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Contribution games in social networks
 In Proc. 18th European Symposium on Algorithms (ESA
, 2010
"... We consider network contribution games, where each agent in a social 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 u ..."
Abstract

Cited by 2 (1 self)
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We consider network contribution games, where each agent in a social 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. For example, 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. A special focus of the paper are minimum effort games, where the reward of a relationship depends onlyonthe minimum effort ofanyofthe participants. Finally, we showtight bounds for approximate equilibria and convergence of dynamics in these games. 1
Contribution Games in Networks
, 2010
"... 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 re ..."
Abstract

Cited by 1 (0 self)
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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 equilibriaofthisgame, andcharacterizetheexistence, computationalcomplexity, andquality 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.
The Fashion Game: Network Extension of Matching Pennies
"... Abstract. It is impossible, in general, to extend an asymmetric twoplayer game to networks, because there must be two populations, the row one and the column one, but we do not know how to define innerpopulation interactions. This is not the case for Matching Pennies, as we can interpret the row pla ..."
Abstract
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Abstract. It is impossible, in general, to extend an asymmetric twoplayer game to networks, because there must be two populations, the row one and the column one, but we do not know how to define innerpopulation interactions. This is not the case for Matching Pennies, as we can interpret the row player as a conformist, who prefers to coordinate her opponentâ€™s action, while the column player can be interpreted as a rebel, who likes to anticoordinate. Therefore we can naturally define the interaction between two conformists as the coordination game, and that between two rebels as the anticoordination game. It turns out that the above network extension of Matching Pennies can be used to investigate the phenomenon of fashion, and thus it is named as the fashion game. The fashion game possesses an obvious mixed Nash equilibrium, yet we are especially interested in pure Nash equilibrium (PNE for short), whose existence cannot be guaranteed. In this paper, we focus on the PNE testing problem, namely given an instance of the fashion game, answer whether it possesses a PNE or not. Our first result is on the negative side: PNE testing, in general, is hard. For the PNE testing problem restricted to several special structures, i.e. lines, rings, complete graphs and trees, either a simple characterization or an efficient algorithm is provided.