Queues and Cooperative Games

Abstract: Cooperative game theory deals mainly, if not solely, with the issue of how participants share the costs (or rewards) associated with a joint venture or a situation they are involved with. Queues are usually associated with competition but in fact customers who use the same service facility are cooperating (otherwise each would have used his own server). The common costs they generate come in the form of wasted waiting time. Hence the question is how to share these costs. For example, large jobs may need to compensate small ones. Here cooperative games modeling and solution concepts enter. We exemplify this via the use of the Aumann-Shapley prices.
A similar question arises when a number of servers pool their resources in order to reduce the total wait. A natural question is how much each one of them is contributing towards this reduction. We show how the situation faced by servers is that of cooperative games for which the solution concepts such as the Shapley value can be applied. We mostly look at the question of whether the cores of the resulting games are empty.