Nobody Takes It All: Analysis of dynamic propagation of knowledge in a social network

Abstract: In this paper, we analyse how knowledge is shared in a social network, with the purpose of defining recurring patterns and equilibria. We develop a formal model, the Know-It-All game, based on the PageRank algorithm and other related game theoretical models, such as the Buck-holding game. The game provides a set-up where the players choose to either share their knowledge with the neighbours or to keep it to themselves. We observe that this simultaneous choice made by the players results in certain equilibrium conditions with stable knowledge-sharing loops. This analysis is then extended to large and complex networks through a machine learning algorithm. We find the effect of knowledge complexity and knowledge transmissibility on these sharing loops, complementing the existing literature on knowledge-sharing networks. The model converges on many states in which players cooperate to reach a common good without communication or retaliation. No player can obtain the most out of the game alone, therefore, Nobody Takes It All.