9 December 2011, Computational Social Choice Seminar, Sunil Simon
We study, using game-theoretic concepts, the consequences of adopting products by agents who form a social network. We use the threshold model of social networks in which the nodes influenced by their neighbours can adopt one out of several alternatives, and associate with each social network a strategic game between the agents. Like certain classes of potential games, these games exhibit the "join the crowd" property where the payoff of each player weakly increases if more players choose the same strategy. However, unlike potential games, such network games may have no (pure) Nash equilibrium. For restricted classes, where the underlying graph of the network is a DAG or has no source nodes, we show that a Nash equilibrium always exists. In these two cases we characterize Nash equilibria and clarify the status of the finite improvement property.
We also explain how these results can be used to analyze consequences of the addition of new products to a social network. In particular we show that in some cases such an addition can permanently destroy market stability.
This is joint work with Krzysztof Apt.