Cooperation in service systems with impatient customers

Abstract

Our objective in this paper is to study the cooperation among many independent service providers when the customers are impatient. The service providers collaborate through the sharing of servers to achieve a better service experience. When there is a gain from cooperation, a fundamental question arises – how to share the gain among the group members? Cooperative game theory is an indispensable tool to study this problem. In cooperative game theory, players are allowed to take joint action to synergise their strategies through trusted and credible communication. Coalition is used as the basic modelling unit instead of individual players in cooperative game theory. Stability is a major criterion used to decide how to share the gain from cooperation. When members of a coalition do not deviate due to lack of incentive, the allocation is considered to be stable. A collection of all such allocations constitute the core of the game. In this project, we use chance constrained game(Charnes & Granot, 1976), a variant of characteristic function game with transferable utility where the utility function is defined to be a random variable. We assume fixed service capacities with Markovian assumptions for distribution of service time and inter arrival time. We show that the most profitable coalition is the grand coalition involving all service providers. We also prove that the game has a non-empty core.