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Delegation equilibrium payoffs in integer-splitting games∗

Published online by Cambridge University Press:  07 March 2013

Sylvain Sorin  and
Cheng Wan
Sylvain Sorin
Affiliation:
Combinatoire et Optimisation, IMJ, CNRS UMR 7586, Faculté de Mathématiques, Université P. et M. Curie – Paris 6, Tour 15-16, 1er étage, 4 Place Jussieu, 75005 Paris. sorin@math.jussieu.fr; cheng.wan.2005@polytechnique.org Laboratoire d’Econométrie, École Polytechnique, France
Cheng Wan
Affiliation:
Combinatoire et Optimisation, IMJ, CNRS UMR 7586, Faculté de Mathématiques, Université P. et M. Curie – Paris 6, Tour 15-16, 1er étage, 4 Place Jussieu, 75005 Paris. sorin@math.jussieu.fr; cheng.wan.2005@polytechnique.org
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Abstract

This work studies a new strategic game called delegation game. A delegation game isassociated to a basic game with a finite number of players where each player has a finiteinteger weight and her strategy consists in dividing it into several integer parts andassigning each part to one subset of finitely many facilities. In the associateddelegation game, a player divides her weight into several integer parts, commits each partto an independent delegate and collects the sum of their payoffs in the basic game playedby these delegates. Delegation equilibrium payoffs, consistent delegation equilibriumpayoffs and consistent chains inducing these ones in a delegation game are defined.Several examples are provided.

Keywords

Basic integer-splitting gamedelegation gamedelegation equilibrium payoffsconsistent delegation equilibrium payoffsconsistent chains
Type
Research Article
Information
RAIRO - Operations Research , Volume 47 , Issue 1 , January 2013 , pp. 47 - 58
Copyright
© EDP Sciences, ROADEF, SMAI, 2013

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References

U. Bhaskar, L. Fleischer and C.-C. Huang, The price of collusion in series-parallel networks, in Integer Programming and Combinatorial Optimization, edited by F. Eisenbrand and F.B. Shepherd. Springer Berlin Heidelberg. Lecture Notes in Comput. Sci. (2010) 313–326.
Cominetti, R., Correa, J.R. and Stier-Moses, N.E., The impact of oligopolistic competition in networks. Oper. Res. 57 (2009) 1421–1437. Google Scholar
Harker, P.T., Multiple equilibrium behaviors on networks. Transport. Sci. 22 (1988) 39–46. Google Scholar
A. Hayrapetyan, É. Tardos and T. Wexler, The effect of collusion in congestion games (extended abstract), edited by J.M. Kleinberg. ACM, New York, Proc. of the 38th Annual ACM Symposium on Theory of Computing (2006) 89–98.
C.-C. Huang, Collusion in atomic splittable routing games, edited by L. Aceto, M. Henzinger and J. Sgall. Springer Berlin Heidelberg, Proc. of the 38th International Conference on Automata, Languages and Programming (2011) 564–575.
Rosenthal, R.W., A class of games possessing pure-strategy Nash equilibria. Int. J. Game Theory 2 (1973) 65–67. Google Scholar
Selten, R., A reexamination of the perfectness concept for equilibrium points in extensive games. Int. J. Game Theory 4 (1973) 25–55. Google Scholar
Wan, C., Coalitions in network congestion games. Math. Oper. Res. 37 (2012) 654–669. Google Scholar
C. Wan, Contributions à la théorie des jeux d’évolution et de congestion. Ph.D. thesis, Université Pierre et Marie Curie (Paris 6), France (2012).
Wardrop, G., Some theoretical aspects of road traffic research communication networks. Proc. Inst. Civ. Eng. II (1952) 325–378. Google Scholar