A General View about Games Abstention, Absence, Alternatives
DOI:
https://doi.org/10.14665/1614-4007-24-2-007Keywords:
Cooperative Games, Characteristic Function, Alternatives, Abstention, AbsenceAbstract
In this paper we introduce a new and more general kind of cooperative games in which players have many alternatives to choose, or many goals to try to realize, but also have the possibility of abstaining or of being absent for a while. In these games we define coalitions and study their properties observing how it is possible to obtain all the classical definitions of cooperative game theory inside this new setting.
Downloads
References
Amer, R., Carreras F., Magana A. (1998, 1) The Banzhaf - Colemann Index for Games with r Alternatives. Optimization, Vol. 44: 175-198.
Amer R., Carreras F., Magana A. (1998, 2) Extension of Values to Games with Multiple Alternatives, Annals of Operation Research, Vol. 84: 63-78.
Amer R., Carreras F. (2001) Power, Cooperation Index and Coalition Structures. in Holler M.J. and Owen G. (eds) Power Indices and Coalition Formation, Kluwer Academic Publisher, New York, pp.153-174.
Bolger E. M.(1983) The Banzhaf Index for Multicandidate Presidential Election. SIAM J. Algebraic and Discrete Method, 4: 442-458.
Bolger E. M. (1986) Power Indices for Multicandidate Voting Games. International Journal of Game Theory, Vol. 15, n.3: 175-186.
Bolger E. M. (1993) A Value for Games with n Voters and r Alternatives. International Journal of Game Theory, 22: 319-314.
Bolger E. M. (2000) A Consistent Vale for Games with n Players and r Alternatives. International Journal of Game Theory, Vol. 29: 93-99.
Denti, E., Prati, N. (2001) An algorithm for winning coalitions in indirect control of corporations. Decisions in Economics and Finance - A Journal of Applied Mathematics, vol.24, n.2: 153-158.
Denti, E., Prati, N. (2004) Relevance of Winning Coalitions in Indirect Control of Corporations. In Gambarelli G. (ed.), Essays on Cooperative Games – In honor of Guillermo Owen, Special Issue of Theory and Decision, vol. 36: 138-192.
Felsenthal D. S., Machover M. (1997) Ternary Voting Games. International Journal of Game Theory, n. 26: 335-351.
Felsenthal D. S., Machover M. (1998) The measurement of Voting Power, Theory and Practice, Problems and Paradoxes. Edward Elgar, Northampton, USA.
Felsenthal D. S., Machover M. (2001) Models and Reality: The Curious Case of Absent Abstention. In Holler M. J., Owen G. (eds) Power Indices and Coalition Formation., Kluwer Academic Publisher, Boston, pp. 87-103.
Fishburn P. C. (1973) The Theory of Social Choice. Princeton University Press.
Freixas J. and Zwicker W.S. (2003). Weighted Voting, Abstention, and Multiple Levels of Approval. Social Choice Welfare 21: 399 - 431;
Freixas J. (2005 1) Banzhaf Measures for Games with Several Levels of Approval in the Input and Output. Annals of Operations Research 137: 45-66.
Freixas J. (2005 2) The Shapley - Shubik Power Index for Games with Several Levels of Approval in the Input and in Output, Decision Support Systems n. 39: 185-195.
Gambarelli G. (1996) Takeover Algorithms. Modelling Techniques for Financial Markets and Bank Management. In Bertocchi M., Cavalli E., Komlosi S. (eds), Proceedings of the 16-th and 17-th Euro Working Group of Financial Modelling Meeting, Heidelberg: Physica Verlag, pp. 212-222.
Gambarelli, G., Owen G. (1994) Indirect Control of Corporations. International Journal of Game Theory, 23: 287-302.
Greco S. (1994) Indici di Potere per Giochi a Maggioranza Ponderata di Governo e Opposizione. In Atti del IXX Convegno Amases, Modena: 283-296. In Italian
Holler M. J., Owen G. (2001 1) Power Indices and Coalition Formation. Kluwer Academic Publisher.
Holler M. J., Owen G. (2001 2) Why Power Indices and Coalition Formation?, In Holler M.J., Owen G. (eds) Power Indices and Coalition Formation, Kluwer, pp. 1-14.
Owen, G. (1995) Game Theory (third edition). Academic Press, San Diego, California.
Prati, N. (2002) Giochi Cooperativi Senza Impegno Totale: Una Introduzione. Working Paper, Dipartimento dell’ Impresa e dei Mercati Finanziari, Università di Udine, Udine, Italy, 2-2002. In Italian.
How to Cite
Issue
Section
The author gives permission to Transition Academia Press to publish the article in print and/or electronic format.
If/when an article is accepted for publication, Author will be asked to transfer copyright of the article to Transition Academia Press. Transition Academia Press will retain copyright of all published material and reserves the right to re-use any such material in any print and/or electronic format. Author willing to retain their copyright from the Editors might request a fair condition, on the base of a bilateral agreement.
