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Equilibrium points in constrained minimization and games

  • Hierarchical Models And Computation
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Book cover Dynamic Games in Economic Analysis

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 157))

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Abstract

We are concerned with the following problem: "Two agents (or player) want to minimize their own cost-functionals with some constraints on decision variables". Stackelberg and Nash equilibria are considered and different situations arising in the research of sufficient conditions for the existence of equilibria in the two cases are studied. Applications of those results to a class of differential games and to incentive strategies theory are showed.

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References

  1. J.P. Aubin:“Mathematical methods of games and economic theory”, Studies in mathematics and its applications, North-Holland, Amsterdam, 1979.

    Google Scholar 

  2. T. Basar and G.J. Olsder:“Dynamic noncooperative game theory”, Academic Press, London, 1982.

    Google Scholar 

  3. A. Friedman:“Differential games”, Pure and applied mathematics, John Wiley & Sons Inc., New York, 1971.

    Google Scholar 

  4. R. Lucchetti, F. Mignanego and G. Pieri:“Existence theorems of equilibrium points in Stackelberg games with constraints”, Optimization, Vol.18 (1987), 857–866.

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  5. F.Mignanego: to appear.

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  6. G. Owen:“Game theory”, 2nd edition, Academic Press, New York, 1982.

    Google Scholar 

  7. G. Pieri:“Condizioni sufficienti per l'esistenza della soluzione per problemi di minimizzazione a bilivello, con vincoli, in spazi di Banach”, Rivista di matematica pura ed applicata, Vol.5 (1989), 41–48.

    Google Scholar 

  8. M. Simaan and B. Cruz Jr:“On the Stackelberg strategy in nonzero-sum games”, J.O.T.A., Vol.11 (1973), 533–555.

    Google Scholar 

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Ralmo Pertti Hämäläinen Harri Kalevi Ehtamo

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© 1991 Springer-Verlag

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Mignanego, F., Pieri, G. (1991). Equilibrium points in constrained minimization and games. In: Hämäläinen, R.P., Ehtamo, H.K. (eds) Dynamic Games in Economic Analysis. Lecture Notes in Control and Information Sciences, vol 157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006249

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  • DOI: https://doi.org/10.1007/BFb0006249

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53785-4

  • Online ISBN: 978-3-540-47096-0

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