Stable allocations for choice-based collaborative price setting

TL;DR

This paper introduces a novel cooperative game model for sustainable urban mobility pricing, proposing a core-guaranteeing allocation rule that ensures stable, fair profit sharing among transport operators while considering societal paybacks.

Contribution

It develops a new market share exchange rule that guarantees core allocations and stability in collaborative urban mobility pricing models, addressing limitations of existing rules.

Findings

The market share exchange rule guarantees core stability.

It ensures fair profit distribution among transport operators.

The rule remains stable even with societal profit repayments.

Abstract

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.