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Strategic divide and choose

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  • Nicolò, Antonio
  • Yu, Yan

Abstract

We consider the classic cake-division problem when the cake is a heterogeneous good represented by an interval in the real line. We provide a mechanism to implement, in an anonymous way, an envy-free and efficient allocation when agents have private information on their preferences. The mechanism is a multi-step sequential game form in which each agent at each step receives a morsel of the cake that is the intersection of what she asks for herself and what the other agent concedes to her.

Suggested Citation

  • Nicolò, Antonio & Yu, Yan, 2008. "Strategic divide and choose," Games and Economic Behavior, Elsevier, vol. 64(1), pages 268-289, September.
  • Handle: RePEc:eee:gamebe:v:64:y:2008:i:1:p:268-289
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    1. Barbanel, J. B. & Brams, S. J., 2001. "Cake Division with Minimal Cuts: Envy-Free Procedures for 3 Person, 4 Persons, and Beyond," Working Papers 01-07, C.V. Starr Center for Applied Economics, New York University.
    2. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
    3. Vincent P. Crawford, 1977. "A Game of Fair Division," Review of Economic Studies, Oxford University Press, vol. 44(2), pages 235-247.
    4. Berliant, Marcus & Thomson, William & Dunz, Karl, 1992. "On the fair division of a heterogeneous commodity," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 201-216.
    5. Edelman, Paul & Fishburn, Peter, 2001. "Fair division of indivisible items among people with similar preferences," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 327-347, May.
    6. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August.
    7. Steven J. Brams & Peter C. Fishburn, 2000. "Fair division of indivisible items between two people with identical preferences: Envy-freeness, Pareto-optimality, and equity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 247-267.
    8. Crawford, V. P. & Heller, W. P., 1979. "Fair division with indivisible commodities," Journal of Economic Theory, Elsevier, vol. 21(1), pages 10-27, August.
    9. Thomson, W., 1991. "Resource-Monotonic Solutions to the Problem of Fair Divosion when Preferences are Single-Peaked ," RCER Working Papers 301, University of Rochester - Center for Economic Research (RCER).
    10. Weingast, Barry R. & Wittman, Donald, 2008. "The Oxford Handbook of Political Economy," OUP Catalogue, Oxford University Press, number 9780199548477.
    11. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-1039, July.
    12. Thomson, William, 2005. "Divide-and-permute," Games and Economic Behavior, Elsevier, vol. 52(1), pages 186-200, July.
    13. William Thomson, 1996. "Concepts Of Implementation," The Japanese Economic Review, Japanese Economic Association, vol. 47(2), pages 133-143, June.
    14. Steven J. Brams & Paul H. Edelman & Peter C. Fishburn, 2003. "Fair Division Of Indivisible Items," Theory and Decision, Springer, vol. 55(2), pages 147-180, September.
    15. Olivier Compte & Philippe Jehiel, 2004. "Gradualism in Bargaining and Contribution Games," Review of Economic Studies, Oxford University Press, vol. 71(4), pages 975-1000.
    16. Maniquet, Francois & Sprumont, Yves, 2000. "On resource monotonicity in the fair division problem," Economics Letters, Elsevier, vol. 68(3), pages 299-302, September.
    17. Demko, Stephen & Hill, Theodore P., 1988. "Equitable distribution of indivisible objects," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 145-158, October.
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    Cited by:

    1. Erel Segal-Halevi & Shmuel Nitzan, 2014. "Cake Cutting – Fair and Square," Working Papers 2014-01, Bar-Ilan University, Department of Economics.
    2. repec:eee:mateco:v:70:y:2017:i:c:p:1-28 is not listed on IDEAS
    3. repec:eee:matsoc:v:90:y:2017:i:c:p:100-110 is not listed on IDEAS
    4. Rodrigo A. Velez & Antonio Nicolo, 2016. "Divide and compromise," Working Papers 20160710-001, Texas A&M University, Department of Economics.

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