Allocating Indivisible Resources under Price Rigidities in Polynomial Time

TL;DR

This paper presents a polynomial-time dynamic mechanism for allocating indivisible resources under price rigidities, balancing efficiency and social needs, and addressing strategic considerations.

Contribution

It introduces a polynomial algorithm for over-demanded set detection and a dynamic mechanism with rationing to find constrained Walrasian equilibria under price rigidities.

Findings

Efficient polynomial algorithm for over-demanded set detection

Mechanism achieves constrained Walrasian equilibrium in polynomial time

Addresses strategic behavior and profit computation in the allocation process

Abstract

In many realistic problems of allocating resources, economy efficiency must be taken into consideration together with social equality, and price rigidities are often made according to some economic and social needs. We study the computational issues of dynamic mechanisms for selling multiple indivisible items under price rigidities. We propose a polynomial algorithm that can be used to find over-demanded sets of items, and then introduce a dynamic mechanism with rationing to discover constrained Walrasian equilibria under price rigidities in polynomial time. We also address the computation of sellers' expected profits and items' expected prices, and discuss strategical issues in the sense of expected profits.