In this paper, we take a novel perspective on line planning in public transportation: We interpret line planning as a game where the passengers are players who aim at minimizing individual objective functions composed of travel time, transfer penalties, and a share of the overall cost of the solution. We discuss the relation among equilibria of this game and line planning solutions found by optimization approaches. Furthermore, we investigate the algorithmic viability of our approach as a solution method for line planning problems, using a best-response algorithm to find equilibria. We investigate under which conditions a passenger's best-response can be calculated efficiently and which properties are needed to guarantee convergence of the best-response algorithm.

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Keywords Game theory, Line planning, Routing, Routing game, Transportation
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Series ERIM Top-Core Articles
Journal European Journal of Operational Research
Schiewe, A. (Alexander), Schiewe, P. (Philine), & Schmidt, M.E. (2018). The line planning routing game. European Journal of Operational Research. doi:10.1016/j.ejor.2018.10.023