Advanced Search
MyIDEAS: Login to save this paper or follow this series

On the relationship between the open-loop Nash equilibrium in LQ-games and the inertia of a matrix

Contents:

Author Info

  • Engwerda, J.C.
  • Weeren, A.J.T.M.

    (Tilburg University, Faculty of Economics and Business Administration)

Abstract

In this paper we consider the location of the eigenvalues of the composite matrix ( -A S1 S2 ) ( Q1 At 0 ) ( Q2 0 At ) , where the matrices Si and Qi are assumed to be semi-positive definite. Two interesting observations, which are not or only partially mentioned in literature before, challenge this study. The first observation is that this matrix appears naturally in a both necessary and sufficient condition for the existence of a unique open-loop Nash solution in the 2-player linear-quadratic dynamic game and, more in particular, its inertia play an important role in the analysis of the convergence of the associated state in this game. The second observation is that from the eigenvalue and eigenstructure of this matrix all solutions for the algebraic Riccati equations corresponding with the above mentioned dynamic game can be directly calculated and, moreover, also the eigenvalues of the associated closed-loop system. Simulation experiments suggest that the composite matrix will have at least n eigenvalues (here n is the state dimension of the system) with a positive real part. Unfortunately, it turns out that this property of the inertia of this matrix in general does not hold. Some specific cases for which the property does hold are discussed.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://arno.uvt.nl/show.cgi?fid=2992
Our checks indicate that this address may not be valid because: 404 Not Found. If this is indeed the case, please notify (Richard Broekman)
Download Restriction: no

Bibliographic Info

Paper provided by Tilburg University, Faculty of Economics and Business Administration in its series Research Memorandum with number 672.

as in new window
Length:
Date of creation: 1994
Date of revision:
Handle: RePEc:dgr:kubrem:1994672

Contact details of provider:
Web page: http://www.tilburguniversity.edu/nl/over-tilburg-university/schools/economics-and-management/

Related research

Keywords:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Weeren, A.J.T.M. & Schumacher, J.M. & Engwerda, J.C., 1994. "Asymptotic analysis of Nash equilibria in nonzero-sum linear-quadratic differential games: The two player case," Research Memorandum 634, Tilburg University, Faculty of Economics and Business Administration.
Full references (including those not matched with items on IDEAS)

Citations

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:dgr:kubrem:1994672. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Richard Broekman).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.