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Contribution Games in Networks

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Abstract

We consider network contribution games, where each agent in a network has a budget of effort that he can contribute to different collaborative projects or relationships. Depending on the contribution of the involved agents a relationship will flourish or drown, and to measure the success we use a reward function for each relationship. Every agent is trying to maximize the reward from all relationships that it is involved in. We consider pairwise equilibria of this game, and characterize the existence, computational complexity, and quality of equilibrium based on the types of reward functions involved. When all reward functions are concave, we prove that the price of anarchy is at most 2. For convex functions the same only holds under some special but very natural conditions. Another special case extensively treated are minimum effort games, where the reward of a relationship depends only on the minimum effort of any of the participants. In these games, we can show existence of pairwise equilibrium and a price of anarchy of 2 for concave functions and special classes of games with convex functions. Finally, we show tight bounds for approximate equilibria and convergence of dynamics in these games.

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Authors and Affiliations

  1. Dept. of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, USA

    Elliot Anshelevich

  2. Dept. of Computer Science, RWTH Aachen University, Aachen, Germany

    Martin Hoefer

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  1. Elliot Anshelevich
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  2. Martin Hoefer
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Correspondence to Martin Hoefer.

Additional information

An extended abstract of this paper has been accepted for publication in the proceedings of the 18th European Symposium on Algorithms (ESA 2010).

E. Anshelevich supported in part by NSF CCF-0914782. M. Hoefer supported by DFG through UMIC Research Center at RWTH Aachen University and by grant Ho 3831/3-1.

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Anshelevich, E., Hoefer, M. Contribution Games in Networks. Algorithmica 63, 51–90 (2012). https://doi.org/10.1007/s00453-011-9520-7

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