arXiv subjects

Pinaki Mandal

Publications and source records attributed to Pinaki Mandal.

5 recordsLinked to original sources

arXiv2025

Efficient reallocation of indivisible resources: Pair-efficiency versus Pareto-efficiency

In the object reallocation problem, achieving Pareto-efficiency is desirable, but may be too demanding for implementation purposes. In contrast, pair-efficiency, which is the minimal efficiency requirement, is more suitable. Despite being a significant relaxation, however, pair-efficiency ensures Pareto-efficiency for any strategy-proof and individually rational rule when agents' preferences are unrestricted. What if agents' preferences have specific restricted structures, such as single-peakedness or single-dippedness? We often encounter such situations in real-world scenarios. This study aims to investigate whether pair-efficiency is sufficient to ensure Pareto-efficiency in such cases. Our main contribution in this paper is establishing the equivalence between pair-efficiency and Pareto-efficiency when dealing with single-peaked or single-dipped preference profiles. This equivalence holds without needing to assume any other properties of the rule. We further show that both the single-peaked domain and the single-dipped domain are the "maximal" domains where this equivalence holds.

econ.TH↗

arXiv2023

Equivalence between individual and group strategy-proofness under stability

This paper studies the (group) strategy-proofness aspect of two-sided matching markets under stability. For a one-to-one matching market, we show an equivalence between individual and group strategy-proofness under stability. We obtain this equivalence assuming the domain satisfies a richness condition. However, the result cannot be extended to the many-to-one matching markets. We further consider a setting with single-peaked preferences and characterize all domains compatible for stability and (group) strategy-proofness.

econ.TH↗

arXiv2023

Compatibility between Stability and Strategy-Proofness: A Single-Peaked Preferences Investigation

In two-sided matching markets, ensuring both stability and strategy-proofness poses a significant challenge; it is impossible when agents' preferences are unrestricted. But what if agents' preferences have specific restricted structures? Such scenarios frequently arise in real-world applications. This study explores the possibility of achieving both stability and strategy-proofness by focusing on scenarios where agents' preferences follow a structured pattern called single-peakedness. We focus on the simplest case - the well-known marriage problem, which is a one-to-one matching market. Despite its simplicity, this model is a useful starting point for exploration in many cases. Our main contribution is identifying all single-peaked subdomains on which stability and (weak/strong group) strategy-proofness are compatible, which we present through two key results. The first one characterizes all single-peaked subdomains with stable and (weakly group) strategy-proof matching rules, and identifies such a matching rule on these domains. The second one is an impossibility result that shows the incompatibility between stability and strong group strategy-proofness on single-peaked subdomains.

econ.TH↗

arXiv2022

Simple dominance of fixed priority top trading cycles

We study the implementation of fixed priority top trading cycles (FPTTC) rules via simply dominant mechanisms (Pycia and Troyan, 2019) in the context of assignment problems, where agents are to be assigned at most one indivisible object and monetary transfers are not allowed. We consider both models - with and without outside options, and characterize all simply dominant FPTTC rules in both models. We further introduce the notion of simple strategy-proofness to resolve the issue with agents being concerned about having time-inconsistent preferences, and discuss its relation with simple dominance.

econ.TH↗

arXiv2021

On percolation in a generalized backbend process

We have generalized the idea of backbend in a nearest-neighbor oriented bond percolation process by considering a backbend sequence $β: \mathbb{Z}_+ \to \mathbb{Z}_+ \cup \{\infty\}$, and defining a $β$-backbend path from the origin as a path that never retreats further than $β(h)$ levels back from its record level $h$. We study the relationship between the critical probabilities of different percolation processes based on different backbend sequences on half-space, full-space, and half-slabs of the $d$-dimensional ($d \geq 2$) body-centered cubic (BCC) lattice. We also give sufficient conditions on the backbend sequences such that there will be no percolation at the critical probabilities of the corresponding percolation processes on half-space and full-space of the BCC lattice.

math.PR↗