Geodesic
«Operations Research Games»
Bollettino della Unione matematica italiana, Série 8, 8A (2005) no. 1, pp. 107-122.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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.
In this paper we present a wide class of games, the so-called Operations Research Games, that are the natural extension of classical Operations Research problems when many decision-makers interact. We consider cooperative games with transferable utility. After recalling the main features of this class of games and of the most usual solution concepts, three examples of Operations Research Games-production games, spanning tree games and sequencing games- are presented. 
@article{BUMI_2005_8_8A_1_a5,
     author = {Fragnelli, Vito and Tadei, Roberto},
     title = {{\guillemotleft}Operations {Research} {Games{\guillemotright}}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {107--122},
     publisher = {mathdoc},
     volume = {Ser. 8, 8A},
     number = {1},
     year = {2005},
     zbl = {1118.91006},
     mrnumber = {176842},
     language = {it},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2005_8_8A_1_a5/}
}
TY  - JOUR
AU  - Fragnelli, Vito
AU  - Tadei, Roberto
TI  - «Operations Research Games»
JO  - Bollettino della Unione matematica italiana
PY  - 2005
SP  - 107
EP  - 122
VL  - 8A
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2005_8_8A_1_a5/
LA  - it
ID  - BUMI_2005_8_8A_1_a5
ER  - 
%0 Journal Article
%A Fragnelli, Vito
%A Tadei, Roberto
%T «Operations Research Games»
%J Bollettino della Unione matematica italiana
%D 2005
%P 107-122
%V 8A
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2005_8_8A_1_a5/
%G it
%F BUMI_2005_8_8A_1_a5
Fragnelli, Vito; Tadei, Roberto. «Operations Research Games». Bollettino della Unione matematica italiana, Série 8, 8A (2005) no. 1, pp. 107-122. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8A_1_a5/

[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

[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. | DOI | MR | Zbl

[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. | DOI | MR

[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. | DOI | MR | Zbl

[7] I. Curiel, Cooperative Game Theory and Applications, Kluwer Academic Publisher, Dordrecht, The Netherlands (1997). | DOI | MR | Zbl

[8] I. Curiel - G. Pederzoli - S. Tijs, Sequencing Games, European Journal of Operations Research, 7 (40) (1989), 344-351. | DOI | MR

[9] M. Davis - M. Maschler, The Kernel of a Cooperative Game, Naval Research Logistics Quarterly, 12 (1965), 223-259. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[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. | DOI | MR

[13] V. Fragnelli - I. Garcia-Jurado - L. Mendez-Naya, A Note on Bus Games, Economics Letters, 82 (2004), 99-106. | DOI | MR | Zbl

[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 | Zbl

[16] D. Granot - G. Huberman, Minimum Cost Spanning Tree Games, Mathematical Programming, 21 (1981), 1-18. | DOI | MR | Zbl

[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

[18] E. Kalai - E. Zemel, Totally Balanced Games and Games of Flow, Mathematics of Operations Research, 7 (1982), 476-478. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[20] J. Kuipers, Minimum Cost Forest Games, International Journal of Game Theory, 26 (1997), 367-377. | DOI | MR | Zbl

[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

[23] A. Meca - J. Timmer - I. Garca-Jurado - P. Borm, Inventory Games, European Journal of Operational Research, 156 (2004), 127-139. | DOI | MR

[24] B. O’Neill, A Problem of Rights Arbitration from the Talmud, Mathematical Social Sciences, 2 (1984), 345-371. | DOI | MR

[25] G. Owen, On the Core of Linear Production Games, Mathematical Programming, 9 (1975), 358-370. | DOI | MR | Zbl

[26] G. Owen, Values of Games with a Priori Unions, Lecture Notes in Economic and Mathematical Systems, 141 (1977), 76-88. | MR | Zbl

[27] G. Pederzoli, Communication games, Control and Cybernetics, 20 (1991), 67-86. | MR

[28] J. A. M. Potters - I. Curiel - S. Tijs, Traveling Salesman Games, Mathematical Programming, 53 (1992), 199-211. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[31] D. Schmeidler, The Nucleolus of a Characteristic Function Game, SIAM Journal of Applied Mathematics, 17 (1969), 1163-1170. | DOI | MR | Zbl

[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

[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. | DOI | MR

[34] L. S. Shapley - M. Shubik, The Assignment Game I: The Core, International Journal of Game Theory, 7 (1) (1972), 111-130. | DOI | MR | Zbl

[35] W. Smith, Various Optimizer for Single-Stage Production, Naval Research Logistics Quarterly, 3 (1956), 59-66. | DOI | MR

[36] M. Shubik, Strategy and Market Structure: Competition, Oligopoly, and the Theory of Games, Wiley, New York, USA (195). | MR | Zbl

[37] P. D. Straffin - J. P. Heaney, Game Theory and the Tennessee Valley Authority, Management Science, 32 (1986), 1015-1028. | Zbl

[38] S. Tijs - A. Meca - M. A. Lopez, Benefit Sharing in Holding Situations, di prossima pubblicazione su European Journal of Operational Research (2004). | DOI | MR

[39] S. Tijs - T. Parthasarathy - J. Potters - R. Prasad, Permutation Games: Another Class of Totally Balanced Games, OR Spektrum, 6 (1984), 119-123. | Zbl

[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 | Zbl