Applying game theory to library networks

The application of game theory to library networks consists of four basic subjects: the development of a systematic way to study individual coalitions, the calculation of the costs of a network, the calculation of the gross benefits for the whole network, the stability of the network. This article concentrates on the first and last of these subjects. Coalitions are compared in a systematic way by first defining coalitions and introducing the concept of a division. The latter is defined as a unique combination of coalitions such that every participating library is a member of one and only one coalition and the division exhausts all “n” libraries. The definition of division stability depends on the payoff vector being in the “core.” This happens when members of the coalitions in the division have more to distribute among themselves than they would in any other division. When a division is stable, any variation in the coalition structure will reduce total net benefits to coalition members. In practice, the choices open to the individual library may not be as plentiful as the theoretical analysis suggests. Thinking of networks performing a single function, most members will belong to a single coalition with remaining coalitions in the optimal division having zero members.