Higher-order conditions for local equilibria in a discontinuous Gale economic model

• Autorzy: Michalak A. , Studniarski M.
• Języki publikacji: EN

Abstrakty

EN

The paper introduces the concept of a strict local equilibrium of order k in the Gale economic model. We obtain higher-order necessary and sufficient conditions for such equilibria without assuming continuity of the utility functions. These conditions are formulated in terms of generalized lower and upper directional derivatives, introduced by Studniarski (1986). A stability theorem for strict local equilibria of order k is also included.

Słowa kluczowe

EN

Gale model; equilibrium; higher-order conditions; generalized directional derivatives

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2017
• Tom: Vol. 46, no. 1
• Strony: 37--47
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Michalak A.

• Department of Econometrics, Faculty of Economics and Sociology, University of Łódź, Rewolucji 1905 r. No. 41, 90-214 Łódź, Poland

autor

Studniarski M.

• Chair of Algorithms and Databases, Faculty of Mathematics and Computer Science, University of Łódź, S. Banacha No. 22, 90-238 Łódź, Poland

Bibliografia

• [1] Bao T.Q. and Mordukhovich B.S. (2010) Set-valued optimization in welfare economics. Adv. Math. Econ. 13, 113–153.
• [2] Bula I. (2003) Discontinuous functions in Gale economic model. Math. Model. Anal. 8(2), 93–102. Dasgupta P. and Maskin E.(1986a) The existence of equilibrium in discontinuous economic games, I: Theory. Rev. Econ. Stud. 53(1), 1–26.
• [3] Dasgupta P. and Maskin E. (1986b) The existence of equilibrium in discontinuous economic games, II: Applications. Rev. Econ. Stud. 53(1), 27–41.
• [4] Hyers D. H. (1978) On the stability of minimum points. J. Math. Anal. Appl. 62, 530–537.
• [5] Hyers D.H. (1985) Stability of minimum points for problems with constraints. In: Lecture Notes in Pure and Appl. Math., 100.
• [6] Dekker, New York. Differential geometry, calculus of variations, and their applications, 283– 289.
• [7] Michalak A. and Studniarski M. (2014) Necessary and sufficient conditions for a Pareto optimal allocation in a discontinuous Gale economic model. Opuscula Math. 34(4), 827–835.
• [8] Mordukhovich B.S. (2006) Variational Analysis and Generalized Differentiation, vol. II: Applications. Springer, Berlin.
• [9] Nessah R. and Tian G. (2016) On the existence of Nash equilibrium in discontinuous games. Econ. Theory, 61, 515–540.
• [10] Rahmo E.-D. and Studniarski M. (2012) Higher-order conditions for strict local Pareto minima in terms of generalized lower and upper directional derivatives. J. Math. Anal. Appl. 393, 212–221. Studniarski M. (1986) Necessary and sufficient conditions for isolated local minima of nonsmooth functions. SIAM J. Control Optim. 24, 1044–1049.
• [11] Tian G. (1992) Existence of equilibrium in abstract economies with discontinuous payoffs and non-compact choice spaces. J. Math. Econ. 21, 379–388.
• [12] Tian G. (2015) On the existence of equilibria in games with arbitrary strategy spaces and preferences. J. Math. Econ. 60, 9–16.
• [13] Tian G. (2016) On the existence of price equilibrium in economies with excess demand functions. Econ. Theory Bull. 4, 5–16.
• [14] Tian G. and Zhou J. (1992) The maximum theorem and the existence of Nash equilibrium of (generalized) games without lower semicontinuities. J. Math. Anal. Appl. 166, 351–364.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).