Skip to main content
SpringerLink
Log in

Cooperative interval games: a survey

  • Original Paper
  • Published:
Central European Journal of Operations Research Aims and scope Submit manuscript

Abstract

The (re)distribution of collective gains and costs is a central question for individuals and organizations contemplating cooperation under uncertainty. The theory of cooperative interval games provides a new game theoretical angle and suitable tools for answering this question. This survey aims to briefly present the state-of-the-art in this young field of research, discusses how the model of cooperative interval games extends the cooperative game theory literature, and reviews its existing and potential applications in economic and operations research situations with interval data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Alparslan Gök SZ (2009) Cooperative interval games. PhD. Dissertation, Middle East Technical University

  • Alparslan Gök SZ, Branzei R, Fragnelli V, and Tijs S (2008a) Sequencing interval situations and related games. Institute of Applied Mathematics, METU and Tilburg University, Center for Economic Research, The Netherlands, CentER DP 63 (preprint no. 113)

  • Alparslan Gök SZ, Branzei R, Tijs S (2008b) Cores and stable sets for interval-valued games. Institute of Applied Mathematics, METU and Tilburg University, Center for Economic Research, The Netherlands, CentER DP 17 (preprint no. 90)

  • Alparslan Gök SZ, Branzei R, Tijs S (2008c) Big boss interval games. Institute of Applied Mathematics, METU and Tilburg University, Center for Economic Research, The Netherlands, CentER DP 47 (preprint no. 103)

  • Alparslan Gök SZ, Branzei R, Tijs S (2008d) Airport interval games and their Shapley value (to appear in Oper Res Decis)

  • Alparslan Gök SZ, Branzei R, Tijs S (2009) Convex interval games. J Appl Math Decis Sci 2009(Article ID 342089): 14. doi:10.1115/2009/342089

    Google Scholar 

  • Alparslan Gök SZ, Branzei R, Tijs S (2009b) The interval Shapley value: an axiomatization. Institute of Applied Mathematics, METU (to appear in Central Eur J Oper Res (CEJOR)), doi:10.1007/s10100-009-0096-0 (preprint no. 130)

  • Alparslan Gök SZ, Miquel S, Tijs S (2009c) Cooperation under interval uncertainty. Math Methods Oper Res 69: 99–109

    Article  Google Scholar 

  • Aubin JP (1974) Coeur et valeur des jeux .ous á paiements latéraux. Comptes Rendus de l.Académie des Sciences Paris 279(A): 891–894

    Google Scholar 

  • Bilbao M (2000) Cooperative games on combinatorial structures. Theory and decision library, series C. Kluwer, Dordrecht

    Google Scholar 

  • Branzei R, Alparslan Gök SZ (2008) Bankruptcy problems with interval uncertanity. Econ Bull 3(56): 1–10

    Google Scholar 

  • Branzei R, Alparslan Gök SZ (2009) On the convexity of interval dominance cores. Institute of Applied Mathematics, METU (preprint no. 139)

  • Branzei R, Dimitrov D, Tijs S (2003) Shapley-like values for interval bankruptcy games. Econ Bull 3: 1–8

    Google Scholar 

  • Branzei R, Dall’Aglio M, Tijs S (2008a) Interval game theoretic division rules. Tilburg University, Center for Economic Research, The Netherlands, CentER DP 97

  • Branzei R, Dimitrov D, Tijs S (2008b) Models in cooperative game theory. Game Theory Math Methods (Springer)

  • Branzei R, Mallozzi L, Tijs S (2008c) Peer group situations and games with interval uncertainty. Dipartimento di Matematica e Applicazioni, Universita’ di Napoli (preprint no. 64)

  • Branzei R, Tijs S, Alparslan Gök SZ (2008d) Some characterizations of convex interval games. AUCO Czech Econ Rev 3(2): 217–224

    Google Scholar 

  • Branzei R, Tijs S, Alparslan Gök SZ (2008e) How to handle interval solutions for cooperative interval games. Institute of Applied Mathematics, METU (preprint no. 110)

  • Carpente L, Casas-Méndez B, García-Jurado I, van den Nouweland A (2007) The truncated core for games with limited aspirations, vol 1010. Department of economics—working papers series, The University of Melbourne (preprint no. 110)

  • Carpente L, Casas-Méndez B, García-Jurado I, van den Nouweland A (2008) Coalitional interval games for strategic games in which players cooperate. Theory Decis 65(3): 253–269

    Article  Google Scholar 

  • Charnes A, Granot D (1973) Prior solutions: extensions of convex nucleolus solutions to chance-constrained games. In: Proceedings of the computer science and statistics seventh symposium at Iowa state University, pp 323–332 (preprint no. 110)

  • Drechsel J, Kimms A (2008) An algorithmic approach to cooperative interval-valued games and interpretation problems. Working paper, University of Duisburg-Essen (preprint no. 110)

  • Dutta B, Ray D (1989) A concept of egalitarianism under participation constraints. Econometrica 57: 615–635

    Article  Google Scholar 

  • Fernández FR, Hinojosa MA, Puerto J (2002) Core solutions in vector-valued games. J Optimiz Theory Appl 112(2): 331–360

    Article  Google Scholar 

  • Gillies DB (1959) Solutions to general non-zero-sum games. In: Tucker AW, Luce RD (eds) Contributions to the theory of games IV, annals of mathematical studies vol 40. Princeton University Press, Princeton, pp 47–85

    Google Scholar 

  • Hart S, Mas-Colell A (1989) Potential, value, and, consistency. Econometrica 57: 589–614

    Article  Google Scholar 

  • Hsiao C-R, Raghavan TES (1992) Monotonicity and dummy free property for multi-choice cooperative games. Int J Game Theory 21: 301–312

    Article  Google Scholar 

  • Jahn J (1983) Duality in vector optimization. Math Program 25: 343–355

    Article  Google Scholar 

  • Mallozzi L, Scalzo V, Tijs S (2009) Fuzzy interval cooperative games. Dipartimento di Matematica e Applicazioni, Universita’ di Napoli (preprint no. 1)

  • Mares M (2001) Fuzzy cooperative games: cooperation with vague expectations. Physica Verlag, Heidelberg

    Google Scholar 

  • Moore R (1979) Methods and applications of interval analysis. SIAM, Philadelphia

    Google Scholar 

  • Moretti S, Alparslan Gök SZ, Branzei R, Tijs S (2008) Connection situations under uncertainty. Institute of Applied Mathematics, METU and Tilburg University, Center for Economic Research, The Netherlands, CentER DP 64 (preprint no. 112)

  • Muto S, Nakayama M, Potters J, Tijs S (1988) On big boss games. Econ Stud Q 39(4): 303–321

    Google Scholar 

  • Puerto J, Fernández FR, Hinojosa MA (2008) Partially ordered cooperative games: extended core and Shapley value. Ann Oper Res 158(1): 143–159

    Article  Google Scholar 

  • Schmeidler D (1969) The nucleolus of a characteristic function game. SIAM J Appl Math 17: 1163–1170

    Article  Google Scholar 

  • Shapley LS (1953) A value for n-person games. Ann Math Stud 28: 307–317

    Google Scholar 

  • Shapley LS (1971) Cores of convex games. Int J Game Theory 1: 11–26

    Article  Google Scholar 

  • Suijs J, Borm P, De Waegenaere A, Tijs S (1999) Cooperative games with stochastic payoffs. Eur J Oper Res 113: 193–205

    Article  Google Scholar 

  • Tijs S (1981) Bounds for the core and the τ-value. In: Moeschlin O, Pallaschke D (eds) Game theory and mathematical economics. North Holland, Amsterdam, pp 123–132

    Google Scholar 

  • Tijs S (1990) Big boss games, clan games and information market games. In: Ichiishi T, Neyman A, Tauman Y (eds) Game theory and applications. Academic Press, San Diego, pp 410–412

    Google Scholar 

  • Tijs S (2003) Introduction to game theory. SIAM, Hindustan Book Agency, India

    Google Scholar 

  • Timmer J, Borm P, Tijs S (2005) Convexity in stochastic cooperative situations. Int Game Theory Rev 7: 25–42

    Article  Google Scholar 

  • Yanovskaya E, Branzei R, Tijs S (2008) Monotonicity properties of interval solutions and the Dutta–Ray solution for convex interval games. Tilburg University, Center for Economic Research, The Netherlands, CentER DP 102

Download references

Author information

Authors and Affiliations

  1. Faculty of Computer Science, “Alexandru Ioan Cuza” University, Iasi, Romania

    R. Branzei

  2. Richard Yvey School of Business, University of Western Ontario, London, Ontario, Canada

    O. Branzei

  3. Institute of Applied Mathematics, Middle East Technical University, 06531, Ankara, Turkey

    S. Zeynep Alparslan Gök

  4. Faculty of Arts and Sciences, Department of Mathematics, Süleyman Demirel University, 32 260, Isparta, Turkey

    S. Zeynep Alparslan Gök

  5. Center and Department of Econometrics and OR, Tilburg University, Tilburg, The Netherlands

    S. Tijs

  6. Department of Mathematics, University of Genoa, Genoa, Italy

    S. Tijs

Authors
  1. R. Branzei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. Branzei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Zeynep Alparslan Gök
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Tijs
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Zeynep Alparslan Gök.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Branzei, R., Branzei, O., Alparslan Gök, S.Z. et al. Cooperative interval games: a survey. Cent Eur J Oper Res 18, 397–411 (2010). https://doi.org/10.1007/s10100-009-0116-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10100-009-0116-0

Keywords

JEL Classification

Search

Navigation