Fair Ride Allocation on a Line

Yuki Amano; Ayumi Igarashi; Yasushi Kawase; Kazuhisa Makino; Hirotaka Ono

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arXiv · 2007.08045

Fair Ride Allocation on a Line

Yuki Amano·Ayumi Igarashi·Yasushi Kawase·Kazuhisa Makino·Hirotaka Ono

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Abstract

The airport game is a classical and well-known model of fair cost-sharing for a single facility among multiple agents. This paper extends it to the so-called assignment setting, that is, for multiple facilities and agents, each agent chooses a facility to use and shares the cost with the other agents. Such a situation can be often seen in sharing economy, such as sharing fees for office desks among workers, taxis among customers of possibly different destinations on a line, and so on. Our model is regarded as a coalition formation game based on the fair cost-sharing of the airport game; we call our model \emph{a fair ride allocation on a line}. As criteria of solution concepts, we incorporate Nash stability and envy-freeness into our setting. We show that a Nash-stable feasible allocation that minimizes the social cost of agents can be computed efficiently if a feasible allocation exists. For envy-freeness, we provide several structural properties of envy-free allocations. Based on these, we design efficient algorithms for finding an envy-free allocation when at least one of (1) the number of facilities, (2) the capacity of facilities, and (3) the number of agent types, is small. Moreover, we show that a consecutive envy-free allocation can be computed in polynomial time. On the negative front, we show the NP-hardness of determining the existence of an allocation under two relaxed envy-free concepts.

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BibTeX RIS

Yuki Amano, Ayumi Igarashi, Yasushi Kawase, Kazuhisa Makino, Hirotaka Ono. 2020-07-16. Fair Ride Allocation on a Line. https://arxiv.org/abs/2007.08045

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