Abstract
Motivated by privacy and security concerns in online social networks, we study the role of social
pressure in opinion games. These are games, important in economics and sociology, that model the
formation of opinions in a social network. We enrich the definition of (noisy) best-response dynamics for opinion games by introducing the pressure,
increasing with time, to reach an agreement.
We prove that for clique social networks, the dynamics always converges to consensus (no matter
the level of noise) if the social pressure is high
enough. Moreover, we provide (tight) bounds on
the speed of convergence; these bounds are polynomial in the number of players provided that the
pressure grows sufficiently fast. We finally look beyond cliques: we characterize the graphs for which
consensus is guaranteed, and make some considerations on the computational complexity of checking
whether a graph satisfies such a condition