Abstract
We study multistage models of resource allocation with several agents. Individual interests of agents are determined with their private objective functions, given by discounted sums of one-step utilities over the whole period of planning. Social preferences are expressed with public objective functions. We define the utility functions in such a way that aggregation of individual utilities results in the exponential public utility. Constructed private objective functions are competitive in the sense that the actions of agents affect the incomes of partners. Consequently, these models are treated as non- cooperative dynamic games. We construct the Nash equilibria for these games satisfying the criteria of maximization of public utility. Both finite and infinite horizons of planning are examined.
This study was supported by the grant N 00-02-00202a of Russian Humanities Foundation which is gratefully acknowledged.
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References
Beckmann, M.J. (1974): “Resource allocation over time,” in: Mathematical Models in Economics. Amsterdam-London-N.Y.-Warszawa. 171–178
Brock, W.A., and L.J. Mirman (1972): “Optimal economic grouth and uncertainty: the discounted case,” Journal of Economic Theory, 4(3), 479–513.
L.J. Mirman (1973): “Optimal economic grouth and uncertainty: the no discounted case,” International Economic Review, 14(3), 560–573.
Gale, D. (1967): “An optimal development in a multisector economy,” Review of Economic Studies, 34, 1–18.
Domansky, V. (1999): “Dynamic stochastic games of resource allocation between production and consumption,” International Game Theory Review, 1 (2), 149–158.
Dynkin, E.B., and A.A. Yushkevich (1979): Controlled Markov processes. N.Y. Springer-Verlag.
Lucas, R.E. JR., and N.L. Stokey (1984): “Optimal grouth with many consumers,” Journal of Economic Theory, 32, 139–171.
Mirman, L.J. (1971): “Uncertainty and optimal consumption decisions,” Econometrica, 39, 179–186.
Mirman, L.J. (1973): “The steady state behavior of a class of one-sector grouth models with uncertain technology,” Journal of Economic Theory, 5(6).
Phelps, E.S. (1962): “The accumulation of risky capital: a sequential utility analysis,” Econometrica, 30(4), 729–743.
Radner, R.A. (1973): “Optimal stationary consumption with stochastic production and resources,” Journal of Economic Theory, 6(1), 68–90.
Ramsey, F. (1928): “A mathematical theory of savings,” Economic Journal, 38, 543–559.
Stokey, N.L., and R.E. Lucas, JR. (1989): Recursive methods in economic dynamics. Harvard University Press.
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Domansky, V., Kreps, V. (2002). Social Equilibria for Competitive Resource Allocation Models. In: Tangian, A.S., Gruber, J. (eds) Constructing and Applying Objective Functions. Lecture Notes in Economics and Mathematical Systems, vol 510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56038-5_21
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DOI: https://doi.org/10.1007/978-3-642-56038-5_21
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