Pairwise mergers in bipartite matching games with an application in collaborative logistics

Merging among players in a cooperative game can alter the structure of the core. This paper shows that in bipartite matching games, if pairs of players from different sides merge, the structure of the core remains unchanged. This allows us to extend the well-known result regarding the characterization of the core with dual solutions for simple games to their associated pairwise merger games. We introduce the class of vehicle scheduling games as an area of application for our result.