Quantifying Inefficiency of Fair Cost-Sharing Mechanisms for Sharing Economy

Sharing economy, a distributed peer-to-peer eco-nomic paradigm, gives rise to a variety of social interactionsfor economic reasons. One common distributed decision-makingprocess is the coalition formation to share certain replaceable re-sources collaboratively, for example, sharing hotel rooms amongtravelers, sharing taxi-rides among passengers, and sharingregular passes among users. Motivated by the applications ofsharing economy, this paper studies a coalition formation gamesubject to the capacity of K participants per coalition. Theparticipants in each coalition are supposed to split the associatedcost according to a given cost-sharing mechanism. A stablecoalition structure is established, when no group of participantscan opt out to form another coalition that leads to lowerindividual payments. We quantify the inefficiency of distributeddecision-making processes under a cost-sharing mechanism bythe strong price of anarchy (SPoA), comparing a worst-case stablecoalition structure and a social optimum. In particular, we deriveSPoA for common fair cost-sharing mechanisms (e.g., equal-split,proportional-split, egalitarian and Nash bargaining solutions ofbargaining games, and usage based cost-sharing). We show thatthe SPoA for equal-split, proportional-split, and usage based cost-sharing (under certain conditions) is Θ(logK), whereas the onefor egalitarian and Nash bargaining solutions is O(√K logK).Therefore, distributed decision-making processes under commonfair cost-sharing mechanisms induce only moderate inefficiency.