Abstract
In this paper, we obtain a set of pairwise stable outcomes in two-sided hybrid matching market with price externalities. In this market, the valuation of agents depends upon money. The most important feature of our work is to devise an algorithm that characterizes the stable matchings as fixed points of an increasing function T. We also prove the termination and correctness of this fixed point algorithm. Furthermore, we study the lattice structure of the set of stable outcomes by direct implication of Tarski's fixed point theorem.
Highlights
Since many years matching theory has been widely studied by economists, game theorists and mathematicians due to its extensive applications in many related fields
Some recent relevant work in opinion dynamics includes Shang [1] and [2] in which the author presented a general model for the opinion formation in the averager-copier-voter network having non-rational agents and resilient consensus against malicious agents who deliberately change their opinions with the goal of manipulating the performance of entire network
We present an algorithm that obtain the stable matching as a fixed point of an increasing function
Summary
Since many years matching theory has been widely studied by economists, game theorists and mathematicians due to its extensive applications in many related fields. In the present work we apply Tarski’s fixed point theorem to study the lattice structure of two sided matching market with externalities i.e; the agents are flexible and can negotiate on price. We present an algorithm that obtain the stable matching as a fixed point of an increasing function.
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