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