We consider a scenario in which leaders are required to recruit teams of followers. Each leader cannot recruit all followers, but interaction is constrained according to a bipartite network. The objective for each leader is to reach a state of local stability in which it controls a team whose size is equal to a given constraint. We focus on distributed strategies, in which agents have only local information of the network topology and propose a distributed algorithm in which leaders and followers act according to simple local rules. The performance of the algorithm is analyzed with respect to the convergence to a stable solution. Our results are as follows. For any network, the proposed algorithm is shown to converge to an approximate stable solution in polynomial time, namely the leaders quickly form teams in which the total number of additional followers required to satisfy all team size constraints is an arbitrarily small fraction of the entire population. In contrast, for general graphs there can be an exponential time gap between convergence to an approximate solution and to a stable solution.
 We argue that algorithmic modeling is a powerful approach to understanding the collective dynamics of human behavior. We consider the task of pairing up individuals connected over a network, according to the following model: each individual is able to propose to match with and accept a proposal from a neighbor in the network; if a matched individual proposes to another neighbor or accepts another proposal, the current match will be broken; individuals can only observe whether their neighbors are currently matched but have no knowledge of the network topology or the status of other individuals; and all individuals have the common goal of maximizing the total number of matches. By examining the experimental data, we identify a behavioral principle called prudence, develop an algorithmic model, analyze its properties mathematically and by simulations, and validate the model with human subject experiments for various network sizes and topologies. Our results include i) a -approximate maximum matching is obtained in logarithmic time in the network size for bounded degree networks; ii) for any constant , a -approximate maximum matching is obtained in polynomial time, while obtaining a maximum matching can require an exponential time; and iii) convergence to a maximum matching is slower on preferential attachment networks than on small-world networks. These results allow us to predict that while humans can find a “good quality” matching quickly, they may be unable to find a maximum matching in feasible time. We show that the human subjects largely abide by prudence, and their collective behavior is closely tracked by the above predictions. Theoretical work suggests that structural properties of naturally occurring networks are important in shaping behavior and dynamics. However, the relationships between structure and behavior are difficult to establish through empirical studies, because the networks in such studies are typically fixed. We studied networks of human subjects attempting to solve the graph or network coloring problem, which models settings in which it is desirable to distinguish one9s behavior from that of one9s network neighbors. Networks generated by preferential attachment made solving the coloring problem more difficult than did networks based on cyclical structures, and “small worlds” networks were easier still. We also showed that providing more information can have opposite effects on performance, depending on network structure. Networks can affect a group's ability to solve a coordination problem. We utilize laboratory experiments to study the conditions under which groups of subjects can solve coordination games. We investigate a variety of different network structures, and we also investigate coordination games with symmetric and asymmetric payoffs. Our results show that network connections facilitate coordination in both symmetric and asymmetric games. Most significantly, we find that increases in the number of network connections encourage coordination even when payoffs are highly asymmetric. These results shed light on the conditions that may facilitate coordination in real-world networks. A growing literature on human networks suggests that the way we are connected influences both individual and group outcomes. Recent experimental studies in the social and computer sciences have claimed that higher network connectivity helps individuals solve coordination problems. However, this is not always the case, especially when we consider complex coordination tasks; we demonstrate that networks can have both constraining edges that inhibit collective action and redundant edges that encourage it. We show that the constraints imposed by additional edges can impede coordination even though these edges also increase communication. By contrast, edges that do not impose additional constraints facilitate coordination, as described in previous work. We explain why the negative effect of constraint trumps the positive effect of communication by analyzing coordination games as a special case of widely-studied constraint satisfaction problems. The results help us to understand the importance of problem complexity and network connections, and how different types of connections can influence real-world coordination. Many distributed collective decision-making processes must balance diverse individual preferences with a desire for collective unity. We report here on an extensive session of behavioral experiments on biased voting in networks of individuals. In each of 81 experiments, 36 human subjects arranged in a virtual network were financially motivated to reach global consensus to one of two opposing choices. No payments were made unless the entire population reached a unanimous decision within 1 min, but different subjects were paid more for consensus to one choice or the other, and subjects could view only the current choices of their network neighbors, thus creating tensions between private incentives and preferences, global unity, and network structure. Along with analyses of how collective and individual performance vary with network structure and incentives generally, we find that there are well-studied network topologies in which the minority preference consistently wins globally; that the presence of “extremist” individuals, or the awareness of opposing incentives, reliably improve collective performance; and that certain behavioral characteristics of individual subjects, such as “stubbornness,” are strongly correlated with earnings.