NIRA-3: An improved MATLAB package for finding Nash equilibria in infinite games

Krawczyk, Jacek and Zuccollo, James (2006): NIRA-3: An improved MATLAB package for finding Nash equilibria in infinite games.

Abstract

A powerful method for computing Nash equilibria in constrained, multi-player games is created when the relaxation algorithm and the Nikaido-Isoda function are used together in a suite of MATLAB routines. This paper updates the MATLAB suite described in \cite{Berridge97} by adapting them to MATLAB 7. The suite is now capable of solving both static and open-loop dynamic games. An example solving a coupled constraints game using the suite is provided.

• Item Type: MPRA Paper
• Institution: Victoria University of Wellington
• Language: English
• Keywords: Nikaido-Isoda function; Coupled constraints
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling

References

@PAPER{Berridge97, author = {S Berridge and J B Krawczyk}, title = {Relaxation algorithms in finding {N}ash equilibria}, journal = {}, howpublished = {Research Papers in Economics}, year = {1997}, note = {RePEc:wpa:wuwpco:9707002}, }

@BOOK{Fudenberg91, title = {Game Theory}, publisher = {MIT Press, Cambridge, Massachusetts, London, England}, year = {1991}, author = {D Fudenberg and J Tirole}, }

@MISC{Haurie02, author = {Haurie, A. and J. B. Krawczyk}, title = {An Introduction to Dynamic Games}, howpublished = {Internet textbook}, year = {2002}, note = {http://ecolu-info.unige.ch/$\sim$haurie/fame/textbook.pdf}, }

@ARTICLE{Haurie97, author = {A Haurie and J B Krawczyk}, title = {Optimal charges on river effluent from lumped and distributed sources}, journal = {Environmental Modelling and Assessment}, year = {1997}, volume = {2}, pages = {93--106}, number = {3}, }

@ARTICLE{Krawczyk05, author = {J B Krawczyk}, title = {Coupled constraint {N}ash equilibria in environmental games}, journal = {Resource and Energy Economics}, year = {2005}, volume = {27}, pages = {157--181}, }

@ARTICLE{Krawczyk00, author = {J B Krawczyk and S Uryasev}, title = {Relaxation algorithms to find {N}ash equilibria with economic applications}, journal = {Environmental Modelling and Assessment}, year = {1999}, volume = {5}, pages = {63--73}, }

@TECHREPORT{McKelvey91, author = {R D McKelvey}, title = {A {L}iapunov function for {N}ash equilibria}, institution = {California Institute of Technology}, year = {1991}, }

@ARTICLE{Rosen65, author = {J B Rosen}, title = {Existence and uniqueness of equilibrium points for concave n-person games}, journal = {Econometrica}, year = {1965}, volume = {33}, pages = {520--534}, number = {3}, }

@ARTICLE{Uryasev94, author = {S Uryasev and R Y Rubinstein}, title = {On relaxation algorithms in computation of noncooperative equilibria}, journal = {IEEE Transactions on Automatic Control}, year = {1994}, volume = {39}, pages = {1263--1267}, number = {6}, }