Social Network Games
Sunil Simon, Krzysztof R. Apt

TL;DR
This paper models product adoption in social networks as strategic games, analyzing the existence and complexity of Nash equilibria, and identifies specific graph structures where these problems are computationally tractable.
Contribution
It introduces a novel game-theoretic framework for social network product adoption and determines the computational complexity of equilibrium existence for various network structures.
Findings
Nash equilibria may not exist in these games.
Deciding equilibrium existence is NP-complete in general.
Certain graph classes allow polynomial-time solutions for equilibrium problems.
Abstract
One of the natural objectives of the field of the social networks is to predict agents' behaviour. To better understand the spread of various products through a social network arXiv:1105.2434 introduced a threshold model, in which the nodes influenced by their neighbours can adopt one out of several alternatives. To analyze the consequences of such product adoption we associate here with each such social network a natural strategic game between the agents. In these games the payoff of each player weakly increases when more players choose his strategy, which is exactly opposite to the congestion games. The possibility of not choosing any product results in two special types of (pure) Nash equilibria. We show that such games may have no Nash equilibrium and that determining an existence of a Nash equilibrium, also of a special type, is NP-complete. This implies the same result for a…
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Taxonomy
TopicsGame Theory and Applications · Opinion Dynamics and Social Influence · Complex Network Analysis Techniques
