Further open problems in cooperative games

• Autorzy: Fragnelli V. , Gambarelli G.

Identyfikatory

DOI

10.5277/ord140404

• Języki publikacji: EN

Abstrakty

EN

In 2013, the International Game Theory Review published two special issues on open problems in cooperative games: the first regarding theory and the second applications. In this paper, our aim is to present some problems currently “on our table” that were not included in the two issues mentioned above, either because the topics were too specific or they arose after publication. The problems are divided into theoretical problems, general models that may be applied to different fields and applicative problems.

Słowa kluczowe

EN

cooperative games; values; applications

PL

gry kooperatywne; wartości; aplikacje

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Operations Research and Decisions
• Rocznik: 2014
• Tom: Vol. 24, No. 4
• Strony: 51--62
• Opis fizyczny: Bibliogr. 38 poz.

Twórcy

autor

Fragnelli V.

• Department of Science and Innovative Technologies, University of Eastern Piedmont, Italy

autor

Gambarelli G.

• Department of Management, Economics and Quantitative Methods, University of Bergamo, Italy

Bibliografia

• [1] AUMANN R.J., MASCHLER M., The bargaining set for cooperative games, [in:] M. Dresher, L.S. Shapley, A.W. Tucker (Eds.), Advances in game theory, Princeton University Press, Princeton 1964, 443–476. Further open problems in cooperative games 61
• [2] BANZHAF J.F., Weighted voting doesn’t work: A mathematical analysis, Rutgers Law Review, 1965, 19, 317–343.
• [3] BERTINI C., GAMBARELLI G., SCARELLI A., VARGA Z., Equilibrium solution in a game between a cooperative and its members, AUCO Czech Economic Review, 2011, 5, 162–171.
• [4] BERTINI C., GAMBARELLI G., STACH I., Some open problems in the application of power indices to finance and politics, Homo Oeconomicus, 2014 (to appear).
• [5] BERTINI C., GAMBARELLI G., URISTANI A., Indices of collusion among judges and an anti-collusion average, [in:] S. Greco, R. Marques Pereira, M. Squillante, R.R. Yager, J. Kacprzyk (Eds.), Preferences and decisions. Models and applications in studies in fuzziness and soft computing, Springer,Berlin 2010, 195–210.
• [6] BRIATA F., DALL’AGLIO M., FRAGNELLI V., Dynamic collusion and collusion games in Knaster’s procedure, AUCO Czech Economic Review, 2012, 6, 199–208.
• [7] CARFÌ D., GAMBARELLI G., URISTANI A., Balancing pairs of interfering elements, [in:] Financial management. Measurement of performance and evaluation of investment appraisal, Zeszyty Naukowe Uniwersytetu Szczecińskiego nr 760, Szczecin University Press, Szczecin 2013, 435–442 (in Polish).
• [8] CASAS-MENDEZ B., FRAGNELLI V., GARCIA-JURADO I., Weighted bankruptcy rules and the museum pass problem, European Journal of Operational Research, 2011, 215, 161–168.
• [9] CASAS-MENDEZ B., FRAGNELLI V., GARCIA-JURADO I., A survey of allocation rules for the museum pass problem, Journal of Cultural Economics, 2014, 38, 191–205.
• [10] CHESSA M., FRAGNELLI V., The bargaining set for sharing the power, Annals of Operations Research, 2014 (to appear).
• [11] DE AGOSTINI R., FRAGNELLI V., A fair tariff system for water management, [in:] A. Dinar, J. Albiac, J. Sanchez-Soriano (Eds.), Game theory and policy making in natural resources and the environment, Routledge, London 2008. 236–247.
• [12] DENTI E., PRATI N., Relevance of winning coalitions in indirect control of corporations, [in:] G. Gambarelli (Ed.), Essays on cooperative games – in Honor of Guillermo Owen, Special Issue of Theory and Decision, 2004, 36, 183–192.
• [13] FRAGNELLI V., A note on the Owen set of linear programming games and Nash equilibria, Theoryand Decision, 2004, 56, 205–213.
• [14] FRAGNELLI V., How to divide the costs of urban solid wastes collection among citizens?, Economics and Policy of Energy and the Environment, 2012, 3, 51–64.
• [15] FRAGNELLI V., A note on communication structures, [in:] M.J. Holler, H. Nurmi (Eds.), Power, voting, and voting power. 30 years after, Springer-Verlag, Berlin 2013, 467–473.
• [16] FRAGNELLI V., GAGLIARDO S., GASTALDI F., Integer solutions to bankruptcy problems with noninteger claims, TOP, 2014, 22, 892–933.
• [17] FRAGNELLI V., GAMBARELLI G. (Eds.), Open problems in the theory of cooperative games, Special Issue of International Game Theory Review, 2013, 15 (2).
• [18] FRAGNELLI V., GAMBARELLI G. (Eds.), Open problems in the applications of cooperative games, Special Issue of International Game Theory Review, 2013, 15 (3).
• [19] FRAGNELLI V., GARCÍA-JURADO I., NORDE H., PATRONE F., TIJS S., How to share railway infrastructure costs?, [in:] F. Patrone, I. García-Jurado, S. Tijs (Eds.), Game practice. Contributions from applied game theory, Kluwer, Amsterdam 1999, 91–101.
• [20] FRAGNELLI V., IANDOLINO A., A cost allocation problem in urban solid wastes collection and disposal, Mathematical Methods of Operations Research, 2004, 59, 447–464.
• [21] FRAGNELLI V., MARINA M.E., Strategic manipulations and collusions in Knaster procedure, AUCO Czech Economic Review, 2009, 3, 143–153.
• [22] GAMBARELLI G., A new approach for evaluating the Shapley value, Optimization, 1990, 21, 445–452
• [23] GAMBARELLI G., Strategics for the repayment of external debt, Proceedings of the International Conference on Information and Systems, Dalian Maritime University Publishing House, Dalian 1992, 566–573.
• [24] GAMBARELLI G., Transforming games from characteristic into normal form, International Game Theory Review, 2007, 9, 87–104.
• [25] GAMBARELLI G., The coherent majority average for Juries’ evaluation processes, Journal of Sport Sciences, 2008, 26, 1091–1095.
• [26] GAMBARELLI G., IAQUINTA G., PIAZZA M., Anti-collusion indices and averages for the evaluation of performances and judges, Journal of Sports Sciences, 2012, 30, 411–417.
• [27] GAMBARELLI G., OWEN G., Indirect control of corporations, International Journal of Game Theory, 1994, 23, 287–302.
• [28] VAN GELLEKOM J.R.G., POTTERS J.A.M., REIJNIERSE H., ENGEL M.C., TIJS S.H., Characterization of the Owen set of linear production processes, Games and Economic Behavior, 2000, 32, 139–156.
• [29] HERRERO C., MARTINEZ R., Egalitarian rules in claims problems with indivisible goods, Instituto Valenciano de Investigaciones Económicas (IVIE), WP-AD 2004-20, Valencia, Spain, 2004, 1–24.
• [30] HERRERO C., MARTINEZ R., Balanced allocation methods for claims problems with indivisibilities, Social Choice and Welfare, 2008, 30, 603–617.
• [31] MYERSON R., Graphs and cooperation in games, Mathematics of Operations Research, 1977, 2, 225–229.
• [32] VON NEUMANN J., MORGENSTERN O., Theory of games and economic behaviour, Princeton University Press, Princeton 1944.
• [33] NORDE H., FRAGNELLI V., GARCÍA-JURADO I., PATRONE F., TIJS S., Balancedness of infrastructure cost games, European Journal of Operational Research, 2002, 136, 635–654.
• [34] OWEN G., Multilinear extensions of games, Management Science, 1972, 18, 64–79.
• [35] SAMET D., ZEMEL E., On the core and dual set of linear programming games, Mathematics of Operations Research, 1984, 9, 309–316.
• [36] SHAPLEY L.S., A value for n-person games, [in:] A.W. Tucker, H.W. Kuhn (Eds.), Contributions to the theory of games II, Princeton University Press, Princeton 1953, 307–317.
• [37] SHAPLEY L.S., SHUBIK M., A method for evaluating the distributions of power in a committee system, American Political Science Review, 1954, 48, 787–792.
• [38] THOMSON W., Axiomatic and game-theoretic analysis of bankruptcy and taxation problems. A survey, Mathematical Social Sciences, 2003, 45, 249–297.