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Recently, Apt and Markakis introduced a model for product adoption in social networks with multiple products, where the agents, influenced by their neighbours, can adopt one out of several alternatives (products). To analyze these networks we introduce social network games in which product adoption is obligatory. We show that when the underlying graph is a simple cycle, there is a polynomial time algorithm allowing us to determine whether the game has a Nash equilibrium. In contrast, in the arbitrary case this problem is NP-complete. We also show that the problem of determining whether the game is weakly acyclic is co-NP hard. Using these games we analyze various types of paradoxes that can arise in the considered networks. One of them corresponds to the well-known Braess paradox in congestion games. In particular, we show that social networks exist with the property that by adding an additional product to a specific node, the choices of the nodes will unavoidably evolve in such a way that everybody is strictly worse off.
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
We consider agents in a social network competing to be selected as partners in collaborative, mutually beneficial activities. We study this through a model in which an agent i can initiate a limited number k_i>0 of games and selects the ideal partner
Network games are widely used as a model for selfish resource-allocation problems. In the classical model, each player selects a path connecting her source and target vertices. The cost of traversing an edge depends on the {em load}; namely, number o
In this paper we extend a popular non-cooperative network creation game (NCG) to allow for disconnected equilibrium networks. There are n players, each is a vertex in a graph, and a strategy is a subset of players to build edges to. For each edge a p
Congestion games are a classical type of games studied in game theory, in which n players choose a resource, and their individual cost increases with the number of other players choosing the same resource. In network congestion games (NCGs), the reso