Order preservation with dummies in the musseum pass problem

TL;DR

This paper introduces a new axiom called order preservation with dummies for revenue sharing in museum pass problems, leading to characterizations of rule families that extend existing models and encompass a broader problem domain.

Contribution

It replaces the dummy axiom with a milder order preservation axiom, characterizing convex combinations of uniform and Shapley rules, and broadens the problem domain.

Findings

Characterizes rule families as convex combinations of uniform and Shapley rules.

Generalizes existing results in revenue sharing literature.

Expands the problem domain beyond previous models.

Abstract

We study the problem of sharing the revenue obtained by selling museum passes from the axiomatic perspective. In this setting, we propose replacing the usual dummy axiom with a milder requirement: order preservation with dummies. This new axiom formalizes the philosophical idea that even null agents/museums may have the right to receive a minimum allocation in a sharing situation. By replacing dummy with order preservation with dummies, we characterize several families of rules, which are convex combinations of the uniform and Shapley approaches. Our findings generalize several existing results in the literature. Also, we consider a domain of problems that is richer than the domain proposed by Ginsburgh and Zang (2003) in their seminal paper on the museum pass problem.