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Max Celebrity Games

  • C. Àlvarez
  • A. Messeguè
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10088)

Abstract

We introduce Max celebrity games a new variant of Celebrity games defined in [4]. In both models players have weights and there is a critical distance \(\beta \) as well as a link cost \(\alpha \). In the max celebrity model the cost of a player depends on the cost of establishing links to other players and on the maximum of the weights of those nodes that are farther away than \(\beta \) (instead of the sum of weights as in celebrity games). The main results for \(\beta >1\) are that: computing a best response for a player is NP-hard; the optimal social cost of a celebrity game depends on the relation between \(\alpha \) and \(w_{max}\); ne always exist and ne graphs are either connected or a set of \(r\ge 1\) connected components where at most one of them is not an isolated node; for the class of connected ne graphs we obtain a general upper bound of \(2 \beta +2\) for the diameter. We also analyze the price of anarchy (PoA) of connected ne graphs and we show that there exist games \(\varGamma \) such that \(\text {PoA} (\varGamma )=\varTheta (n/\beta )\); modifying the cost of a player we guarantee that all ne graphs are connected, but the diameter might be \(n-1\). Finally, when \(\beta =1\), computing a best response for a player is polynomial time solvable and the \(\text {PoA} = O(w_{max}/w_{min})\).

Keywords

Cost Function Nash Equilibrium Social Cost Undirected Graph Critical Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was partially supported by funds from the AGAUR of the Government of Catalonia under project ref. SGR 2014:1034 (ALBCOM). C. Àlvarez was partially supported by the Spanish Ministry for Economy and Competitiveness (MINECO) and the European Union (FEDER funds), under grants ref. TIN2013-46181-C2-1-R (COMMAS).

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.ALBCOM Research Group, Computer Science DepartmentUPCBarcelonaSpain

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