffusion Control
نویسندگان
چکیده
We consider a symmetric stochastic differential game where each player can control the diffusion intensity of an individual dynamic state process, and players whose states at deterministic finite time horizon are among best [Formula: see text] all receive fixed prize. Within mean field limit version game, we compute explicit equilibrium, threshold strategy that consists choosing maximal fluctuation when is below given minimal otherwise. show for large n, n-tuple provides approximate Nash equilibrium n-player game. also derive rate which reward best-response converge to other, as number n tends infinity. Finally, compare games with two-player case. Funding: Support from Deutsche Forschungsgemeinschaft [Grant AN 1024/5-1] acknowledged. The research N. Kazi-Tani supported by Agence Nationale de la Recherche ANR-21-CE46-0002-03]. C. Zhou National Natural Science Foundation China 11871364], Singapore Ministry Education [Grants A-8000453-00-00, A-0004273-00-00 A-0004277-00-00] MERLION 2020 award A-0004589-00-00].
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ژورنال
عنوان ژورنال: Mathematics of Operations Research
سال: 2023
ISSN: ['0364-765X', '1526-5471']
DOI: https://doi.org/10.1287/moor.2023.1373