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Fragnelli, Vito and Tadei, Roberto:
«Operations Research Games»
Bollettino dell'Unione Matematica Italiana Serie 8 8-A (2005) —La Matematica nella Società e nella Cultura, fasc. n.1, p. 107-122, Unione Matematica Italiana (Italian)
pdf (264 Kb), djvu (152 Kb). | MR2144888 | Zbl 1118.91006

Sunto

In questo articolo viene presentata una vasta classe di giochi, gliOperations Research Games, che costituiscono la naturale estensione dei problemi classici della Ricerca Operativa al caso in cui sono presenti più decisori, che interagiscono fra di loro. Si tratta di giochi cooperativi a utilità trasferibile. Dopo aver richiamato le caratteristiche principali di tali giochi e dei concetti di soluzione più comuni, vengono presentati alcuni esempi di Operations Research Games, quali i giochi di produzione, i giochi di connessione ed i giochi di sequenziamento.
Referenze Bibliografiche
[1] R. J. AUMANN - M. MASCHLER, The Bargaining Set for Cooperative Games, in Advances in Game Theory (Annals of Mathematics Studies, 52) (Dresher M, Shapley LS, Tucker AW eds.), Princeton, Princeton University Press, 443-476 (1964). | MR 176842
[2] J. F. BANZHAF, Weighted Voting doesn’t Work: A Mathematical Analysis, Rutgers Law Review, 19 (1965), 317-343.
[3] C. BIRD, On Cost Allocation for a Spanning Tree: A Game Theoretic Approach, Networks, 6 (1976), 335-350. | fulltext (doi) | MR 441390 | Zbl 0357.90083
[4] E. BJØRNDAL - M. KOSTER - S. TIJS, Weighted Allocation Rules for Standard Fixed Tree Games, CentER Discussion Paper 79, Tilburg University (1999).
[5] P. BORM - H. HAMERS - R. HENDRICKX, Operations Research Games: A Survey, TOP, 9 (2001), 139-216. | fulltext (doi) | MR 1878668
[6] R. BRANZEI - G. FERRARI - V. FRAGNELLI - S. TIJS, Two Approaches to the Problem of Sharing Delay Costs in Joint Projects, Annals of Operations Research, 109 (2002), 359-374. | fulltext (doi) | MR 1929740 | Zbl 1005.91010
[7] I. CURIEL, Cooperative Game Theory and Applications, Kluwer Academic Publisher, Dordrecht, The Netherlands (1997). | fulltext (doi) | MR 1797365 | Zbl 0948.91501
[8] I. CURIEL - G. PEDERZOLI - S. TIJS, Sequencing Games, European Journal of Operations Research, 7 (40) (1989), 344-351. | fulltext (doi) | MR 1004986
[9] M. DAVIS - M. MASCHLER, The Kernel of a Cooperative Game, Naval Research Logistics Quarterly, 12 (1965), 223-259. | fulltext (doi) | MR 207404 | Zbl 0204.20202
[10] J. DEEGAN - E. W. PACKEL, A New Index of Power for Simple n-Person Games, International Journal of Game Theory, 7 (1978), 113-123. | fulltext (doi) | MR 507589 | Zbl 0389.90093
[11] R. DELPIANO, Tesi di laurea, Corso di Laurea in Matematica per le Scienze dell’Ingegneria, Politecnico di Torino (2003).
[12] V. FRAGNELLI - I. GARCIA-JURADO - L. MENDEZ-NAYA, On Shortest Path Games, Mathematical Methods of Operations Research, 52 (2000), 139- 216. | fulltext (doi) | MR 1797251
[13] V. FRAGNELLI - I. GARCIA-JURADO - L. MENDEZ-NAYA, A Note on Bus Games, Economics Letters, 82 (2004), 99-106. | fulltext (doi) | MR 2028199 | Zbl 1254.91288
[14] F. GARIN, Tesi di laurea, Corso di Laurea in Matematica per le Scienze dell’Ingegneria, Politecnico di Torino (2002).
[15] D. B. GILLIES, Some Theorems on n-person Games, PhD Thesis, Princeton University (1953). | MR 2612094 | Zbl 0050.14406
[16] D. GRANOT - G. HUBERMAN, Minimum Cost Spanning Tree Games, Mathematical Programming, 21 (1981), 1-18. | fulltext (doi) | MR 618611 | Zbl 0461.90099
[17] H. HAMERS - P. BORM - R. VAN DE LEENSEL - S. TIJS, Cost Allocation in the Chinese Postman Problem, European Journal of Operations Research, 118 (1999), 153-163. | Zbl 0945.90072
[18] E. KALAI - E. ZEMEL, Totally Balanced Games and Games of Flow, Mathematics of Operations Research, 7 (1982), 476-478. | fulltext (doi) | MR 667936 | Zbl 0498.90030
[19] J. B. KRUSKAL, On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem, Proceedings of the American Mathematical Society, 7 (1956), 48-50. | fulltext (doi) | MR 78686 | Zbl 0070.18404
[20] J. KUIPERS, Minimum Cost Forest Games, International Journal of Game Theory, 26 (1997), 367-377. | fulltext (doi) | MR 1467837 | Zbl 0880.90157
[21] M. LI CALZI, Un eponimo ricorrente: Nash e la teoria dei giochi, Bollettino UMI, sez. A, 6 (2003), 3-26. | fulltext bdim | fulltext EuDML
[22] S. C. LITTLECHILD - G. OWEN, A Simple Expression for the Shapley Value in a Special Case, Management Science, 20 (1973), 370-372. | Zbl 0307.90095
[23] A. MECA - J. TIMMER - I. GARCA-JURADO - P. BORM, Inventory Games, European Journal of Operational Research, 156 (2004), 127-139. | fulltext (doi) | MR 2057454
[24] B. O’NEILL, A Problem of Rights Arbitration from the Talmud, Mathematical Social Sciences, 2 (1984), 345-371. | fulltext (doi) | MR 662176
[25] G. OWEN, On the Core of Linear Production Games, Mathematical Programming, 9 (1975), 358-370. | fulltext (doi) | MR 403700 | Zbl 0318.90060
[26] G. OWEN, Values of Games with a Priori Unions, Lecture Notes in Economic and Mathematical Systems, 141 (1977), 76-88. | MR 456544 | Zbl 0395.90095
[27] G. PEDERZOLI, Communication games, Control and Cybernetics, 20 (1991), 67-86. | MR 1136853
[28] J. A. M. POTTERS - I. CURIEL - S. TIJS, Traveling Salesman Games, Mathematical Programming, 53 (1992), 199-211. | fulltext (doi) | MR 1148013 | Zbl 0749.90094
[29] R. C. PRIM, Shortest Connection Networks and Some Generalizations, Bell System Technical Journal, 36 (1957), 1389-1401.
[30] J. SANCHEZ-SORIANO - M. A. LOPEZ - I. GARCIA-JURADO, On the Core of Transportation Games, Mathematical Social Sciences, 41 (2001), 215- 225. | fulltext (doi) | MR 1806686 | Zbl 0973.91005
[31] D. SCHMEIDLER, The Nucleolus of a Characteristic Function Game, SIAM Journal of Applied Mathematics, 17 (1969), 1163-1170. | fulltext (doi) | MR 260432 | Zbl 0191.49502
[32] L. S. SHAPLEY, A Value for n-Person Games, in Contributions to the Theory of Games, Vol II (Annals of Mathematics Studies 28) (Kuhn HW, Tucker AW eds.), Princeton University Press, Princeton, USA: 307-317 (1953). | MR 53477
[33] L. S. SHAPLEY - M. SHUBIK, A Method for Evaluating The Distribution of Power in a Committee System, American Political Science Review, 48 (1954), 787-792. | fulltext (doi) | MR 989821
[34] L. S. SHAPLEY - M. SHUBIK, The Assignment Game I: The Core, International Journal of Game Theory, 7 (1) (1972), 111-130. | fulltext (doi) | MR 311290 | Zbl 0236.90078
[35] W. SMITH, Various Optimizer for Single-Stage Production, Naval Research Logistics Quarterly, 3 (1956), 59-66. | fulltext (doi) | MR 89109
[36] M. SHUBIK, Strategy and Market Structure: Competition, Oligopoly, and the Theory of Games, Wiley, New York, USA (195). | MR 118510 | Zbl 0095.14801
[37] P. D. STRAFFIN - J. P. HEANEY, Game Theory and the Tennessee Valley Authority, Management Science, 32 (1986), 1015-1028. | Zbl 0452.90100
[38] S. TIJS - A. MECA - M. A. LOPEZ, Benefit Sharing in Holding Situations, di prossima pubblicazione su European Journal of Operational Research (2004). | fulltext (doi) | MR 2101907
[39] S. TIJS - T. PARTHASARATHY - J. POTTERS - R. PRASAD, Permutation Games: Another Class of Totally Balanced Games, OR Spektrum, 6 (1984), 119-123. | Zbl 0537.90101
[40] I. VARIO, Tesi di laurea, Corso di Laurea in Matematica per le Scienze dell’Ingegneria, Politecnico di Torino.
[41] J. VON NEUMANN - O. MORGENSTERN, Theory of Games and Economic Behavior (2nd ed. 1947, 3rd ed. 1953), Princeton University Press, Princeton, USA (1944). | MR 21298 | Zbl 0063.05930

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