The Web Graph as an Equilibrium

We present a game-theoretic model for the creation of content networks such as the worldwide web. The action space of a node in our model consists of choosing a set of outgoing links as well as click probabilities on these links. A node’s utility is then the product of the traffic through this node, captured by its PageRank in the Markov chain created by the strategy profile, times the quality of the node, a surrogate for the website’s utility per visit, such as repute or monetization potential. The latter depends on the intrinsic quality of the node’s content, as modified by the chosen outgoing links and probabilities. We only require that the quality be a concave function of the node’s strategy (the distribution over outgoing links), and we suggest a natural example of such a function. We prove that the resulting game always has a pure Nash equilibrium. Experiments suggest that these equilibria are not hard to compute, avoid the reciprocal equilibria of other such models, have characteristics broadly consistent with what we know about the worldwide web, and seem to have favorable price of anarchy.