Cooperative Logistics Games

Roughly speaking, Game Theory deals with analysing conflict and cooperation situations in which two or more rational and intelligent agents are involved. There are many real and theoretical situations which can be examined from the point of view of Game Theory. Therefore it is not difficult to find in the literature a rich variety of applications of Game Theory to many and very diverse fields of knowledge. In particular, Game Theory plays a significant role in Economics, but we can also find applications to Computer Science and Engineering. Game Theory can be roughly divided into two main areas: cooperative and non cooperative games. The basic key for distinguishing between these two areas is whether it is possible or not to reach binding agreements. When binding agreements are possible, we are then faced with a cooperative situation. Thus, in a cooperative environment the concept of coalition plays an important role and very often the main goal is to achieve the cooperation of all agents. In this chapter we will assume that binding agreements among the agents are possible and therefore we will use the cooperative approach for analysing some logistics problems. On the other hand, there are a number of theoretical and conceptual connections between Game Theory and Operations Research (OR). For example, we should mention the connection between the duality in mathematical programming and the minimax theorems for zero-sum games (see Raghavan, 1994); the linear complementary theory and the bimatrix games (see Lemke, 1965), or the optimal control theory and the differential games (see Friedman, 1994) among others. Furthermore we can find applications of OR to Game Theory, for example the characterization of balanced games using the duality concept (Bondareva, 1963 and Shapley, 1967). Likewise, Game Theory contributes to completing the analysis of OR problems when there is more than one agent involved in the corresponding situation. Thus, after optimising a particular system by means of OR techniques, in which there are two or more agents involved, who have to collaborate in order to be able to achieve that optimal result, saying something about how to distribute the extra benefits or the costs saved by cooperation among those agents seems reasonable and necessary. Hence cooperative games can play a role in the complete analysis of the situation. In the literature, not only we can find many OR problems studied from the point of view of cooperative games in the sense mentioned previously, but also OR problems analysed from