  Horizontal agreements can fall within the scope of exemptions to antitrust
competition if they are expected to create pro-consumer benefits. Inspired by
such horizontal agreements, we introduce a cooperative game in which a set of
transport operators can collectively decide at what price to offer sustainable
urban mobility services to a pool of travelers. The travelers choose amongst
the mobility services according to a multinomial logit model, and the operators
aim at maximizing their joint profit under a constant market share constraint.
After showing that various well-known allocation rules (i.e., proportional
rules and the Shapley value) do not always generate core allocations, we
present a core-guaranteeing allocation rule, the market share exchange rule.
This rule first allocates to each transport operator the profit he or she
generates under collaboration, and then subsequently compensates those
transport operators that lose part of their market share, which is paid by the
ones that receive some extra market share. This exchange of market share is
facilitated by a unique price, which can be expressed as the additional return
by cooperating per unit of market share. Finally, we show that, under some
natural conditions, the market share exchange rule still sustains the
collaboration when the transport operators need to pay back part of the joint
profit to society.
