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Consistency and its Converse: an Introduction

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  • Thomson, W.

Abstract

This essay is an introduction to the recent literature on the "consistency principle" and its "converse". An allocation rule is consistent if for any problem in its domain of definition and any alternative that it selects for it, then for the associated "reduced problem" obtained by imagining the departure of any subgroup of the agents with their "components of the alternative" and reassessing the options open to that subgroup.

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Bibliographic Info

Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 448.

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Length: 42 pages
Date of creation: 1998
Date of revision:
Handle: RePEc:roc:rocher:448

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Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.

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Keywords: CONSISTENCY ; ECONOMICS ; THEORY;

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References

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  1. Ju, Biung-Ghi, 2008. "Efficiency and consistency for locating multiple public facilities," Journal of Economic Theory, Elsevier, Elsevier, vol. 138(1), pages 165-183, January.
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  4. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, Springer, vol. 15(3), pages 187-200.
  5. Tadenuma, Koichi & Thomson, William, 1993. "The fair allocation of an indivisible good when monetary compensations are possible," Mathematical Social Sciences, Elsevier, Elsevier, vol. 25(2), pages 117-132, February.
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  9. Dutta, B, 1990. "The Egalitarian Solution and Reduced Game Properties in Convex Games," International Journal of Game Theory, Springer, Springer, vol. 19(2), pages 153-69.
  10. Roemer, John E., 1988. "Axiomatic bargaining theory on economic environments," Journal of Economic Theory, Elsevier, Elsevier, vol. 45(1), pages 1-31, June.
  11. Thomson, William, 1994. "Consistent extensions," Mathematical Social Sciences, Elsevier, Elsevier, vol. 28(1), pages 35-49, August.
  12. Maniquet, Francois, 1996. "Horizontal equity and stability when the number of agents is variable in the fair division problem," Economics Letters, Elsevier, Elsevier, vol. 50(1), pages 85-90, January.
  13. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, Elsevier, vol. 45(2), pages 330-341, August.
  14. Svensson, Lars-Gunnar, 1983. "Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness," Econometrica, Econometric Society, Econometric Society, vol. 51(4), pages 939-54, July.
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  19. Nir Dagan, 1996. "A Note on Thomson's Characterizations of the Uniform Rule," Economic theory and game theory, Nir Dagan 003, Nir Dagan.
  20. Thomson, William, 1988. "A study of choice correspondences in economies with a variable number of agents," Journal of Economic Theory, Elsevier, Elsevier, vol. 46(2), pages 237-254, December.
  21. Tadenuma, Koichi & Thomson, William, 1991. "No-Envy and Consistency in Economies with Indivisible Goods," Econometrica, Econometric Society, Econometric Society, vol. 59(6), pages 1755-67, November.
  22. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer, Springer, vol. 28(4), pages 511-520.
  23. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, Elsevier, vol. 63(2), pages 219-245, August.
  24. Tadenuma, K, 1992. "Reduced Games, Consistency, and the Core," International Journal of Game Theory, Springer, Springer, vol. 20(4), pages 325-34.
  25. Hokari, Toru & Thomson, William, 2008. "On properties of division rules lifted by bilateral consistency," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1057-1071, December.
  26. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, Elsevier, vol. 36(2), pages 195-213, August.
  27. Peleg, Bezalel, 1985. "An axiomatization of the core of cooperative games without side payments," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 203-214, April.
  28. Nir Dagan & Oscar Volij, 1997. "Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems," Economic theory and game theory, Nir Dagan 004, Nir Dagan.
  29. Sasaki, Hiroo & Toda, Manabu, 1992. "Consistency and characterization of the core of two-sided matching problems," Journal of Economic Theory, Elsevier, Elsevier, vol. 56(1), pages 218-227, February.
  30. Chun, Youngsub, 2002. "The Converse Consistency Principle in Bargaining," Games and Economic Behavior, Elsevier, Elsevier, vol. 40(1), pages 25-43, July.
  31. Yeh, Chun-Hsien, 2006. "Reduction-consistency in collective choice problems," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 637-652, September.
  32. Hokari, Toru, 2005. "Consistency implies equal treatment in TU-games," Games and Economic Behavior, Elsevier, Elsevier, vol. 51(1), pages 63-82, April.
  33. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series, Institute of Economic Research, Seoul National University no1, Institute of Economic Research, Seoul National University.
  34. Ergin, Haluk I., 2000. "Consistency in house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 77-97, August.
  35. Carmen Bevia, 1996. "Identical preferences lower bound solution and consistency in economies with indivisible goods," Social Choice and Welfare, Springer, Springer, vol. 13(1), pages 113-126, January.
  36. Youngsub Chun, 2011. "Consistency and monotonicity in sequencing problems," International Journal of Game Theory, Springer, Springer, vol. 40(1), pages 29-41, February.
  37. Manabu Toda, 2006. "Monotonicity and Consistency in Matching Markets," International Journal of Game Theory, Springer, Springer, vol. 34(1), pages 13-31, April.
  38. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp421, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  39. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, Elsevier, vol. 45(3), pages 249-297, July.
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