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Cake Division by Majority Decision

Author

Listed:
  • Hans Gersbach
  • Bernhard Pachl

Abstract

We consider a collective choice process where three players make proposals sequentially on how to divide a given quantity of resources. Afterwards, one of the proposals is chosen by majority decision. If no proposal obtains a majority, a proposal is drawn by lot. We establish the existence of the set of subgame perfect equilibria, using a suitable refinement concept. In any equilibrium, the first agent offers the whole cake to the second proposal-maker, who in turn offers the whole cake back to the first agent. The third agent is then indifferent about dividing the cake between himself and the first or the second agent.

Suggested Citation

  • Hans Gersbach & Bernhard Pachl, 2006. "Cake Division by Majority Decision," CESifo Working Paper Series 1872, CESifo Group Munich.
  • Handle: RePEc:ces:ceswps:_1872
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    File URL: http://www.cesifo-group.de/DocDL/cesifo1_wp1872.pdf
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    References listed on IDEAS

    as
    1. Roth, Alvin E, 1985. "A Note on Risk Aversion in a Perfect Equilibrium Model of Bargaining," Econometrica, Econometric Society, vol. 53(1), pages 207-211, January.
    2. repec:cup:apsrev:v:83:y:1989:i:04:p:1181-1206_08 is not listed on IDEAS
    3. Nielsen, Lars Tyge, 1984. "Risk sensitivity in bargaining with more than two participants," Journal of Economic Theory, Elsevier, vol. 32(2), pages 371-376, April.
    4. Harrington, Joseph Jr., 1986. "A non-cooperative bargaining game with risk averse players and an uncertain finite horizon," Economics Letters, Elsevier, vol. 20(1), pages 9-13.
    5. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    6. Roth, Alvin E & Rothblum, Uriel G, 1982. "Risk Aversion and Nash's Solution for Bargaining Games with Risky Outcomes," Econometrica, Econometric Society, vol. 50(3), pages 639-647, May.
    7. Mueller, Dennis C., 1978. "Voting by veto," Journal of Public Economics, Elsevier, vol. 10(1), pages 57-75, August.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    division of a cake; majority decisions; tie-breaking rules;

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