Fair Ride Allocation on a Line
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With the advent of the ride-sharing platform, the carpooling has become increasingly more popular and widespread. In this paper, we propose a new model of the fair ride-sharing problem, where agents with different destinations share rides and divide the total cost among the members of each group according to the Shapley value. We consider several fairness and stability notions, such as envy-freeness and Nash stability, and obtain a number of existence and computational complexity results. Specifically, we show that when the agents' destinations are aligned on a line graph, a Nash stable allocation that minimizes the social cost of agents exists and can be computed efficiently. For this simple spatial structure, we also obtain parameterized complexity results for finding an envy-free allocation with respect to various parameters.
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