Common Knowledge on Networks

Common knowledge of intentions is crucial to basic social tasks ranging from cooperative hunting to oligopoly collusion, riots, revolutions, and the evolution of social norms and human culture. Yet little is known about how common knowledge leaves a trace on the dynamics of a social network. Here we show how an individual’s network properties—primarily local clustering and betweenness centrality—provide strong signals of the ability to successfully participate in common knowledge tasks. These signals are distinct from those expected when practices are contagious, or when people use less-sophisticated heuristics that do not yield true coordination. This makes it possible to infer decision rules from observation. We also find that tasks that require common knowledge can yield significant inequalities in success, in contrast to the relative equality that results when practices spread by contagion alone. In the game known as Rousseau’s Stag Hunt [1], participants must decide between hunting a stag, or rabbits, before knowing what the others have chosen to do. Rabbits can be caught by individuals, but provide a lower reward than a stag. A stag can be caught, but only if others also decide to join the hunt, and a failed hunt is a serious setback. Even when an individual desires to join a hunt, she may not know that others know this. In the face of this uncertainty, she may go after rabbits instead and gain a meager, but relatively assured, benefit. Yet the other members of her group followed similar logic. All preferred to hunt stag, but all ended up hunting rabbits. This is the problem of common knowledge. The problem of the stag hunt is widespread in the modern world. An entrepreneur decides between a stable salary at a major corporation, or joining with others in a San Francisco startup. In determining whether potential team-mates are willing to forego their own backup plans and commit to joint effort, he faces the same problem as Rousseau’s hunter. So, too, does an individual considering joining a demonstration against an unpopular regime, where small crowds may be violently dispersed, but safety, and political change, lies in numbers [2]. Much work has been done on the mechanisms that can drive cooperation, but ensuring that all individuals involved have the capability to coordinate is an equally difficult Department of Psychological and Brain Sciences, Indiana University, 1101 E. 10th St., Bloomington IN 47405. [email protected] School of Informatics and Computing, Indiana University, 901 E. 10th St., Bloomington, IN 47408 & Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501. [email protected]