Pairwise Stability in Two Sided Market with Strictly Increasing Valuation Functions

TL;DR

This paper analyzes a two-sided market with strictly increasing valuation functions and develops an algorithm to prove the existence of stable matchings considering discrete money transfers.

Contribution

It introduces a new model with strictly increasing valuation functions and provides an algorithm to establish the existence of stable matchings in this setting.

Findings

Existence of stable matchings proven for the model

Algorithm for stability verification developed

Model incorporates discrete monetary transfers

Abstract

This paper deals with two-sided matching market with two disjoint sets, i.e. the set of buyers and the set of sellers. Each seller can trade with at most with one buyer and vice versa. Money is transferred from sellers to buyers for an indivisible goods that buyers own. Valuation functions, for participants of both sides, are represented by strictly increasing functions with money considered as discrete variable. An algorithm is devised to prove the existence of stability for this model.