Introduction to the mathematics of amibiguity

Uncertainty in Economic Theory: Essays in Honor of David Schmeidler's 65th Birthday

Volumn , Issue , 2004, Pages 46-107

  Marinacci, Massimo ^a   Montrucchio, Luigi ^a  

^a UNIVERSITY OF TURIN   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77957812715     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4324/9780203358061     Document Type: Chapter

References (71)

1. Aliprantis, C. D. and K. C. Border (1999) Infinite dimensional analysis, Springer-Verlag, New York.
2. Aumann, R. and L. Shapley (1974) Values of non-atomic games, Princeton University Press, Princeton.
3. Bassanezi, R. C. and G.H. Greco (1984) SulP additività dell' integrale, Rendiconti Seminario Matematico Università di Padova, 72, 249-275.
4. BenPorath, E., I. Gilboa and D. Schmeidler (1997) On the measurement of inequality under uncertainty, Journal ofEconomic Theory, 75, 194-204. (Reprinted as Chapter 22 in this volume.).
5. Bhaskara Rao, K. P. S., M. Bhaskara Rao (1983) Theory of charges, Academic Press, New York.
6. Biswas, A. K., T. Parthasarathy, J. A. M. Potters, and M. Voorneveld (1999) Large cores and exactness, Games and Economic Behavior, 28, 1-12.
7. Bondareva, O. (1963) Certain applications of the methods of linear programming to the theory of cooperative games, (in Russian) Problemy Kibernetiki, 10, 119-139.
8. Boros, E. and P. L. Hammer (2002) Pseudo-Boolean optimization, Discrete Applied Mathematics, 123, 155-225.
9. Carlier, G. and R. A. Dana, Core of convex distortions of a probability on a non-atomic space, Journal of Economic Theory, 173, 199-222, 2003.
10. Chateauneuf, A. and Jaffray, J.-Y. (1989) Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion, Mathematical Social Sciences, 17, 263-283.
11. Choquet, G. (1953) Theory of capacities, Annales de l'Institut Fourier, 5, 131-295.
12. Delbaen, F. (1974) Convex games and extreme points, Journal of Mathematical Analysis and Applications, 45, 210-233.
13. Dellacherie, C. (1971) Quelques commentaires sur le prolongements de capacités, Séminaire Probabilités V, Lecture Notes in Math. 191, Springer-Verlag, New York.
14. Dellacherie, C. and P.-A. Meyer (1978) Probabilities and potential, North-Holland, Amsterdam.
15. Dempster, A. (1967) Upper and lower probabilities induced by a multivalued mapping, Annals of Mathematical Statistics, 38, 325-339.
16. Dempster, A. (1968) A generalization of Bayesian inference, Journal of the Royal Statistical Society (B), 30, 205-247.
17. Denneberg, D. (1994) Non-additive measure and integral, Kluwer, Dordrecht.
18. Denneberg, D. (1997) Representation of the Choquet integral with the a -additive Mobius transform, Fuzzy Sets and Systems, 92, 139-156.
19. De Waegenaere, A. and P. Wakker (2001) Nonmonotonic Choquet integrals, Journal of Mathematical Economics, 36, 45-60.
20. Dunford, N. and J. T. Schwartz (1958) Linear operators, part I: general theory, Wiley-Intersience, London.
21. Einy, E. and B. Shitovitz (1996) Convex games and stable sets, Games and Economic Behavior, 16, 192-201.
22. Epstein, L. G. and T. Wang (1996) "Beliefs about beliefs" without probabilities, Econometrica, 64, 1343-1373.
23. Fan, K. (1956) On systems of linear inequalities, in Linear inequalities and related systems, Annals of Math. Studies, 38, 99-156.
24. Ghirardato, P. (1997) On independence for non-additive measures, with a Fu-bini theorem, Journal of Economic Theory, 73, 261-291.
25. Gilboa, I. and E. Lehrer (1991) Global games, International Journal of Game Theory, 20, 129-147.
26. Gilboa, I. and D. Schmeidler (1994) Additive representations of non-additive measures and the Choquet integral, Annals of Operations Research, 52, 43-65.
27. Gilboa, I. and D. Schmeidler (1995) Canonical representation of set functions, Mathematics of Operations Research, 20, 197-212.
28. Grabisch, M., J.-L. Marichal and M. Roubens (2000) Equivalent representations of set functions, Mathematics of Operations Research, 25, 157-178.
29. Greco, G. H. (1976) Integrale monotono, Rendiconti Seminario Matematico Università di Padova, 57, 149-166.
30. Greco, G. H. (1981) Surlamesurabilité d'une fonction numérique par rapport à une famille d'ensembles. Rendiconti Seminario Matematico Università di Padova, 65, 163-176.
31. Greco, G. H. (1982) Sulla rappresentazione di funzionali mediante integrali, Rendiconti Seminario Matematico Università di Padova, 66, 21-42.
32. Huber, P. J. and V. Strassen (1973) "Minimax tests and the Neyman-Pearson lemma capacities,' Annals of Statistics, 1, 251-263.
33. Ichiishi, T. (1981) Super-modularity: applications to convex games and to the greedy algorithm for LP, Journal of Economic Theory, 25, 283-286.
34. Kannai, Y. (1969) Countably additive measures in cores of games, Journal of Mathematical Analysis and Applications, 27, 227-240.
35. Kelley, J. L. (1959) Measures on Boolean algebras, Pacific Journal of Mathematics, 9, 1165-1177.
36. Kikuta, K. (1988) A condition for a game to be convex, Mathematica Japónica, 33, 425-430.
37. Kikuta, K. and L. S. Shapley (1986) Core stability in n-person games, mimeo (2000).
38. Maccheroni, F. and M. Marinacci, An Heine-Borei theorem for ba(∑), mimeo (2000).
39. Maccheroni, F. and W. H. Ruckle (2002) BV as a dual space, Rendiconti Seminario Matematico Università di Padova, 107, 101-109.
40. Marinacci, M. (1996) Decomposition and representation of coalitional games, Mathematics of Operations Research, 21, 1000-1015. (Reprinted as Chapter 12 in this volume.).
41. Marinacci, M. (1997) Finitely additive and epsilon Nash equilibria, International Journal of Game Theory, 26, 315-333.
42. Marinacci, M. and L. Montrucchio (2003) Subcalculus for set functions and cores of TU games, Journal of Mathematical Economics, 39, 1-25.
43. Marinacci, M. and L. Montrucchio (2004) A Characterization of the core of convex games through Gateaux derivatives, Journal of Economic Theory, 116, 229-248.
44. Moulin, H. (1995) Cooperative microeconomics, Princeton University Press, Princeton.
45. Myerson, R. (1991) Game theory, Harvard University Press, Cambridge.
46. Nguyen, H. T. (1978) On random sets and belief functions, Journal of Mathematical Analysis and Applications, 65, 531-542.
47. Owen, G. (1972) Multilinear extensions of games, Management Science, 18, 64-79.
48. Owen, G. (1995) Game theory, Academic Press, New York.
49. Philippe, E, G. Debs and J.- Y. Jaffray (1999) Decision making with monotone lower probabilities of infinite order, Mathematics of Operations Research, 24, 767-784.
50. Revuz, A. (1955) Fonctions croissantes et mesures sur les espaces topologiques ordonnés, Annates de l Instituí Fourier, 6, 187-269.
51. Rota, G. C. (1964) Theory of Mobius functions, Z. Wahrsch. und Verw. Geb., 2, 340-368.
52. Rudin, W. (1973) Functional analysis, McGraw-Hill, New York.
53. Rudin, W. (1987) Real and complex analysis (3rd edition), McGraw-Hill, New York.
54. Salinetti, G. and R. Wets (1986) On the convergence in distribution of measurable multi-functions (random sets), normal integrands, stochastic processes and stochastic infima, Mathematics of Operations Research, 11, 385-419.
55. Schmeidler, D. (1968) On balanced games with infinitely many players, Research Program in Game Theory and Mathematical Economics, RM 28, The Hebrew University of Jerusalem.
56. Schmeidler, D. (1972) Cores of exact games, Journal of Mathematical Analysis and Applications, 40, 214-225.
57. Schmeidler, D. (1986) Integral representation without additivity, Proceedings of the American Mathematical Society, 97, 255-261.
58. Schmeidler, D. (1989) Subjective probability and expected utility without additivity, Econometrica, 57, 571-587. (Reprinted as Chapter 5 in this volume.).
59. Schultz, M. H. (1969) L∞-multivariate approximation theory, SIAM Journal on Numerical Analysis, 6, 161-183.
60. Shafer, G. (1976) A mathematical theory of evidence, Princeton University Press, Princeton.
61. Shapley, L. S. (1953) A value for n-person games, in Contributions to the Theory of Games (H. Kuhn and A. W. Tucker, eds), Princeton University Press, Princeton.
62. Shapley, L. S. (1967) On balanced sets and cores, Naval Research Logistic Quarterly, 14, 453-460.
63. Shapley, L. S. (1971) Cores of convex games, International Journal of Game Theory, 1, 12-26.
64. Sharkey, W. W. (1982) Cooperative games with large cores, International Journal of Game Theory, 11, 175-182.
65. Sipos, J. (1979a) Integral with respect to a pre-measure, MathematicaSlovaca, 29, 141-155.
66. Sipos, J. (1979b) Non linear integrals, Mathematica Slovaca, 29, 257-270.
67. Wakker, P. (1993) Unbounded utility for Savage's 'foundations of statistics' and other models, Mathematics of Operations Research, 18, 446-485.
68. Webster, R. (1994) Convexity, Oxford University Press, Oxford.
69. Widder, D. V. (1941) The Laplace transform, Princeton University Press, Princeton.
70. Wolfenson, M. and T.-L. Fine (1982) Bayes-like decision making with upper and lower probabilities, Journal of the American Statistical Association, 11, 80-88.
71. Zhou, L. (1998) Integral representation of continuous comonotonically additive functionals, Transactions of the American Mathematical Society, 350, 1811-1822.