Robust Soft-Constrained Nash Equilibria in the Multi-Player Discrete-Time Descriptor Dynamic Game

Muhammad Wakhid Musthofa () and Jacob Engwerda ()
Additional contact information
Muhammad Wakhid Musthofa: UIN Sunan Kalijaga Yogyakarta
Jacob Engwerda: Retiree Tilburg University

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 5, 29 pages

Abstract: Abstract This paper considers the design of robust control strategies for a discrete-time descriptor system influenced by multiple players with their own disturbance attenuation levels. Assuming players use linear feedback strategies, the Nash equilibrium strategies are derived for a non-cooperative setting. In a simulation study on water extraction from a common resource, it is demonstrated what the potential effects are if players use different attenuation levels. Also, the impact of the number of players and divergent preferences on results are investigated. To derive the equilibrium strategies, first, the solution of the zero-sum discrete-time dynamic game where one player is playing against nature is presented. Using this result, we present sufficient conditions for the existence of a soft-constrained linear feedback Nash equilibrium (SLFNE) for the multi-player soft-constrained linear quadratic regular dynamic game. From this result, we obtain then directly robust disturbance attenuation controllers for the system, where every player satisfies his own attenuation level.

Keywords: Multi-player soft-constrained dynamic game; Soft-constrained linear feedback Nash equilibrium; Discrete-time systems; Descriptor systems; 91A06; 91A25; 91A50 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-025-02695-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:206:y:2025:i:2:d:10.1007_s10957-025-02695-4

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-025-02695-4

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().