Cooperative games under interval uncertainty: On the convexity of the interval undominated cores

Central European Journal of Operations Research

Volumn 19, Issue 4, 2011, Pages 523-532

  Branzei, R ^a   Gök, S Z Alparslan ^b,c   Branzei, O ^d  

^a ALEXANDRU IOAN CUZA UNIVERSITY OF IASI   (Romania)

^b SULEYMAN DEMIREL UNIVERSITY   (Turkey)

^c MIDDLE EAST TECHNICAL UNIVERSITY   (Turkey)

^d UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

Convex games; Cooperative games; Core; Dominance core; Interval games; Uncertainty

Indexed keywords

EID: 79953160956     PISSN: 1435246X     EISSN: 16139178     Source Type: Journal    
DOI: 10.1007/s10100-010-0141-z     Document Type: Article

References (29)

1. Ahuja G, Polidoro F Jr, Mitchell W (2009) Structural homophily or social asymmetry? The formation of alliances by poorly embedded firms. Strateg Manag J 30(9): 941-958.
2. Alparslan Gök SZ (2009) Cooperative interval games. PhD. Dissertation, Middle East Technical University.
3. Alparslan Gök SZ, Branzei R, Tijs S (2008) Cores and stable sets for interval-valued games. Preprint no. 90, Institute of Applied Mathematics, METU and Tilburg University, Center for Economic Research, The Netherlands, Center DP 17.
4. Alparslan Gök SZ, Branzei R, Tijs S (2009) Convex interval games. J Appl Math Decis Sci, Article ID 342089, 14 p. doi: 10. 1115/2009/342089.
5. Alparslan Gök SZ, Miquel S, Tijs S (2009) Cooperation under interval uncertainty. Math Methods Oper Res 69: 99-109.
6. Alparslan Gök SZ, Weber GW (2009) Cooperative games under ellipsoidal uncertainty. Preprint no. 148, Institute of Applied Mathematics, METU (2009) (to appear in the proceedings of PCO 2010, 3rd Global conference on power control and optimization, 2-4 February 2010, Gold Coast, Queensland, Australia).
7. Branzei O (2005) Product innovation in heterogeneous R& D networks: pathways to exploration and exploitation. Unpublished Doctoral Dissertation, University of British Columbia.
8. Branzei R, Dimitrov D, Tijs S (2008) Models in cooperative game theory. Springer, Berlin (CEJOR).
9. Branzei R, Branzei O, Alparslan Gök SZ, Tijs S (2009) Cooperative interval games: a survey. Central Eur J Oper Res (CEJOR). doi: 10. 1007/s10100-009-0116-0.
10. Branzei R, Mallozzi L, Tijs S (2008) Peer group situations and games with interval uncertainty. Preprint no. 64, Dipartimento di Matematica e Applicazioni, Universita' di Napoli (2008) (to appear in Int J Math Game Theory Algebra).
11. Chang C (2000) Note: remarks on the theory of the core. Naval Res Logist 47: 455-458.
12. Charnes A, Granot D (1973) Prior solutions: extensions of convex nucleolus solutions to chance-constrained games. Proceedings of the computer science and statistics seventh symposium at Iowa State University, pp 323-332.
13. Gillies DB (1959) Solutions to general non-zero-sum games. In: Tucker AW, Luce RD (eds) Contributions to theory of games IV, annals of mathematical studies 40. Princeton University Press, Princeton, pp 47-85.
14. Granot D (1977) Cooperative games in stochastic characteristic function form. Manag Sci 23: 621-630.
15. Gray B (2000) Assessing inter-organizational collaboration: multiple conceptions and multiple methods. In: Faulkner D, de Rond M (eds) Cooperative strategy: economic, business, and organizational issues. Oxford University Press, New York.
16. Kimms A, Drechsel J (2009) Cost sharing under uncertainty: an algorithmic approach to cooperative interval-valued games. BuR-Business Research 2 (urn: nbn: de: 0009-20-21721).
17. Lavie D, Lechner C, Singh H (2007) The performance implications of timing of entry and involvement in multipartner alliances. Acad Manag J 50(3): 578-604.
18. Loveridge R (2000) The firm as differentiator and integrator of networks: layered communities of practice and discourse. In: Faulkner D, de Rond M (eds) Cooperative strategy: economic, business, and organizational issues. Oxford University Press, New York.
19. Mallozzi L, Scalzo V, Tijs S (2009) Fuzzy interval cooperative games. Preprint no. 1, Dipartimento di Matematica e Applicazioni R. Caccioppoli, Università di Napoli.
20. Mares M (2001) Fuzzy cooperative games: cooperation with vague expectations. Physica-Verlag, Heidelberg.
21. Mares M, Vlach M (2004) Fuzzy classes of cooperative games with transferable utility. Scientiae Mathematicae Japonicae 60(2): 269-278.
22. Moore R (1979) Methods and applications of interval analysis. SIAM Studies in Applied Mathematics, Philadelphia.
23. Nishizaki I, Sakawa M (2001) Fuzzy and multiobjective games for conflict resolution. Physica-Verlag, Heidelberg.
24. Puerto J, Fernández FR, Hinojosa Y (2008) Partially ordered cooperative games: extended core and Shapley value. Ann Oper Res 158: 143-159.
25. Rafels C, Tijs S (1997) On the cores of cooperative games and the stability of the Weber set. Int J Game Theory 26: 491-499.
26. Suijs J, Borm P, De Waegenaere A, Tijs S (1999) Cooperative games with stochastic payoffs. Eur J Oper Res 113: 193-205.
27. Timmer J (2001) Cooperative behaviour, uncertainty and operations research. Center Dissertation Series: Tilburg.
28. Timmer J, Borm P, Tijs S (2005) Convexity in stochastic cooperative situations. Int Game Theory Rev 7(1): 25-42.
29. Wagner HM, Whitin TM (1958) Dynamic version of the economic lot size model. Manag Sci 5(1): 89-96.