Complex problems in science, business, and engineering typically require some tradeoff between exploitation of known solutions and exploration for novel ones, where, in many cases, information about known solutions can also disseminate among individual problem solvers through formal or informal networks. Prior research on complex problem solving by collectives has found the counterintuitive result that inefficient networks, meaning networks that disseminate information relatively slowly, can perform better than efficient networks for problems that require extended exploration. In this paper, we report on a series of 256 Web-based experiments in which groups of 16 individuals collectively solved a complex problem and shared information through different communication networks. As expected, we found that collective exploration improved average success over independent exploration because good solutions could diffuse through the network. In contrast to prior work, however, we found that efficient networks outperformed inefficient networks, even in a problem space with qualitative properties thought to favor inefficient networks. We explain this result in terms of individual-level explore-exploit decisions, which we find were influenced by the network structure as well as by strategic considerations and the relative payoff between maxima. We conclude by discussing implications for realworld problem solving and possible extensions. any problems that arise in science, business, and engineering are "complex" in the sense that they require optimization along multiple dimensions, where changes in one dimension can have different effects depending on the values of the other dimensions. A common way to represent problem complexity of this nature is with a "fitness landscape," a multidimensional mapping from some choice of solution parameters to some measure of performance, where complexity is expressed by the "ruggedness" of the landscape (1, 2). A simple problem, that is, would correspond to a relatively smooth landscape in which the optimal solution can be found by strictly local and incremental exploration around the current best solution. By contrast, a complex problem would correspond to a landscape with many potential solutions ("peaks") separated by low-performance "valleys." In the event that the peaks are of varying heights, purely local exploration on a rugged landscape can lead to solutions that are locally optimal but globally suboptimal. The result is that when solving complex problems, problem solvers must strike a balance between local exploitation of already discovered solutions and nonlocal exploration for potential new solutions (3, 4). In many organizational contexts, the tradeoff between exploration and exploitation is affected by the presence of other problem solvers who are attempting to solve the same or similar problems, and who communicate with each other through some network of formal or informal social ties (5-10). Intuitively, it seems clear that communication networks should aid collaborative problem solving by allowing individual problem solvers to benefit from the experience of others, wherein the faster good solutions are spread, the better off every problem solver will be. However, recent work on the relation between network structure and collaborative problem solving (11-13) has concluded that when faced with complex problems, networks of agents that exhibit lower efficiency can outperform more efficient networks, where "efficiency" refers to the speed with which information about trial solutions can spread throughout the network. Although at first surprising, this finding is consistent with earlier results (3, 8) that slow or intermediate rates of learning in organizations result in higher long-run performance than fast rates. In both cases, the explanation is that slowing down the rate at which individuals learn, either from the "organizational code" (3) or from each other (8, 11, 13) , forces them to undertake more of their own exploration, which, in turn, reduces the likelihood that the collective will converge prematurely on a suboptimal solution. Although this explanation is persuasive, the evidence is based largely on agent-based simulations (2, 3, 8, 11, 13, 14) , which necessarily make certain assumptions about the agents' behavior, and therefore could be mistaken in ways that fundamentally undermine the conclusions. In addition, one recent experiment involving real human subjects (12) found an advantage for inefficient networks in problem spaces requiring exploration. However, the practical constraints associated with running the experiments in a physical laboratory limited the size and variability of the networks considered as well as the complexity of the corresponding fitness landscapes; thus, it remains unclear to what extent the experimental findings either corroborate the simulation results or generalize to other scenarios. Given these uncertainties, it would be desirable to test hypotheses about network structure and performance in humansubjects experiments in a way that circumvents the constraints of a physical laboratory. Fortunately, it has recently become possible to run laboratory-style human subject experiments online. Although virtual laboratories suffer from certain disadvantages relative to their physical counterparts, several recent studies have shown that many of these disadvantages can be overcome (15) (16) (17) . In fact, a number of classic psychological and behavioral economics experiments conducted using Amazon's Mechanical Turk, a popular crowd-sourcing (18) site that is increasingly used by behavioral science researchers to recruit and pay human subjects, have recovered results indistinguishable from those recorded in physical laboratories (19, 20) . In this paper, we report on a series of online experiments, conducted using Amazon's Mechanical Turk, that explore the relation between network structure and collaborative learning for a complex problem with a wide range of network topologies. Several of our results are consistent with prior theorizing about problem solving in organizational settings. In particular, we find that networked groups generally outperform equal-sized collections of independent problem solvers (8), that exploration can be costly for individuals but is beneficial for the collective (3), and that centrally positioned individuals experience better performance than peripheral individuals (21, 22) . However, we find no evidence to support the hypothesized superiority of inefficient
The exploration-exploitation tradeoff in a collaborative problem solving task has been discussed by REF .
Collaborative learning in networks
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Psychology Medicine