Quantifying Inefficiency of Fair Cost-Sharing Mechanisms for Sharing Economy

TL;DR

This paper analyzes the inefficiency of various fair cost-sharing mechanisms in sharing economy coalition formation, quantifying how far stable structures are from optimal social outcomes.

Contribution

It derives bounds on the strong price of anarchy for common fair cost-sharing mechanisms in sharing economy coalition games.

Findings

SPoA for equal-split, proportional-split, usage-based mechanisms is Θ(log K)

SPoA for egalitarian and Nash bargaining solutions is O(√K log K)

Distributed decision-making under these mechanisms induces moderate inefficiency

Abstract

Sharing economy is a distributed peer-to-peer economic paradigm, which gives rise to a variety of social interactions for economic purposes. One fundamental distributed decision-making process is coalition formation for sharing certain replaceable resources collaboratively, for example, sharing hotel rooms among travelers, sharing taxi-rides among passengers, and sharing regular passes among users. Motivated by the applications of sharing economy, this paper studies a coalition formation game subject to the capacity of $K$ participants per coalition. The participants in each coalition are supposed to split the associated cost according to a given cost-sharing mechanism. A stable coalition structure is established when no group of participants can opt out to form another coalition that leads to lower individual payments. We quantify the inefficiency of distributed decision-making processes under a cost-sharing mechanism by the strong price of anarchy (SPoA), comparing a worst-case stable coalition structure and a social optimum. In particular, we derive SPoA for common fair cost-sharing mechanisms (e.g., equal-split, proportional-split, egalitarian and Nash bargaining solutions of bargaining games, and usage based cost-sharing). We show that the SPoA for equal-split, proportional-split, and usage based cost-sharing (under certain conditions) is $\Theta(\log K)$, whereas the one for egalitarian and Nash bargaining solutions is $O(\sqrt{K} \log K)$. Therefore, distributed decision-making processes under common fair cost-sharing mechanisms induce only moderate inefficiency.