Extension of Monotonic Functions and Representation of Preferences

Published Online:https://doi.org/10.1287/moor.2020.1095

References

  • [1] Afriat S (1967) The construction of utility functions from expenditure data. Internat. Econom. Rev. 8(1):67–77.CrossrefGoogle Scholar
  • [2] Aliprantis CD, Border KC (2006) Infinite Dimensional Analysis (Springer, Berlin).Google Scholar
  • [3] Aliprantis CD, Burkinshaw O (2006) Positive Operators (Springer, Dordrecht, Germany).CrossrefGoogle Scholar
  • [4] Araujo A (1985) Lack of Pareto optimal allocations in economies with infinitely many commodities: The need for impatience. Econometrica 53(2):455–461.CrossrefGoogle Scholar
  • [5] Aumann RJ (1962) Utility theory without the completeness axiom. Econometrica 30(3):445–462.CrossrefGoogle Scholar
  • [6] Basu K, Mitra T (2003) Aggregating infinite utility streams with intergenerational equity: The impossibility of being Paretian. Econometrica 71(5):1557–1563.CrossrefGoogle Scholar
  • [7] Bewley TF (1972) Existence of equilibria in economies with infinitely many commodities. J. Econom. Theory 4(3):514–540.CrossrefGoogle Scholar
  • [8] Bewley TF (1986) Knightian decision theory: Part I. Cowles Foundation Discussion Paper No. 807, Yale University, New Haven, CT.Google Scholar
  • [9] Bewley TF (1991) A very weak theorem on the existence of equilibria in atomless economies with infinitely many commodities. Khan MA, Yannelis NC, eds. Equilibrium Theory in Infinite Dimensional Spaces (Springer-Verlag, Berlin), 224–232.CrossrefGoogle Scholar
  • [10] Bosi G, Caterino A, Ceppitelli R (2010) Existence of continuous utility functions for arbitrary binary relations: Some sufficient conditions. Tatra Mountains Math. Publications 46(1):15–27.Google Scholar
  • [11] Bosi G, Caterino A, Ceppitelli R (2016) Normally preordered spaces and continuous multi-utilities. Appl. General Topology 17(1):71–81.CrossrefGoogle Scholar
  • [12] Brown DJ, Lewis LM (1981) Myopic economic agents. Econometrica 49(2):359–368.CrossrefGoogle Scholar
  • [13] Campión MJ, Candeal JC, Induráin E (2006) The existence of utility functions for weakly continuous preferences on a Banach space. Math. Soc. Sci. 51(2):227–237.CrossrefGoogle Scholar
  • [14] Cerreia-Vioglio S (2016) Objective rationality and uncertainty averse preferences. Theoret. Econom. 11(2):523–545.CrossrefGoogle Scholar
  • [15] Cerreia-Vioglio S, Ok EA (2018) The rational core of preference relations. IGIER Working Paper No. 632, Bocconi University, Milan.Google Scholar
  • [16] Cerreia-Vioglio S, Giarlotta A, Greco S, Maccheroni F, Marinacci M (2020) Rational preference and rationalizable choice. Econom. Theory 69:61–105.CrossrefGoogle Scholar
  • [17] Chambers CP, Echenique F (2016) Revealed Preference Theory, Econometric Society Monographs (Cambridge University Press, New York).CrossrefGoogle Scholar
  • [18] Chambers CP, Echenique F (2018) On multiple discount rates. Econometrica 86(4):1325–1346.CrossrefGoogle Scholar
  • [19] Cohn DL (2010) Measure Theory (Birkhäuser, New York).Google Scholar
  • [20] de Clippel G (2015) On the redundancy of the implicit welfarist axiom in bargaining theory. J. Econom. Theory 157:624–647.CrossrefGoogle Scholar
  • [21] Debreu G (1954) Representation of a preference ordering by a numerical function. Thrall R, Coombs C, Davies R, eds. Decision Processes (Wiley, New York), 159–166.Google Scholar
  • [22] Debreu G (1964) Continuity properties of a Paretian utility. Internat. Econom. Rev. 5(3):285–293.CrossrefGoogle Scholar
  • [23] Dekel E, Lipman BL, Rustichini A (2001) Representing preferences with a unique subjective state space. Econometrica 69(4):891–934.CrossrefGoogle Scholar
  • [24] Duggan J (1999) A general extension theorem for binary relations. J. Econom. Theory 86(1):1–16.CrossrefGoogle Scholar
  • [25] Dziewulski P (2018) Revealed time-preference. Games Econom. Behav. 112:67–77.CrossrefGoogle Scholar
  • [26] Evren Ö (2017) Second-order representations: Anything goes. Working paper, New Economic School, Moscow.Google Scholar
  • [27] Evren Ö, Ok EA (2011) On the multi-utility representation of preference relations. J. Math. Econom. 47(4-5):554–563.CrossrefGoogle Scholar
  • [28] Giarlotta A, Greco S (2013) Necessary and possible preference structures. J. Math. Econom. 49(2):163–172.CrossrefGoogle Scholar
  • [29] Gilboa I, Maccheroni F, Marinacci M, Schmeidler D (2010) Objective and subjective rationality in a multiple prior model. Econometrica 78(2):755–770.CrossrefGoogle Scholar
  • [30] Gul F, Pesendorfer W (2001) Temptation and self-control. Econometrica 69(6):1403–1435.CrossrefGoogle Scholar
  • [31] Hara K, Ok EA, Riella G (2019) Coalitional expected multi-utility theory. Econometrica 87(3):933–980.CrossrefGoogle Scholar
  • [32] Herden G (1989a) On the existence of utility functions. Math. Soc. Sci. 17(3):297–313.CrossrefGoogle Scholar
  • [33] Herden G (1989b) Some lifting theorems for continuous utility functions. Math. Soc. Sci. 18(2):119–134.CrossrefGoogle Scholar
  • [34] Herden G (1990) On a lifting theorem of Nachbin. Math. Soc. Sci. 19(1):37–44.CrossrefGoogle Scholar
  • [35] Hervés-Beloso C, Monteiro PK (2010) Strictly monotonic preferences on continuum of goods commodity spaces. J. Math. Econom. 46(5):725–727.CrossrefGoogle Scholar
  • [36] Hopenhayn HA, Prescott EC (1992) Stochastic monotonicity and stationary distributions for dynamic economies. Econometrica 60(6):1387–1406.CrossrefGoogle Scholar
  • [37] Hüsseinov F (2010) Monotonic extension. Discussion paper No: 10-04, Bilkent University, Ankara, Turkey.Google Scholar
  • [38] Hüsseinov F (2018) Extension of strictly monotonic functions in order-separable spaces. Working paper, ADA University, Baku, Azerbaijan.Google Scholar
  • [39] Jones LE (1984) A competitive model of commodity differentiation. Econometrica 52(2):507–530.CrossrefGoogle Scholar
  • [40] Klibanoff P, Marinacci M, Mukerji S (2005) A smooth model of decision making under ambiguity. Econometrica 73(6):1849–1892.CrossrefGoogle Scholar
  • [41] Kopylov I (2009) Choice deferral and ambiguity aversion. Theoret. Econom. 4(2):199–225.Google Scholar
  • [42] Kopylov I (2016) Canonical utility functions and continuous preference extensions. J. Math. Econom. 67:32–37.CrossrefGoogle Scholar
  • [43] Lehrer E, Teper R (2011) Justifiable preferences. J. Econom. Theory 146(2):762–774.CrossrefGoogle Scholar
  • [44] Levin VL (1983) A continuous utility theorem for closed preorders on a σ-compact metrizable space. Soviet Mathematics Doklady 28:715–718.Google Scholar
  • [45] Machina MJ, Schmeidler D (1992) A more robust definition of subjective probability. Econometrica 60(4):745–780.CrossrefGoogle Scholar
  • [46] Mas-Colell A (1975) A model of equilibrium with differentiated commodities. J. Math. Econom 2(2):263–295.CrossrefGoogle Scholar
  • [47] Mas-Colell A (1986) The price equilibrium existence problem in topological vector lattices. Econometrica 54(5):1039–1053.CrossrefGoogle Scholar
  • [48] Matzkin RL, Richter MK (1991) Testing strictly concave rationality. J. Econom. Theory 53(2):287–303.CrossrefGoogle Scholar
  • [49] Mehta G (1977) Topological ordered spaces and utility functions. Internat. Econom. Rev. 18(3):779–782.CrossrefGoogle Scholar
  • [50] Mehta G (1988) Some general theorems on the existence of order-preserving functions. Math. Soc. Sci. 15(2):135–143.CrossrefGoogle Scholar
  • [51] Minguzzi E (2013) Normally preordered spaces and utilities. Order 30:137–150.CrossrefGoogle Scholar
  • [52] Monteiro PK (1987) Some results on the existence of utility functions on path connected spaces. J. Math. Econom. 16(2):147–156.CrossrefGoogle Scholar
  • [53] Munkres JR (2000) Topology, 2nd ed. (Prentice Hall, Upper Saddle River, NJ).Google Scholar
  • [54] Nachbin L (1965) Topology and Order (Van Nostrand, Princeton, NJ).Google Scholar
  • [55] Nishimura H (2018) The transitive core: Inference of welfare from nontransitive preference relations. Theoret. Econom. 13(2):579–606.CrossrefGoogle Scholar
  • [56] Nishimura H, Ok EA (2016) Utility representation of an incomplete and nontransitive preference relation. J. Econom. Theory 166:164–185.CrossrefGoogle Scholar
  • [57] Nishimura H, Ok EA (2018) Preference structures. Working paper, New York University, New York.Google Scholar
  • [58] Nishimura H, Ok EA, Quah JKH (2017) A comprehensive approach to revealed preference theory. Amer. Econom. Rev. 107(4):1239–1263.CrossrefGoogle Scholar
  • [59] Peleg B (1970) Utility functions for partially ordered topological spaces. Econometrica 38(1):93–96.CrossrefGoogle Scholar
  • [60] Piermont E, Takeoka N, Teper R (2016) Learning the Krepsian state: Exploration through consumption. Games Econom. Behav. 100:69–94.CrossrefGoogle Scholar
  • [61] Reny PJ (2015) A characterization of rationalizable consumer behavior. Econometrica 83(1):175–192.CrossrefGoogle Scholar
  • [62] Richter MK (1966) Revealed preference theory. Econometrica 34(3):635–645.CrossrefGoogle Scholar
  • [63] Schmeidler D (1971) A condition for the completeness of partial preference relations. Econometrica 39(2):403–404.CrossrefGoogle Scholar
  • [64] Segal U (1987) The Ellsberg paradox and risk aversion: An anticipated utility approach. Internat. Econom. Rev 28(1):175–202.CrossrefGoogle Scholar
  • [65] Sertel MR (1971) Order, topology and preference. Working Paper No. 565-71, MIT Sloan School of Management, Cambridge, MA.Google Scholar
  • [66] Varian H (1982) The nonparametric approach to demand analysis. Econometrica 50(4):945–973.CrossrefGoogle Scholar
  • [67] Wakker P (1988) Continuity of preference relations for separable topologies. Internat. Econom. Rev. 29(1):105–110.CrossrefGoogle Scholar
  • [68] Yannelis NC (1991) The core of an economy without ordered preferences. Khan MA, Yannelis NC, eds. Equilibrium Theory in Infinite Dimensional Spaces (Springer-Verlag, Berlin), 102–123.CrossrefGoogle Scholar
  • [69] Yi G (1993) Continuous extension of preferences. J. Math. Econom. 22(6):547–555.CrossrefGoogle Scholar
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