Pareto Optimal Cooperative Control of Mean-Field Backward Stochastic Differential System in Finite Horizon

G. Saranya (), R. Deepa () and P. Muthukumar ()
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G. Saranya: The Gandhigram Rural Institute (Deemed to be University)
R. Deepa: Panimalar Engineering College
P. Muthukumar: The Gandhigram Rural Institute (Deemed to be University)

Dynamic Games and Applications, 2025, vol. 15, issue 1, No 11, 279-305

Abstract: Abstract This research article aims to investigate a new type of Pareto cooperative differential game governed by backward stochastic differential equations of mean-field type. By the characterization of Pareto optimal solutions, the proposed Pareto game problem is converted into a set of optimal control problems with single weighted objective function which is constrained by mean-field backward stochastic differential equations. First, we derive the necessary conditions for Pareto optimality of the proposed system in finite time horizon. Next, the sufficient conditions are established with the conclusion that the necessary conditions are sufficient under some convexity assumptions. Finally, for the better understanding of theoretical results, we discuss the linear quadratic optimal control problem and a mathematical transportation problem.

Keywords: Cooperative differential game; Mean-field backward stochastic differential equations; Linear quadratic optimal control; Pareto optimal control; Weighted sum optimization; 91A15; 49K15; 60H10; 58E17 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13235-024-00566-7

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