Consensus, Cohesion and Connectivity

Social life clusters into groups held together by ties that also transmit information. When collective problems occur, group members use their ties to discuss what to do and to establish an agreement, to be reached quick enough to prevent discounting the value of the group decision. The speed at which a group reaches consensus can be predicted by the algebraic connectivity of the network, which also imposes a lower bound on the group's cohesion. This specific measure of connectivity is put to the test by re-using experimental data, which confirm the prediction

Topological and Graph-coloring Conditions on the Parameter-independent Stability of Second-order Networked Systems

In this paper, we study parameter-independent stability in qualitatively heterogeneous passive networked systems containing damped and undamped nodes. Given the graph topology and a set of damped nodes, we ask if output consensus is achieved for all system parameter values. For given parameter values, an eigenspace analysis is used to determine output consensus. The extension to parameter-independent stability is characterized by a coloring problem, named the richly balanced coloring (RBC) problem. The RBC problem asks if all nodes of the graph can be colored red, blue and black in such a way that (i) every damped node is black, (ii) every black node has blue neighbors if and only if it has red neighbors, and (iii) not all nodes in the graph are black. Such a colored graph is referred to as a richly balanced colored graph. Parameter-independent stability is guaranteed if there does not exist a richly balanced coloring. The RBC problem is shown to cover another well-known graph coloring scheme known as zero forcing sets. That is, if the damped nodes form a zero forcing set in the graph, then a richly balanced coloring does not exist and thus, parameter-independent stability is guaranteed. However, the full equivalence of zero forcing sets and parameter-independent stability holds only true for tree graphs. For more general graphs with few fundamental cycles an algorithm, named chord node coloring, is proposed that significantly outperforms a brute-force search for solving the NP-complete RBC problem.Comment: 30 pages, accepted for publication in SICO

Design of Randomized Experiments in Networks

Over the last decade, the emergence of pervasive online and digitally enabled environments has created a rich source of detailed data on human behavior. Yet, the promise of big data has recently come under fire for its inability to separate correlation from causation-to derive actionable insights and yield effective policies. Fortunately, the same online platforms on which we interact on a day-to-day basis permit experimentation at large scales, ushering in a new movement toward big experiments. Randomized controlled trials are the heart of the scientific method and when designed correctly provide clean causal inferences that are robust and reproducible. However, the realization that our world is highly connected and that behavioral and economic outcomes at the individual and population level depend upon this connectivity challenges the very principles of experimental design. The proper design and analysis of experiments in networks is, therefore, critically important. In this work, we categorize and review the emerging strategies to design and analyze experiments in networks and discuss their strengths and weaknesses

Cooperation and Contagion in Web-Based, Networked Public Goods Experiments

A longstanding idea in the literature on human cooperation is that cooperation should be reinforced when conditional cooperators are more likely to interact. In the context of social networks, this idea implies that cooperation should fare better in highly clustered networks such as cliques than in networks with low clustering such as random networks. To test this hypothesis, we conducted a series of web-based experiments, in which 24 individuals played a local public goods game arranged on one of five network topologies that varied between disconnected cliques and a random regular graph. In contrast with previous theoretical work, we found that network topology had no significant effect on average contributions. This result implies either that individuals are not conditional cooperators, or else that cooperation does not benefit from positive reinforcement between connected neighbors. We then tested both of these possibilities in two subsequent series of experiments in which artificial seed players were introduced, making either full or zero contributions. First, we found that although players did generally behave like conditional cooperators, they were as likely to decrease their contributions in response to low contributing neighbors as they were to increase their contributions in response to high contributing neighbors. Second, we found that positive effects of cooperation were contagious only to direct neighbors in the network. In total we report on 113 human subjects experiments, highlighting the speed, flexibility, and cost-effectiveness of web-based experiments over those conducted in physical labs

Facts and Figuring: An Experimental Investigation of Network Structure and Performance in Information and Solution Spaces

Using data from a novel laboratory experiment on complex problem solving in which we varied the network structure of 16-person organizations, we investigate how an organization’s network structure shapes performance in problem-solving tasks. Problem solving, we argue, involves both search for information and search for solutions. Our results show that the effect of network clustering is opposite for these two important and complementary forms of search. Dense clustering encourages members of a network to generate more diverse information, but discourages them from generating diverse theories: in the language of March (1991), clustering promotes exploration in information space, but decreases exploration in solution space. Previous research, generally focusing on only one of those two spaces at a time, has produced an inconsistent understanding of the value of network clustering. By adopting an experimental platform on which information was measured separately from solutions, we were able to bring disparate results under a single theoretical roof and clarify the effects of network clustering on problem-solving behavior and performance. The finding both provides a sharper tool for structuring organizations for knowledge work and reveals the challenges inherent in manipulating network structure to enhance performance, as the communication structure that helps one antecedent of successful problem solving may harm the other

Strategic and Secure Interactions in Networks

The goal of this dissertation is to understand how network plays a role in shaping certain strategic interactions, in particular biased voting and bargaining, on networks; and to understand how interactions can be made secure when they are constrained by the network topology. Our works take an interdisciplinary approach by drawing on theories and models from economics, sociology, as well as computer science, and using methodologies that include both theories and behavioral experiments. First, we consider biased voting in networks, which models distributed collective decision making processes where individuals on a network must balance between their private biases or preferences with a collective goal of consensus. Our study of this problem is two-folded. On the theoretical side, we start by introducing a diffusion model called biased voter model, which is a natural extension of the classic voter model. Among other results, we show in the presence of private biases, no matter how small, there exists certain networks where it takes exponential time to converge to a consensus through distributed interaction in networks. This is a stark and interesting contrast to the well-known result that it always takes polynomial time to converge in the voter model, when there are no private biases. On the experimental side, a group human subjects were arranged in various carefully designed virtual networks to solve the biased voting problem. Along with analyses of how collective and individual performance vary with network structure and incentives generally, we find there are well-studied network topologies in which the minority preference consistently wins globally, and that the presence of “extremist” individuals, or the awareness of opposing incentives, reliably improve collective performance Second, we consider bargaining in networks, which has long been studied by economists and sociologists. A basic premise behind the many theoretical study of bargaining in networks is that pure topological differences in agents’ network positions endow them with different bargaining power. As a complementary to these theories, we again conducted a series of highly controlled behavioral experiments, where human subjects were arranged in various carefully designed virtual networks to playing bargaining games. Along with other findings of how individual and collective performance vary with network structures and individual playing styles, we find that the number of neighbors one can negotiate with confers bargaining power, whereas the limit on the number of deals one can close undermines it, and we find that competitions from distant part of the network that are invisible locally also play a significant and subtle role in shaping bargaining powers. And last, we consider the question of how interactions in networks can be made secure. Traditional methods and tools from cryptography, for example secure multi-party computation, can be applied only if each party can talk to everyone else directly; but cannot be directly applied if interactions are distributed over a network without completely eradicating the distributed nature. We develop a general ‘compiler’ that turns each algorithm from a broad class collectively known as message-passing algorithms into a secure one that has exactly the same functionality and communication pattern. And we show a fundamental trade-off between preserving the distributed nature of communication and the level of security one can hope for

Topological and Graph-Coloring Conditions on the Parameter-Independent Stability of Second-Order Networked Systems

In this paper, we study parameter-independent stability in qualitatively heterogeneous passive networked systems containing damped and undamped nodes. Given the graph topology and a set of damped nodes, we ask if output consensus is achieved for all system parameter values. For given parameter values, an eigenspace analysis is used to determine output consensus. The extension to parameter-independent stability is characterized by a coloring problem, named the richly balanced coloring (RBC) problem. The RBC problem asks if all nodes of the graph can be colored red, blue, and black in such a way that (i) every damped node is black, (ii) every black node has blue neighbors if and only if it has red neighbors, and (iii) not all nodes in the graph are black. Such a colored graph is referred to as a richly balanced colored graph. Parameter-independent stability is guaranteed if there does not exist a richly balanced coloring. The RBC problem is shown to cover another well-known graph coloring scheme known as zero forcing sets. That is, if the damped nodes form a zero forcing set in the graph, then a richly balanced coloring does not exist, and thus parameter-independent stability is guaranteed. However, the full equivalence of zero forcing sets and parameter-independent stability holds true only for tree graphs. For more general graphs with few fundamental cycles, an algorithm, named chord node coloring, is proposed that significantly outperforms a brute-force search for solving the NP-complete RBC problem

Behavioral Experiments on a Network Formation Game

We report on an extensive series of behavioral experiments in which 36 human subjects collectively build a communication network over which they must solve a competitive coordination task for monetary compensation. There is a cost for creating network links, thus creating a tension between link expenditures and collective and individual incentives. Our most striking finding is the poor performance of the subjects, especially compared to our long series of prior experiments. We demonstrate that the subjects built difficult networks for the coordination task, and compare the structural properties of the built networks to standard generative models of social networks. We also provide extensive analysis of the individual and collective behavior of the subjects, including free riding and factors influencing edge purchasing decisions