A partial cooperation model for non-unique linear two-level decision problems |
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| Affiliation: | 1. The Key Laboratory of Cancer Biomarkers, Prevention & Treatment Cancer Center, Nanjing Medical University, No. 140 Hanzhong Road, Nanjing 210029, China;2. The Key Laboratory of Antibody Technique of Ministry of Health, Nanjing Medical University, No. 140 Hanzhong Road, Nanjing 210029, China;3. Department of Otolaryngology-Head and Neck Surgery, The First Affiliated Hospital of Nanjing Medical University, No. 300 Guangzhou Road, Nanjing 210011, China;4. Department of Gynecology and Obstetrics, Nanjing Maternal and Children Care Hospital, Nanjing Medical University, Nanjing 210029, China;5. Department of Pathology, Affiliated Hospital of Nantong University, No. 20 Xisi Road, Nantong 226001, China;6. Department of Otolaryngology-Head and Neck Surgery, The Second Affiliated Hospital of Nanjing Medical University, No. 121 Jiang Jia Yuan, Nanjing 210011, China;7. Department of Pathology, The Second Affiliated Hospital of Nanjing Medical University, No. 121 Jiang Jia Yuan, Nanjing 210011, China;8. Department of Otolaryngology-Head and Neck Surgery, Jiangsu Provincial Hospital, No. 65 Jiangsu Road, Nanjing 210029, China;9. Huadong Medical Institute of Biotechniques, No. 293 Zhongshan Dong Road, Nanjing 210002, China |
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| 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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