As it is well known, the theory of cooperative games finds applications in many fields. The goal of this paper is to highlight some applications of cooperative games, resulting from the cooperation between the Universities of Bergamo and Krakow, and some related open problems. The paper is organized in three main sections. The first deals with the description of some specific fields where the theory of cooperative games has been applied (i.e. interfering elements, international economics and marketing cooperatives). The second section discusses general results about power indices. The third section presents several applications to Finance and Politics. We discuss these models and the related open problems in a simple and informal way to facilitate understanding by scholars from fields other than game theory.
cooperative games, power indices, finance, politics, interfering elements, international economics, marketing cooperatives
 M.L. Balinski, H.P. Young, The Quota Method of Apportionment, American Mathematical Monthly, No.82, 1975, pp. 701-730.
 J.F. Banzhaf, Weighted Voting Doesn't Work: a Mathematical Analysis, Rutgers Law Review, No.19, 1965, pp. 317-343.
 C. Bertini, J. Freixas. G. Gambarelli, I. Stach, Comparing Power Indices, in: V. Fragnelli and G. Gambarelli (eds.) Open Problems in the Theory of Cooperative Games, Special Issue of International Game Theory Review, Vol.15, No.2, 2013, pp. 1340004-1–1340004-19.
 C. Bertini, J. Freixas, G. Gambarelli, I. Stach, Some Open Problems in Simple Games, in: V. Fragnelli and G. Gambarelli (eds.) Open Problems in the Theory of Cooperative Games, Special Issue of International Game Theory Review, Vol.15, No.2, 2013, pp. 1340005-1–1340005-18.
 C. Bertini, G. Gambarelli, A. Scarelli, Z. Varga, Equilibrium Solution in a Game between a Cooperative and Its Members, AUCO Czech economic review, No.5, 2011, pp. 162-171.
 C. Bertini, G. Gambarelli, I. Stach, Apportionment Strategies for the European Parliament, in: G. Gambarelli and M. Holler (eds.) Power Measures III, Homo Oeconomicus, Vol.22, No.4, 2005, pp. 589–604 (republished in: M.J. Holler and H. Nurmi (eds.) Power, Voting, and Voting Power: 30 Years After, Heidelberg: Springer-Verlag, 2013, pp. 541-552).
 C. Bertini, G. Gambarelli, I. Stach, A Method of Seat Distribution in the European Parliament, in: P. Łebkowski (ed.) Zarządzanie przedsiębiorstwem. Teoria i praktyka 2014, AGH University of Science and Technology Press, Krakow, 2014, pp. 271-280.
 C. Bertini, G. Gambarelli, I. Stach, Some Open Problems in the Application of Power Indices to Politics and Finance, Homo Oeconomicus, Vol.32, No.1, 2015, pp. 147-156.
 D. Carfì, A. Donato, G. Gambarelli, Kalai-Smorodinsky Balances for n-Tuples of Interfering Elements, forthcoming 2018.
 D. Carfì, G. Gambarelli, A. Uristani, Balancing Pairs of Interfering Elements, in: Financial management. Measurement of performance and evaluation of investment appraisal (Zarządzanie finansami. Mierzenie wyników przedsiębiorstw i ocena efektywności inwestycji) Zeszyty Naukowe Uniwersytetu Szczecińskiego No.760, Szczecin University Press, Szczecin, 2013, pp. 435-442.
 D. Carfì, G. Gambarelli, Balancing Bi-linearly Interfering Elements, in: C. Bertini, P. Faliszewski, A. Paliński and I. Stach (eds.) Special Issue on Game Theory and Applications, Decision Making in Manufacturing and Services, Vol.9, No.1, 2015, pp. 27-49.
 J.S. Coleman, Control of Collectivities and the Power of Collectivity to Act, in: B. Liberman (ed.) Social Choice, London: Gordon and Breach, 1971, pp. 269-300.
 Y. Crama, L. Leruth, Power Indices and the Measurement of Control in Corporate Structures, in: V. Fragnelli and G. Gambarelli (eds.) Open Problems in the Applications of Cooperative Games, Special Issue of International Game Theory Review, Vol.15, No.3, 2013, pp. 1340017-1–1340017-15.
 E. Denti, N. Prati, 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, No.36, 2004, pp. 183-192.
 V. Fragnelli, G. Gambarelli (eds.) Open problems in the theory of cooperative games, Special Issue of International Game Theory Review, Vol.15, No.2, 2013.
 V. Fragnelli, G. Gambarelli (eds.) Open Problems in the Applications of Cooperative Games, Special Issue of International Game Theory Review, Vol.15, No.3, 2013.
 J. Freixas, G. Gambarelli, Common Properties Among Power Indices, Control and Cybernetics, Vol.26, No.4, 1997, pp. 591-603.
 G. Gambarelli, Portfolio Selection and Firms' Control, Finance, Vol.3, No.1, 1982, pp. 69-83.
 G. Gambarelli, Common Behaviour of Power Indices. International Journal of Game Theory, Vol.12, No.4, 1983, pp. 237-244.
 G. Gambarelli, Strategies for the Repayment of External Debt, Proceedings of the International Conference on Information and Systems, Dalian Maritime University Publishing House, Dalian, 1992, pp. 566-573.
 G. Gambarelli, An Index of De-stability for Controlling Shareholders, in R. Flavell (ed.) Modelling Reality and Personal Modelling, Heidelberg: Physica-Verlag, 1993, pp. 116-127.
 G. Gambarelli, Takeover Algorithms, in: M. Bertocchi, E. Cavalli and S. Komlosi (eds.) Modelling Techniques for Financial Markets and Bank Management, Proceedings of the 16-th and 17-th Euro Working Group of Financial Modelling Meetings, Heidelberg: Physica Verlag, 1996, pp. 212-222.
 G. Gambarelli, Minimax Apportionments, Group Decision and Negotiation, Vol.8, No.6, 1999, pp. 441-461 (republished in: J. Kacprzyk and D. Wagner (eds.) Group Decisions and Voting, Systems Research Institute, Warszawa: Polish Academy of Sciences, 2003, pp. 9-30).
 G. Gambarelli, J. Hołubiec, Power Indices and Democratic Apportionments, in: M. Fedrizzi and J. Kacprzyk (eds.) Proceedings of the 8-th Italian-Polish Symposium on Systems Analysis and Decision Support in Economics and Technology, Warsaw: Onnitech Press, 1990, pp. 240-255.
 G. Gambarelli, G. Owen, Indirect Control of Corporations, International Journal of Game Theory, Vol.23, No.4, 1994, pp. 287-302.
 G. Gambarelli, G. Owen, Power in Political and Business Structures, in: M.J. Holler and M.E. Streit (eds.) Power and fairness, Jahrbuch für Neue Politische Ökonomie, No.20, 2002, pp. 57-68, Tübingen: Mohr Siebeck.
 G. Gambarelli, A. Palestini, Minimax Multi-district Apportionments, in: G. Gambarelli (ed.) Power Measures IV, Special Issue of Homo Oeconomicus, Vol.24, No.3/4, 2007, pp. 335-356.
 G. Gambarelli, S. Pesce, Takeover Prices and Portfolio Theory, in G. Gambarelli (ed.) Essays on Cooperative Games – in Honor of Guillermo Owen, Special Issue of Theory and Decision, Dordrecht: Kluwer Academic Publishers, No.36, 2004, pp. 193-203.
 G. Gambarelli, I. Stach, Power Indices in Politics: Some Results and Open Problems. Homo Oeconomicus (Essays in Honor of Hannu Nurmi), Vol.26, No.3/4, 2009, pp. 417-441.
 G. Gambarelli, A. Uristani, Multicameral Voting Cohesion Games, Central European Journal of Operations Research, Vol.17, No.4, 2009, pp. 433-460.
 D. Karos, H. Peters, Indirect Control and Power in Mutual Control Structures, Games and Economic Behavior, No.92, 2015, pp. 150-165.
 J.W. Milnor, L.S. Shapley, Values of Large Games II: Oceanic Games. Rand Corporation, R.M 2646, Santa Monica, CA, 1961.
 G. Owen, Multilinear Extensions of Games, Management Science, No.18, 1972, pp. 64-79.
 L.S Shapley, M. Shubik, A Method for Evaluating the Distributions of Power in a Committee System, American Political Science Review, No.48, 1954, pp. 787-792
Cite this paper
Cesarino Bertini, Gianfranco Gambarelli, Izabella Stach, Maurizio Zola. (2017) Some Results and Open Problems in Applications of Cooperative Games. International Journal of Economics and Management Systems, 2, 271-276
Copyright © 2017 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0