NISOCSol an algorithm for approximating Markovian equilibria in dynamic games with coupled-constraints

Krawczyk, Jacek and Azzato, Jeffrey (2006): NISOCSol an algorithm for approximating Markovian equilibria in dynamic games with coupled-constraints.

Abstract

In this report, we outline a method for approximating a Markovian (or feedback-Nash) equilibrium of a dynamic game, possibly subject to coupled-constraints. We treat such a game as a "multiple" optimal control problem. A method for approximating a solution to a given optimal control problem via backward induction on Markov chains was developed in Krawczyk (2006). A Markovian equilibrium may be obtained numerically by adapting this backward induction approach to a stage Nikaido-Isoda function (described in Krawczyk & Zuccollo (2006)).

• Item Type: MPRA Paper
• Institution: Victoria University of Wellington
• Language: English
• Keywords: Computational techniques; Noncooperative games; Econometric software; Taxation; Water; Climate; Dynamic programming; Dynamic games; Applications of game theory; Environmental economics; Computational economics; Nikaido-Isoda function; Approximating Markov decision chains
• Subjects: C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C87 - Econometric Software; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q2 - Renewable Resources and Conservation > Q25 - Water; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; E - Macroeconomics and Monetary Economics > E6 - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook > E62 - Fiscal Policy

References

K.J. Arrow & G. Debreu, 1954, "Existence of an Equilibrium for a Competitive Economy", Econometrica, Vol. 22, No. 3, pp. 265-290.

Azzato, J. & J.B. Krawczyk, 2006, "SOCSol4L An improved MATLAB Package for Approximating the Solution to a Continuous-Time Stochastic Optimal Control Problem", Working Paper, School of Economics and Finance, VUW, [MPRA: 1179]. Available at: http://mpra.ub.uni-muenchen.de/1179/ on 2006-12-16.

Basar, T. & G.J. Olsder, 1982, "Dynamic Noncooperative Game Theory", Academic Press, New York.

Contreras, J., M. Klusch & J.B. Krawczyk, 2004, "Numerical solutions to Nash-Cournot equilibria in coupled constraint electricity markets", IEEE Transactions on Power Systems, Vol. 19, No. 1, 195-206, [doi: 10.1109/TPWRS.2003.820692].

Haurie, A. & J.B. Krawczyk, 1997, "Optimal charges on river effluent from lumped and distributed sources", Environmental Modeling and Assessment, Vol. 2, No. 3, pp. 93-106.

Hobbs, B. & J.-S. Pang, 2006, "Nash-Cournot Equilibria in Electric Power Markets with Piecewise Linear Demand Functions and Joint Constraints", Operations Research, forthcoming.

Krawczyk, J.B., 2001, "A Markovian Approximated Solution to a Portfolio Management Problem", Information Technology for Economics and Management, Vol. 1, No. 1. Available at: http://www.item.woiz.polsl.pl/issue/journal1.htm on 2006-12-14.

Krawczyk, J.B., 2005, "Numerical Solutions to Lump-Sum Pension Fund Problems that Can Yield Left-Skewed Fund Return Distributions". In: C. Deissenberg and R.F. Hartl (eds.), Optimal Control and Dynamic Games, Springer, pp. 155-176.

Krawczyk, J.B., 2005, "Coupled constraint Nash equilibria in environmental games", Resource and Energy Economics, Vol. 27, Iss. 2, pp. 157-181.

Krawczyk, J.B., 2006, "Coupled Constraint Markovian Equilibria in Dynamic Games of Compliance", Seminar at Kyoto University Institute of Economic Research, 30 November 2006.

Krawczyk, J.B. & M. Tidball, 2006, "A Discrete-Time Dynamic Game of Seasonal Water Allocation", Journal of Optimization Theory and Applications, Vol. 128, No. 2, pp. 411-429.

Krawczyk, J.B. \& S. Uryasev}, 2000, "Relaxation algorithms to find Nash equilibria with economic applications", Environmental Modeling and Assessment, Vol. 5, No. 1, pp. 63-73.

Krawczyk, J.B. & J. Zuccollo}, 2006, "NIRA-3 An improved MATLAB package for finding Nash equilibria in infinite games", Working Paper, School of Economics and Finance, VUW, [MPRA: 1119]. Available at: http://mpra.ub.uni-muenchen.de/1119/ on 2006-12-16.

McKenzie, L.W., 1959, "On the Existence of General Equilibrium for a Competitive Market", Econometrica, Vol. 27, No. 1, pp. 54-71.

Nikaido, H. & K. Isoda, 1955, "Note on Noncooperative Convex Games", Pacific Journal of Mathematics, Vol. 5, Supp. 1, pp. 807-815.

Rosen, J.B., 1965, "Existence and Uniqueness of Equilibrium Points for Concave N-Person Games", Econometrica, Vol. 33, No. 3, pp. 520-534.