Semi-cooperative strategies for differential games

Alberto Bressan and Wen Shen

International Journal of Game Theory, 2004, vol. 32, issue 4, 593 pages

Abstract: The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative “semi-cooperative” pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic. Copyright Springer-Verlag 2004

Keywords: Ill-posedness of elliptic Cauchy problems; semi-cooperation; Pareto optimum; weak hyperbolicity (search for similar items in EconPapers)
Date: 2004
References: Add references at CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://hdl.handle.net/10.1007/s001820400180 (text/html)
Access to full text is restricted to subscribers.

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:jogath:v:32:y:2004:i:4:p:561-593

Ordering information: This journal article can be ordered from
http://www.springer. ... eory/journal/182/PS2

DOI: 10.1007/s001820400180

Access Statistics for this article

International Journal of Game Theory is currently edited by Shmuel Zamir, Vijay Krishna and Bernhard von Stengel

More articles in International Journal of Game Theory from Springer, Game Theory Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().