New results on the existence of open loop Nash equilibria in discrete time dynamic games via generalized Nash games

Mathew P. Abraham () and Ankur A. Kulkarni ()
Additional contact information
Mathew P. Abraham: Indian Institute of Technology Bombay
Ankur A. Kulkarni: Indian Institute of Technology Bombay

Mathematical Methods of Operations Research, 2019, vol. 89, issue 2, No 1, 157-172

Abstract: Abstract We address the problem of finding conditions which guarantee the existence of open-loop Nash equilibria in discrete time dynamic games (DTDGs). A classical approach to DTDGs involves analyzing the problem using optimal control theory. Sufficient conditions for the existence of open-loop Nash equilibria obtained from this approach are mainly limited to linear-quadratic games (Başar and Olsder in Dynamic noncooperative game theory, 2nd edn, SIAM, Philadelphia, 1999). Another approach of analysis is to substitute the dynamics and transform the game into a static game. But the substitution of state dynamics makes the objective functions of the resulting static problems extremely hard to analyze. We introduce a third approach in which the dynamics are not substituted, but retained as constraints in the optimization problem of each player, resulting thereby in a generalized Nash game. Using this, we give sufficient conditions for the existence of open-loop Nash equilibria for a class of DTDGs where the cost functions of players admit a quasi-potential function. Our results apply with nonlinear dynamics and without stage additive cost functions, and allow constraints on state and actions spaces, and in some cases, yield a generalization of similar results from linear-quadratic games.

Keywords: Discrete time dynamic games; Open-loop Nash equilibrium; Potential games; Nonconvex optimization; Generalized Nash games (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s00186-018-0644-2 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:mathme:v:89:y:2019:i:2:d:10.1007_s00186-018-0644-2

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-018-0644-2

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().