Possible and Necessary Allocations via Sequential Mechanisms

TL;DR

This paper investigates the possible and necessary allocations in sequential mechanisms, providing characterizations and analyzing computational complexity for various classes of these mechanisms.

Contribution

It extends existing characterizations of allocations to several classes of sequential mechanisms and studies the complexity of allocation problems.

Findings

Characterizations of allocations for balanced, recursively balanced, and other policies.

Complexity results for possible and necessary allocation problems.

Extension of Brams and King's characterization to restricted policies.

Abstract

A simple mechanism for allocating indivisible resources is sequential allocation in which agents take turns to pick items. We focus on possible and necessary allocation problems, checking whether allocations of a given form occur in some or all mechanisms for several commonly used classes of sequential allocation mechanisms. In particular, we consider whether a given agent receives a given item, a set of items, or a subset of items for five natural classes of sequential allocation mechanisms: balanced, recursively balanced, balanced alternating, strictly alternating and all policies. We identify characterizations of allocations produced balanced, recursively balanced, balanced alternating policies and strictly alternating policies respectively, which extend the well-known characterization by Brams and King [2005] for policies without restrictions. In addition, we examine the computational complexity of possible and necessary allocation problems for these classes.