Article ID: | iaor20031575 |
Country: | Netherlands |
Volume: | 140 |
Issue: | 1 |
Start Page Number: | 134 |
End Page Number: | 141 |
Publication Date: | Jul 2002 |
Journal: | European Journal of Operational Research |
Authors: | Leung L.C., Cao D. |
Keywords: | programming: mathematical |
This paper examines a linear static Stackelberg game where the follower's optimal reaction is not unique. Traditionally, the problem has been approached using either an optimistic or a pessimistic framework, respectively representing the two extreme situations of full cooperation and zero cooperation from the follower. However, partial cooperation from the follower is a viable option. For partial cooperation, the leader's optimal strategy may be neither optimistic nor pessimistic. Introducing a cooperation index to describe the degree of follower cooperation, we first formulate a partial cooperation model for the leader. The two-level problem is then reformulated into a single-level model. It is shown that the optimistic and pessimistic situations are special cases of the general model, and that the leader's optimal choice may be an intermediate solution.