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Nontransitive-nontotal consumer theory. (English) Zbl 0598.90005
We show the parallel nature of two approaches to nontransitive or nontotal consumers: through ”weak” preferences and though ”strict” preferences”. This yields specific results (e.g., a new equilibrium existence theorem with weak preferences), general results (a metatheorem translating between the two approaches), and general concepts (a new notion of ”rationality”). We give revealed preference axioms to characterize preferences, and prove equivalences among several axiom systems, showing that the apparent weakness of some axiom systems is illusory. We resolve a weak axiom conjecture, and we introduce a new axiom. We prove that our nonclassical consumers generalize classical equilibrium theory.

MSC:
91B10 Group preferences
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[1] Arrow, K.J; Debreu, G, Existence of an equilibrium for a competitive economy, Econometrica, 22, 265-290, (1954) · Zbl 0055.38007
[2] Berge, C, Topological spaces, (1963), Macmillan Co New York · Zbl 0114.38602
[3] Bergstrom, T.C; Parks, R.P; Rader, T, Preferences which have open graphs, J. math. econ., 3, 265-268, (1976) · Zbl 0387.90009
[4] Campbell, D.E, Revealed preference and demand correspondences, (June, 1984), University of Toronto Toronto, Ottawa
[5] Debreu, G, A social equilibrium existence theorem, (), 886-893 · Zbl 0047.38804
[6] Debreu, G, Theory of value, (1959), Wiley New York · Zbl 0193.20205
[7] Fan, K, A generalization of Tychonoff’s fixed point theorem, Math. ann., 142, 305-310, (1961) · Zbl 0093.36701
[8] Gale, D; Mas-Colell, A, An equilibrium existence theorem for a general model without ordered preferences, J. math. econ., 2, 9-15, (1975) · Zbl 0324.90010
[9] Gale, D; Mas-Colell, A, Corrections to an equilibrium existence theorem for a general model without ordered preferences, J. math. econ., 6, 297-298, (1979) · Zbl 0422.90018
[10] Golubitsky, M; Guillemin, V, Stable mappings and their singularities, (1973), Springer-Verlag New York · Zbl 0294.58004
[11] Hildenbrand, W; Kirman, A.P, Introduction to equilibrium analysis, (1976), North-Holland Amsterdam · Zbl 0345.90004
[12] Hurwicz, L; Richter, M.K, Revealed preference without demand continuity assumptions, (), Chap. 3 · Zbl 0294.90006
[13] Kihlstrom, R; Mas-Colell, A; Sonnenschein, H, The demand theory of the weak axiom of revealed preference, Econometrica, 44, 971-978, (1976) · Zbl 0331.90004
[14] Knaster, B; Kuratowski, K; Mazurkiewicz, S, Ein beweis des fixpunktsatzes für n-dimensionale simplexe, Fund. math., 14, 132-137, (1929) · JFM 55.0972.01
[15] Mas-Colell, A, An equilibrium existence theorem without complete or transitive preferences, J. math. econ., 1, 237-246, (1974) · Zbl 0348.90033
[16] McKenzie, L.W, The classical theorem on existence of competitive equilibrium, Econometrica, 49, 819-841, (1981) · Zbl 0461.90008
[17] Nikaido, H, Convex structures and economic theory, (1968), Academic Press New York · Zbl 0172.44502
[18] Richter, M.K, Rational choice, (), Chap. 2 · Zbl 0277.90002
[19] Rose, H, Consistency of preference: the two-commodity case, Rev. econ. stud., 25, 124-125, (1958)
[20] Schmeidler, D, Competitive equilibria in markets with a continuum of traders and incomplete preferences, Econometrica, 37, 578-585, (1969) · Zbl 0184.45201
[21] Shafer, W.J, The nontransitive consumer, Econometrica, 42, 913-919, (1974) · Zbl 0291.90007
[22] Shafer, W.J; Sonnenschein, H.F, Equilibrium in abstract economies without ordered preferences, J. math. econ., 2, 345-348, (1975) · Zbl 0312.90062
[23] Shafer, W.J, Equilibrium in economies without ordered preferences or free disposal, J. math. econ., 3, 135-137, (1976) · Zbl 0348.90030
[24] Sonnenschein, H.F, Demand theory without transitive preferences, with applications to the theory of competitive equilibrium, (), Chap. 10 · Zbl 0277.90012
[25] Valentine, F.A, Convex sets, (1964), McGraw-Hill New York · Zbl 0129.37203
[26] Yannelis, N; Prabhakar, N.D, Existence of maximal elements and equilibria in linear topological spaces, J. math. econ., 12, 233-245, (1983) · Zbl 0536.90019
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