the difficulty of the networks that was approximately the reverse of that for the subjects.

These first experiments were also
the only ones in which we investigat-
ed the effects of global information
views on performance. In a subset of
the experiments, subjects actually saw
the current state of the entire network
(again with their own vertex in the net-
work clearly indicated), not just the col-
ors of their neighbors. Not surprising-
ly, this global view led to dramatically
improved performance in a simple
cycle, where the symmetric structure
of the network and the optimal solu-
tion become immediately apparent.
But strikingly, in preferential attach-
ment networks, global views led to
considerable degradation in collective
performance—perhaps an instance
of “information overload,” or simply
causing subjects to be distracted from
attending to their local piece of the
global problem.

Figure 3. Average time to global solution for coloring and consensus experiments (solid lines) as a function of edge rewiring in a clique-chain network, and simulation times (dashed lines) on the same networks for distributed heuristics. the parametric structure has the opposite effect on the two problems.

consensus coloring

180

average experiment
or simulation time to solution

150

120

90

60

30

consensus

coloring

0

0.0

0.2

0.4 0.6

rewiring probability, q

0.8

1.0

Figure 4. visualization of a consensus experiment with low rewiring parameter, showing collective and individual behaviors, and effects of underlying clique structure.

incentives to be the same color as their neighbors, chosen from a fixed menu of nine colors), on the same set of underlying networks. Despite the vastly different (centralized) computational complexity of these problems—coloring being NP-hard, consensus trivial—the two tasks are cognitively very similar and easy for subjects to switch between: coloring is a problem of social differentiation, consensus one of social coordination.

In these experiments, the networks were drawn from a parametric family that begins with six cliques of size six loosely connected in a chain. A rewiring parameter q determines the fraction of internal clique edges that are replaced with random “long distance” edges, thus allowing interpolation between a highly clustered, “tribal” network, and the Erdös-Renyi random graph model; see Figure 2(a) for an example. The primary finding here was that the effect on collective performance of varying the rewiring parameter is systematic and opposite for the two problems— consensus performance benefits from more rewiring, coloring performance suffers. This effect can be qualitatively captured by simple distributed heuristics, but this does not diminish the striking behavioral phenomenon (see Figure 3). The result suggests that efforts to examine purely structural properties of social and organizational networks, without careful consideration of how structure interacts with the task(s) carried out in those networks, may provide only limited insights on collective behavior.

In addition to such systematic, statistically quantifiable results, our experiments often provide interesting opportunities to visualize collective and individual behavior in more anecdotal fashion. Figure 4 shows the actual play during one of the consensus experiments on a network with only a small amount of rewiring, thus largely preserving the tribal clique structure. Each row corresponds to one of the 36 players, and the horizontal axis represents elapsed time in the experiment. The horizontal bars then show the actual color choice by the player at that moment. The first six rows correspond to the players in the first (partially rewired) clique, the next six to the second clique, and so on. The underlying