A partial cooperation model for non-unique linear two-level decision problems

A partial cooperation model for non-unique linear two-level decision problems

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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: ,
Keywords: programming: mathematical
Abstract:

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.

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