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A Liapunov Function for Nash Equilibria

McKelvey, Richard D. (1998) A Liapunov Function for Nash Equilibria. Social Science Working Paper, 953. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20170817-134102962

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Abstract

In this paper, I construct a Liapunov function for Nash equilibria for finite n–person games in normal form. This function is useful for computation of Nash equilibria, since it converts the problem into a standard minimization problem. It provides an alternative to existing computational methods, which are based either on n - person extensions of the algorithm of Lemke and Howson [1961] (eg., Wilson [1971] and Rosenmiiller [1971]), or on methods for finding the fixed point of the best response correspondence, such as simplicial division algorithms (eg., Todd [1976], and Van der Laan et al. [1987]). This work is also related to that of Brown and von Neumann [1950], and Rosen [1964], who construct differential equation systems for solving certain classes of games.


Item Type:Report or Paper (Working Paper)
Additional Information:This research was funded, in part, by NSF grant #SES-9011828 to the California Institute of Technology. I wish to thank Richard Boylan for some useful discussions.
Group:Social Science Working Papers
Funders:
Funding AgencyGrant Number
NSFSES-9011828
Series Name:Social Science Working Paper
Issue or Number:953
Record Number:CaltechAUTHORS:20170817-134102962
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170817-134102962
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80566
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:21 Aug 2017 17:21
Last Modified:03 Oct 2019 18:32

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