Abstract
We investigate in this paper a version of pure exchange competitive equilibrium under uncertain circumstances. Those uncertain factors are embedded in each agent’s preference, which is characterized by the uncertain utility function. By maximizing the expected utility of each agent, we formulate this kind of pure exchange competitive equilibrium problem into a quasi-variational inequality problem. This idea is applied in a pure exchange economy which consists of two agents and two goods. And we find the competitive equilibrium of this economy with each agent’s preference being an uncertain variable.
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References
Anello G, Donato M, Milasi M (2010) A quasi-variational approach to a competitive economic equilibrium problem without strong monotonicity assumption. J Glob Optim 48:279–287
Arrow K, Debreu G (1954) Existence of an equilibrium for a competitive economy. Econometrica 22:265–290
Border K (1985) Fixed point theorems with applications to economics and game theory. Cambrige University Press, Cambrige
Chen X, Gao J (2013) Uncertain term structure model of interest rate. Soft Comput 17(4):597–604
Dafermos S (1980) Traffic equilibrium and variational inequalities. Transp Sci 14:42–54
Dafermos S (1990) Exchange price equilibrium and variational inequalities. Mathe Program 46:391–402
Dafermos S, Nagurney A (1984) A network formulation of market equilibrium problems and variational inequalities. Oper Res Lett 3:247–250
Ding C, Zhu Y (2014) Two empirical uncertain models for project scheduling problem. J Oper Res Soc 66:1471–1480
Donato M, Milasi M, Vitanza C (2008) Quasi-variational inequality approach of a competitive economic equilibrium problem with utility function: existence of equilibrium. Math Mod Methods Appl Sci 18(3):351–367
Donato M, Milasi M, Vitanza C (2008) An existence result of a quasi-variational inequality associated to an equilibrium problem. J Glob Optim 40:87–97
Donato M, Milasi M, Vitanza C (2016) On study of an economic equilibrium with variational inequality arguments. J Optim Appl 168:464–660
Gabay D, Moulin H (1980) On the uniqueness and stability of Nash equilibria in noncooperative games. In: Benoussan A, Kleindorfer PR, Tapiero CS (eds) Control applied stochastic, of econometrics and mangement science. Series: contributions to economic analysis, 130 . North-Holland, Amsterdam, pp 271–293
Gale D (1955) The law of supply and demand. Math Scand 3:155–169
Gao J, Yang X, Liu D (2017) Uncertain shapley value of coalitional game with application to supply chain alliance. Appl Soft Comput. doi:10.1016/j.asoc.2016.06.018
Ge X, Zhu Y (2012) A necessary condition of optimality for uncertain optimal control problem. Fuzzy Optim Decis Mak 6(4):278–288
Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin
Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10
Liu B (2015) Uncertainty theory, 4th edn. Springer, Berlin
Liu Y, Ha M (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(3):181–186
McKenzie L (1954) On equilibrium in Grahams model of world trade and other competitive systems. Econometrica 22:147–161
Milasi M (2013) Existence theorem for a class of generalized quasi-variational inequalities. J Glob Optim 57:679–688
Nagurney A (1993) Network economics—a variational inequality approach. Kluwer Academic Publishers, Boston
Nikaidô H (1968) Convex structures and economic theory: mathematics in science and engineering. Academic Press, New York
Oden J, Kikuchi N (1980) Recent advances: theory of variational inequalities with applications to problems of flow through porous media. Int J Eng Sci 18:1173–1284
Wald A (1936) On some systems of equations of mathematical economic. Econometrica 19:368–403
Walras L (1874) Elements economique Politique Pure (Elements of Pure Economics). Corbaz, Lausanne
Yang X, Gao J (2013) Uncertain differential games with application to capitalism. J Uncertain Anal Appl 1 (article 17)
Yang X, Gao J (2016) Linear quadratic uncertain differential game with application to resource extraction problem. IEEE Trans Fuzzy Syst 24(4):819–826
Yang X, Gao J (2017) Bayesian equilibria for uncertain bimatrix game with asymmetric information. J Intell Manuf 28(3):515–525
Yang X, Yao K (2016) Uncertain partial differential equation with application to heat conduction. Fuzzy Optim Decis Mak. doi:10.1007/s10700-016-9253-9
Yao K, Ji X (2014) Uncertain decision making and its application to portfolio selection problem. Int J Uncertain Fuzz and Knowl Based Syst 22(1):113–123
Zhou J, Liu Y, Zhang X, Gu X, Wang D (2017) Uncertain risk aversion. J Intell Manuf 28(3):615–624
Zhu Y (2010) Uncertain optimal control with application to a portfolio selection model. Cybern Syst Int J 41(7):535–547
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The first author is also deeply indebted to Shawnee State University of USA for the support during her visiting duration.
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National Natural Science Foundation of China (Grant No. 61673011) and China Scholarship Council (Grant No. 201406840039).
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Chen, Q., Zhu, Y. Pure exchange competitive equilibrium under uncertainty. J Ambient Intell Human Comput 8, 759–768 (2017). https://doi.org/10.1007/s12652-017-0500-x
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DOI: https://doi.org/10.1007/s12652-017-0500-x