The game of agents in transportation problems

This paper deals with the analysis of the structure of the core of the transportation game (a kind of many-to-many assignment market) by means of the well known assignment game (a kind of one-to-one assignment market). To do this, we associate an allocation game to each transport game that we call the agents game. This game is obtained by means of the division of each seller and buyer into as many agents as objects they want to sell or to buy, respectively. Specifically, the relationships that exist between the core of the transportation game and the core of the agents game are analyzed. This analysis contributes to having a better knowledge about the structure of the core of the transportation game whose complete characterization continues to be an open problem. Likewise, as a result of this analysis, a new characterization of the structure of the core of the assignment game is obtained under certain conditions.