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Fair allocation with (semi-single-peaked) preferences over location and quantity

Author

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  • Mihir Bhattacharya

    (Ashoka University)

  • Ojasvi Khare

    (Indian Statistical Institute, Delhi)

Abstract

We consider the problem of dividing and allocating a perfectly divisible heterogeneous good where agents have a preference for location and quantity. We assume that preferences are single-peaked in quantity, i.e., semi-single-peaked which can be represented by continuous indifference curves (ICs). We show existence of envy-free and Pareto efficient allocation rules, and characterize the set of all such rules using the notion of a balanced IC. We define the balanced-curve allocation (BCA) which uses the region between the two balanced ICs to obtain feasible allocations. We show that an allocation rule is envy-free and Pareto efficient if and only if it is in the set specified by the BCA rule. We show that there is no strategy-proof, envy-free and Pareto efficient allocation rule. We provide some insights into the problem when there are more than 2 agents.

Suggested Citation

  • Mihir Bhattacharya & Ojasvi Khare, 2024. "Fair allocation with (semi-single-peaked) preferences over location and quantity," Working Papers 111, Ashoka University, Department of Economics.
    • Handle: RePEc:ash:wpaper:111
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    File URL: https://dp.ashoka.edu.in/ash/wpaper/paper111_0.pdf
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    References listed on IDEAS

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    1. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
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    Allocation;

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