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Resource-monotonicity and Population-monotonicity in Cake-cutting

Author

Listed:
  • Balazs Sziklai

    (Momentum Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences)

  • Erel Segal-Halevi

    (Bar-Ilan University Israel)

Abstract

We study the monotonicity properties of solutions in the classic problem of fair cake-cutting – dividing a single heterogeneous resource among agents with subjective utilities. Resource- and population-monotonicity relate to scenarios where the cake, or the number of participants who divide the cake, changes. It is required that the utility of all participants change in the same direction: either all of them are better-off (if there is more to share) or all are worse-off (if there is less to share). We formally introduce these concepts to the cake-cutting setting and present a meticulous axiomatic analysis. We show that classical cake-cutting protocols, like the Cut and Choose, Banach-Knaster, Dubins–Spanier and many other fail to be monotonic. We also show that, when the allotted pieces must be contiguous, proportionality and Pareto-optimality are incompatible with each of the monotonicity axioms. We provide a resource-monotonic protocol for two players and show the existence of rules that satisfy various combinations of contiguousness, proportionality, Pareto-optimality and the two monotonicity axioms.

Suggested Citation

  • Balazs Sziklai & Erel Segal-Halevi, 2015. "Resource-monotonicity and Population-monotonicity in Cake-cutting," CERS-IE WORKING PAPERS 1552, Institute of Economics, Centre for Economic and Regional Studies.
    • Handle: RePEc:has:discpr:1552
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Anna Bogomolnaia & Hervé Moulin & Fedor Sandomirskiy & Elena Yanovskaya, 2017. "Competitive Division of a Mixed Manna," Econometrica, Econometric Society, vol. 85(6), pages 1847-1871, November.
    2. Anna Bogomolnaia & Hervé Moulin & Fedor Sandomirskiy & Elena Yanovskaia, 2019. "Dividing bads under additive utilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 395-417, March.
    3. Anna Bogomolnaia & Herve Moulin & Fedor Sandomirskiy & Elena Yanovskaya, 2016. "Dividing Goods or Bads Under Additive Utilities," HSE Working papers WP BRP 147/EC/2016, National Research University Higher School of Economics.
    4. Erel Segal-Halevi & Balázs R. Sziklai, 2019. "Monotonicity and competitive equilibrium in cake-cutting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(2), pages 363-401, September.

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    More about this item

    Keywords

    resource-monotonicity; population-monotonicity; cake-cutting; leximin divisions; equitable divisions;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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