Narrow Results

In this paper we study linear symmetric solutions for the space of games in partition function form with n players. In particular, we provide an expression for all linear, symmetric and efficient solutions. Furthermore, adding an additional axiom, we identify a unique value satisfying these properties.

The PERT (Program Evaluation Review Technique) is a operational research tool used to schedule and coordinate activities in a complex project. We present two values for measuring the importance of each activity. Both values are obtained through an axiomatic characterization using three properties. The first value is characterized with separability, monotonicity, and order preservation. The second value is characterized with separability, equal treatment inside a component, and independence of large durations. We also present an application to the problem of how to share the surplus obtained when a project finishes before the expected completion time.

The paper presents some issues currently under studying in the field of Cooperative Games. The related open problems are also mentioned.

We look at the basic applications of cooperative game theory to economic situations. These include bargaining and cooperative equilibria, especially as the number of players increases without bound. The core and the Shapley value are the fundamental tools for these applications. We consider the relation between these two concepts. A comprehensive bibliography of work published over the last decade is included.