Template-Type: ReDIF-Paper 1.0 Author-Name: Mihir Bhattacharya Author-Name-First: Mihir Author-Name-Last: Bhattacharya Author-Email: mihir.bhattacharya@ashoka.edu.in Author-Workplace-Name: Ashoka University Author-Name: Ojasvi Khare Author-Name-First: Ojasvi Author-Name-Last: Khare Author-Email: ojasvi19r@isid.ac.in Author-Workplace-Name: Indian Statistical Institute, Delhi Title: Fair allocation with (semi-single-peaked) preferences over location and quantity 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. length: 30 Creation-Date: 20240404 Revision-Date: Publication-Status: File-URL:https://dp.ashoka.edu.in/ash/wpaper/paper111_0.pdf File-Format: Application/pdf Number: 111 Keywords: Allocation Keywords: Envy-free Keywords: Location Keywords: Quantity Keywords: single-peaked Handle: RePEc:ash:wpaper:111