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In this paper, we address the existence and computation of competitiveequilibrium in the transportation market for autonomous carpooling firstproposed by [Ostrovsky and Schwarz, 2019]. At equilibrium, the market organizescarpooled trips over a transportation network in a socially optimal manner andsets the corresponding payments for individual riders and toll prices on edges.The market outcome ensures individual rationality, stability of carpooledtrips, budget balance, and market clearing properties under heterogeneous riderpreferences. We show that the question of market's existence can be resolved byproving the existence of an integer optimal solution of a linear programmingproblem. We characterize conditions on the network topology and riders'disutility for carpooling under which a market equilibrium can be computed inpolynomial time. This characterization relies on ideas from the theory ofcombinatorial auctions and minimum cost network flow problem. Finally, wecharacterize a market equilibrium that achieves strategyproofness and maximizeswelfare of individual riders.

Efficient Carpooling and Toll Pricing for Autonomous Transportation