Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games

Vasile Drăgan, Ivan Ganchev Ivanov, Ioan-Lucian Popa and Ovidiu Bagdasar
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Vasile Drăgan: “Simion Stoilow” Institute of Mathematics, Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania
Ivan Ganchev Ivanov: Faculty of Economics and Business Administration, Sofia University St. Kliment Ohridski, 1113 Sofia, Bulgaria
Ioan-Lucian Popa: Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
Ovidiu Bagdasar: School of Computing and Engineering, University of Derby, Derby DE22 1GB, UK

Mathematics, 2021, vol. 9, issue 21, 1-15

Abstract: In this paper, we examine a sampled-data Nash equilibrium strategy for a stochastic linear quadratic (LQ) differential game, in which admissible strategies are assumed to be constant on the interval between consecutive measurements. Our solution first involves transforming the problem into a linear stochastic system with finite jumps. This allows us to obtain necessary and sufficient conditions assuring the existence of a sampled-data Nash equilibrium strategy, extending earlier results to a general context with more than two players. Furthermore, we provide a numerical algorithm for calculating the feedback matrices of the Nash equilibrium strategies. Finally, we illustrate the effectiveness of the proposed algorithm by two numerical examples. As both situations highlight a stabilization effect, this confirms the efficiency of our approach.

Keywords: nash equilibria; stochastic LQ differential games; sampled-data controls; equilibrium strategies; optimal trajectories (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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