Sequencing situations with position-dependent effects under cooperation

Abstract

This paper innovatively addresses the effect of cooperation on sequencing situations with position-dependent effects. Specifically, we ensure the convexity of the associated sequencing games under the fulfillment of certain conditions related to the neighbor switching gains. Additionally, we propose two families of allocation rules based on sharing the neighbor switching gains under two distinct procedures, each providing a path from the initial order to an optimal order. From a theoretical point of view, an axiomatization of both families of allocations is provided, and their stability is also ensured under the conditions related to convexity.