Least Cores and Nucleoli in a Multi-Commodity Game

Abstract

In a multi-commodity game, we consider e-cores, least cores and nucleoli, which are originally defined in a conventional n-person cooperative game in characteristic function form. First we review the definition of a multi-commodity game and the concept of the core, and then introduce concepts of e-cores and least cores. Employing excess functions in the multi-commodity game, the cores, the ε-cores and the least cores are redefined, and nucleoli are defined. To compute solutions, we classify excess functions into two categories and give two instances for each category, and briefly mention the difference among them. We develop computational methods for obtaining a point in each of the least cores under some assumptions and illustrate one of the methods with a numerical example. Finally we refer to methods for obtaining a point in each of the nucleoli.