The Sequential Online Chore Division Problem - Definition and Application.

This paper defines a novel formulation of chore division, called S equential O nline C hore D ivision (SOCD), in which participants arrive and depart online, while the chore is being performed. In SOCD, there exists some uncertainty both regarding the total number of participants and their arrival/departure times. Moreover, only one agent can perform the chore at any given moment, and switching the performer incurs a cost. This novel variant of chore division can model real world problems such as the autonomous vehicle convoy formation problem, which has significant social implications. Autonomous vehicles are said to form a convoy when vehicles headed in the same direction follow each other in close proximity. This behavior has been proven to save energy, due to the reduction in aerodynamic drag. Empirical evaluations estimate that a follower can save over $10%$ of its fuel consumption \citelammert2018influences. However, since the leader sees little or no such gains, choosing the leader of such a convoy raises issues of fairness, efficiency, and strategyproofness. Solving these issues is challenging since vehicles can dynamically join and leave the convoy. To address this problem, we propose three mechanisms for fair chore division. The first mechanism is centralized and uses side payments while the other two are distributed and seek to balance the participants' loads. We show that the payment-transfer mechanism, which requires a centralized server, results in optimal fairness and efficiency. For the cases where a central server is not available, we show that the repeated-game mechanism produces allocations which are efficiently-optimal and fair in expectation. For the single-game case, we first prove that optimal fairness is impossible to guarantee. We then show that our proposed single-game mechanism, which offers minimal efficiency loss, achieves ex-ante proportionality.