Finding the Strong Nash Equilibrium: Computation, Existence and Characterization for Markov Games

Julio B. Clempner () and Alexander S. Poznyak ()
Additional contact information
Julio B. Clempner: National Polytechnic Institute
Alexander S. Poznyak: Center for Research and Advanced Studies

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 3, No 15, 1029-1052

Abstract: Abstract This paper suggests a procedure to construct the Pareto frontier and efficiently computes the strong Nash equilibrium for a class of time-discrete ergodic controllable Markov chain games. The procedure finds the strong Nash equilibrium, using the Newton optimization method presenting a potential advantage for ill-conditioned problems. We formulate the solution of the problem based on the Lagrange principle, adding a Tikhonov’s regularization parameter for ensuring both the strict convexity of the Pareto frontier and the existence of a unique strong Nash equilibrium. Then, any welfare optimum arises as a strong Nash equilibrium of the game. We prove the existence and characterization of the strong Nash equilibrium, which is one of the main results of this paper. The method is validated theoretically and illustrated with an application example.

Keywords: Strong equilibrium; Game theory; Markov processes; Pareto; algorithms; Optimizations; 91A12; 91A40; 91A80 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-020-01729-3 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:186:y:2020:i:3:d:10.1007_s10957-020-01729-3

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

DOI: 10.1007/s10957-020-01729-3

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 ().