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pith:TNY573U6

pith:2026:TNY573U6562DILG6C457BFJJ7E

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Stochastic Mean-Field LQ Stackelberg Differential Games with Random Coefficients: Theory and a Deep FBSDE Picard Solver

Jie Xiong, Ying Yang, Zhouyu Wang

Stackelberg optimal controls in mean-field LQ games with random coefficients are characterized by a Riccati-free coupled FBSDE system solved by a deep Picard method.

arxiv:2605.12950 v1 · 2026-05-13 · math.OC

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Claims

C1strongest claim

The Stackelberg optimal control is characterized through a Riccati-free coupled FBSDE system, and the Deep FBSDE Picard Solver preserves the Stackelberg order through follower-response learning, response-sensitivity extraction, leader optimization, and neural augmented Lagrangian enforcement of mean-field consistency constraints.

C2weakest assumption

That the extended Lagrange multiplier method successfully produces an affine operator representation of the follower's optimal response despite the interaction between mean-field terms and random coefficients, and that the resulting FBSDE system admits solutions that the deep Picard solver can approximate reliably.

C3one line summary

Derives a Riccati-free coupled FBSDE characterization for mean-field LQ Stackelberg games with random coefficients and proposes a Deep FBSDE Picard Solver that learns follower responses and enforces mean-field consistency.

References

39 extracted · 39 resolved · 0 Pith anchors

[1] H. Abou-Kandil and P. Bertrand,Analytical solution for an open-loop Stackelberg game, IEEE, 1985 1985

[2] B. Acciaio, J. Backhoff-Veraguas, and R. Carmona,Extended mean field control prob- lems: stochastic maximum principle and transport perspective, SIAM, 2019 2019

[3] C. Beck, W. E, A. Jentzen, Machine learning approximation algorithms for high- dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations, J 2019

[4] A. Bensoussan, M. H. M. Chau, and S. C. P. Yam,Mean field Stackelberg games: Ag- gregation of delayed instructions, SIAM, 2015 2015

[5] A. Bensoussan, M. H. M. Chau, Y. Lai, and S. C. P. Yam,Linear-quadratic mean field Stackelberg games with state and control delays, SIAM, 2017 2017

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Receipt and verification

First computed	2026-05-18T03:09:09.420261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b71dfee9eefb4342cde173bf09529f90dc3e43d40c11766b2ab9bfd43833d78

Aliases

arxiv: 2605.12950 · arxiv_version: 2605.12950v1 · doi: 10.48550/arxiv.2605.12950 · pith_short_12: TNY573U6562D · pith_short_16: TNY573U6562DILG6 · pith_short_8: TNY573U6

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/TNY573U6562DILG6C457BFJJ7E \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9b71dfee9eefb4342cde173bf09529f90dc3e43d40c11766b2ab9bfd43833d78

Canonical record JSON

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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-13T03:34:11Z",
    "title_canon_sha256": "85c3babc31c40e7ba9014030a8da2746499f32503a3b8c1d582e074ce0986efb"
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