Abstract
In this note, we present a method that allows us to decide when a Markov-perfect Nash equilibrium is not Pareto optimum, without the explicit knowledge of the respective solutions. For that purpose, we establish a sufficient condition in terms of an algebraic inequality where the gradient of the value functions of the cooperative and noncooperative games as well as the state and control variables are involved.
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References
Lancaster, K., The Dynamic Inefficiency of Capitalism, Journal of Political Economy, Vol. 87, pp. 1092-1109, 1973.
Hoel, M., Distribution and Growth as a Differential Game between Workers and Capitalists, International Economic Review, Vol. 19, pp. 335-350, 1978.
Leitmann, G., Cooperative and Noncooperative Many-Players Differential Games, Springer Verlag, New York, NY, 1974.
Basar, T., and Olsder, G. J., Dynamic Noncooperative Game Theory, SIAM, Philadelphia, Pennsylvania, 1999.
Halmos, P.R., Measure Theory, Springer Verlag, New York, NY, 1974.
Van der ploeg, F., and De zeeuw, A. J., International Aspects of Pollution Control, Environmental and Resource Economics, Vol. 2, pp. 117-139, 1992.
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Rincón-Zapatero, J., Martín-Herrán, G. Direct Method Comparing Efficient and Nonefficient Payoffs in Differential Games. Journal of Optimization Theory and Applications 119, 395–405 (2003). https://doi.org/10.1023/B:JOTA.0000005453.96575.2a
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DOI: https://doi.org/10.1023/B:JOTA.0000005453.96575.2a