Sex differences in trust and trustworthiness: A meta-analysis of the trust game and the gift-exchange game

We present a meta-analytic review of the literature on sex differences in the trust game (174 effect sizes) and the related gift-exchange game (35 effect sizes). Based on parental investment theory and social role theory we expected men to be more trusting and women to be more trustworthy. Indeed, men were more trusting in the trust game (g = 0.22), yet we found no significant sex difference in trust in the gift-exchange game (g = 0.15). Regarding trustworthiness, we found no significant sex difference in the trust game (g = −0.04), and we found men, not women, to be more trustworthy in the gift-exchange game (g = 0.33). These results suggest that men send more money than women do when their money is going to be multiplied, thereby creating an efficiency gain. This so-called “male multiplier effect” may be explained by a stronger psychological tendency in men to acquire resources.     

Ranking terrorists in networks: A sensitivity analysis of Al Qaeda's 9/11 attack

All over the world, intelligence services are collecting data concerning possible terrorist threats. This information is usually transformed into network structures in which the nodes represent the individuals in the data set and the links possible connections between these individuals. Unfortunately, it is nearly impossible to keep track of all individuals in the resulting complex network. Therefore, Lindelauf et al. (2013) introduced a methodology that ranks terrorists in a network. The rankings that result from this methodology can be used as a decision support system to efficiently allocate the scarce surveillance means of intelligence agencies. Moreover, usage of these rankings can improve the quality of surveillance which can in turn lead to prevention of attacks or destabilization of the networks under surveillance.The methodology introduced by Lindelauf et al. (2013) is based on a game theoretic centrality measure, which is innovative in the sense that it takes into account not only the structure of the network but also individual and coalitional characteristics of the members of the network. In this paper we elaborate on this methodology by introducing a new game theoretic centrality measure that better takes into account the operational strength of connected subnetworks.Moreover, we perform a sensitivity analysis on the rankings derived from this new centrality measure for the case of Al Qaeda's 9/11 attack. In this sensitivity analysis we consider firstly the possible additional information available about members of the network, secondly, variations in relational strength and, finally, the absence or presence of a small percentage of links in the network. We also introduce a case specific method to compare the different rankings that result from the sensitivity analysis and show that the new centrality measure is robust to small changes in the data.     

Measurement error in network data: A re-classification

Research on measurement error in network data has typically focused on missing data. We embed missing data, which we term false negative nodes and edges, in a broader classification of error scenarios. This includes false positive nodes and edges and falsely aggregated and disaggregated nodes. We simulate these six measurement errors using an online social network and a publication citation network, reporting their effects on four node-level measures – degree centrality, clustering coefficient, network constraint, and eigenvector centrality. Our results suggest that in networks with more positively-skewed degree distributions and higher average clustering, these measures tend to be less resistant to most forms of measurement error. In addition, we argue that the sensitivity of a given measure to an error scenario depends on the idiosyncracies of the measure's calculation, thus revising the general claim from past research that the more ‘global’ a measure, the less resistant it is to measurement error. Finally, we anchor our discussion to commonly-used networks in past research that suffer from these different forms of measurement error and make recommendations for correction strategies.     

A new method for finding hierarchical subgroups from networks

We present a new method for decomposing a social network into an optimal number of hierarchical subgroups. With a perfect hierarchical subgroup defined as one in which every member is automorphically equivalent to each other, the method uses the REGGE algorithm to measure the similarities among nodes and applies the k-means method to group the nodes that have congruent profiles of dissimilarities with other nodes into various numbers of hierarchical subgroups. The best number of subgroups is determined by minimizing the intra-cluster variance of dissimilarity subject to the constraint that the improvement in going to more subgroups is better than a network whose n nodes are maximally dispersed in the n-dimensional space would achieve. We also describe a decomposability metric that assesses the deviation of a real network from the ideal one that contains only perfect hierarchical subgroups. Four well known network data sets are used to demonstrate the method and metric. These demonstrations indicate the utility of our approach and suggest how it can be used in a complementary way to Generalized Blockmodeling for hierarchical decomposition.     

A game theoretic approach to measuring degree of centrality in social networks

We present a new measure of degree of centrality in a social network which is based on a natural extension of the Banzhaf (1965) index of power in an N-person game.     

On the core of characteristic function games associated with exchange networks

An exchange network is a social system in which the actors gain valued resources from bilateral transactions, but an opportunity to negotiate a deal is given only to those pairs of actors whose positions are tied with each other in a fixed communication network. A transaction consists in a mutually agreed-on division of a resource pool assigned to a network line. An additional constraint imposed on such a network restricts the range of transaction sets which may happen in a single negotiation round to those consistent with a given “exchange regime.” Under the one-exchange regime every actor is permitted to make no more than one deal per round. Bienenstock and Bonacich [Bienenstock, E.J., Bonacich, P., 1992. The core as a solution to exclusionary networks. Social Networks 14, 231–243] proposed to represent a one-exchange network with an n-person game in characteristic function form. The aim of this paper is to develop a mathematical theory of games associated with homogenous one-exchange networks (network homogeneity means that all lines are assigned resource pools of the same size). The focus is on the core, the type of solution considered most important in game theory. In particular, all earlier results obtained by Bonacich are re-examined and there is given a new graph-theoretic necessary and sufficient condition for the existence of nonempty core for the game representing a homogenous one-exchange network.     

What makes a network go round? Exploring the structure of a strong component with exponential random graph models

A strong component is a subgraph in a directed network where, following the direction of ties, all nodes in the graph are reachable from one another. Mutual reachability implies that every node in the graph is theoretically able to send materials to and/or influence every other node suggesting that strong components are amongst the more egalitarian network structures. Despite this intriguing feature, they remain understudied. Using exponential random graph models (ERGM) for directed networks, we investigate the social and structural processes underlying the generation of strong components. We illustrate our argument using a network of 301 nodes and 703 personal lending ties from Renaissance Florence. ERGM shows that our strong component arises from triadic clustering alongside an absence of higher-order star structures. We contend that these processes produce a strong component with a hierarchical, rather than an egalitarian structure: while some nodes are deeply embedded in a dense network of exchange, the involvement of others is more tenuous. More generally, we argue that such tiered core-periphery strong components will predominate in networks where the social context creates conditions for an absence of preferential attachment alongside the presence of localized closure. Although disparate social processes can give rise to hierarchical strong components linked to these two structural mechanisms, in Florence they are associated with the presence of multiple dimensions of social status and the connectedness of participants across disparate network domains.     

The Manipulation: Socio-economic decision making

We analyze one-shot Prisoner’s Dilemma decisions made by participants of the high-stakes TV game show The Manipulation, and document the influence of social life factors on economic decisions, alongside the participants’ rational considerations. In particular, we employ a social psychology approach to provide a new perspective on the determinants of financial assistance. Our insights from the TV game are corroborated by a controlled laboratory experiment. We find that helping and sharing behavior in strategic situations is explained by Attribution Theory (AT) and beliefs about expected cooperativeness. Specifically, participants’ decisions are influenced by perceived controllability of opponents’ conditions (an attributional characteristic influencing perception of responsibility and related emotions) and social-relations-based beliefs regarding the opponents’ expected cooperativeness.     

Models,methods and network topology: Experimental design for the study of interference

How should a network experiment be designed to achieve high statistical power? Experimental treatments on networks may spread. Randomizing assignment of treatment to nodes enhances learning about the counterfactual causal effects of a social network experiment and also requires new methodology (ex. Aronow and Samii, 2017a, Bowers et al., 2013, Toulis and Kao, 2013). In this paper we show that the way in which a treatment propagates across a social network affects the statistical power of an experimental design. As such, prior information regarding treatment propagation should be incorporated into the experimental design. Our findings justify reconsideration of standard practice in circumstances where units are presumed to be independent even in simple experiments: information about treatment effects is not maximized when we assign half the units to treatment and half to control. We also present an example in which statistical power depends on the extent to which the network degree of nodes is correlated with treatment assignment probability. We recommend that researchers think carefully about the underlying treatment propagation model motivating their study in designing an experiment on a network.     

Statistical power of the social network autocorrelation model

The network autocorrelation model has become an increasingly popular tool for conducting social network analysis. More and more researchers, however, have documented evidence of a systematic negative bias in the estimation of the network effect (ρ). In this paper, we take a different approach to the problem by investigating conditions under which, despite the underestimation bias, a network effect can still be detected by the network autocorrelation model. Using simulations, we find that moderately-sized network effects (e.g., ρ = .3) are still often detectable in modest-sized networks (i.e., 40 or more nodes). Analyses reveal that statistical power is primarily a nonlinear function of network effect size (ρ) and network size (N), although both of these factors can interact with network density and network structure to impair power under certain rare conditions. We conclude by discussing implications of these findings and guidelines for users of the autocorrelation model.     

Moral values and increasing stakes in a dictator game

Using data from a large representative US sample (N = 1519), we compare hypothetical moral fairness values from the Moral Foundations Sacredness Scale with actual fairness behavior in an incentivized dictator game with either low or high stakes. We find that people with high moral fairness values fail to live up to their high fairness standards, when stake size increases. This violates principles from consistency theories according to which moral values are supposedly aligned with moral behavior, but is in line with temptation theories that question the absoluteness of morality values.     

A value for games with coalition structures

This paper presents an axiomatization of a value for games with coalition structures which is an alternative to the Owen Value. The motor of this new axiomatization is a consistency axiom based on an associated game, which is not a reduced game. The new value of an n-player unanimity game is the compound average of the new values of all the (n-1)-player unanimity games. The new value of a unanimity game allocates to bigger coalitions a larger share of the total wealth. Note that the Owen value allocates to all the coalitions the same share independently of their size.     

Missing data in networks: exponential random graph (p1) models for networks with non-respondents

Survey studies of complete social networks often involve non-respondents, whereby certain people within the “boundary” of a network do not complete a sociometric questionnaire—either by their own choice or by the design of the study—yet are still nominated by other respondents as network partners. We develop exponential random graph (p¹) models for network data with non-respondents. We model respondents and non-respondents as two different types of nodes, distinguishing ties between respondents from ties that link respondents to non-respondents. Moreover, if we assume that the non-respondents are missing at random, we invoke homogeneity across certain network configurations to infer effects as applicable to the entire set of network actors. Using an example from a well-known network dataset, we show that treating a sizeable proportion of nodes as non-respondents may still result in estimates, and inferences about structural effects, consistent with those for the entire network.If, on the other hand, the principal research focus is on the respondent-only structure, with non-respondents clearly not missing at random, we incorporate the information about ties to non-respondents as exogenous. We illustrate this model with an example of a network within and between organizational departments. Because in this second class of models the number of non-respondents may be large, values of parameter estimates may not be directly comparable to those for models that exclude non-respondents. In the context of discussing recent technical developments in exponential random graph models, we present a heuristic method based on pseudo-likelihood estimation to infer whether certain structural effects may contribute substantially to the predictive capacity of a model, thereby enabling comparisons of important effects between models with differently sized node sets.     

How do private entrepreneurs transform local social capital into economic capital? Four case studies from rural Denmark

Bourdieu's (1986) General Theory of the Economy of Practices assumes that people perpetually transform tangible and intangible forms of capital according to certain ‘laws of conversion’. On this background, and combining sociology and micro-economics, we analyze specific strings of capital conversion in time and space. More specifically, we raise the question: How do private entrepreneurs transform local social capital into economic capital? We combine in-depth interviews with four private entrepreneurs in rural Denmark with Prisoner's Dilemma game theory. Thus each of our cases illustrates one of the outcomes in the PD matrix. In this way we explain why only one of the four entrepreneurs succeeds in capitalizing social capital.     

Spectral goodness of fit for network models

We introduce a new statistic, ‘spectral goodness of fit’ (SGOF) to measure how well a network model explains the structure of the pattern of ties in an observed network. SGOF provides a measure of fit analogous to the standard R² in linear regression. Additionally, as it takes advantage of the properties of the spectrum of the graph Laplacian, it is suitable for comparing network models of diverse functional forms, including both fitted statistical models and algorithmic generative models of networks. After introducing, defining, and providing guidance for interpreting SGOF, we illustrate the properties of the statistic with a number of examples and comparisons to existing techniques. We show that such a spectral approach to assessing model fit fills gaps left by earlier methods and can be widely applied.     

A mixed membership model-based measure for subgroup integration in social networks

Social networks analysis often involves quantifying subgroup structure in which tie density is greater among nodes in the same subgroup than between subgroups. One such measure, subgroup insularity or segregation, is the extent that subgroups are separate from each other. We introduce a new measure, γ, which is a parameter from the mixed membership stochastic blockmodel (MMSBM; Airoldi et al., 2008), and differs from many existing measures in that γ does not depend on node membership. We compare this measure to several well-known measures and use simulation studies and real data analysis to provide insight into how this measure can be used in practice.     

Trust between individuals and groups: Groups are less trusting than individuals but just as trustworthy

We compare the behavior of groups and individuals in a two-person trust game. The first mover in this game, the sender, receives an endowment and can send any part of it to the responder; the amount sent is tripled, and the responder can then return to the sender any portion of the tripled sum. In a 2 × 2 design, the players in the roles of sender and responder are either individuals or groups of three players (who conduct face-to-face discussions to decide on a collective group strategy). We find that groups in the role of sender send smaller amounts than individuals, and expect lower returns. In particular, groups send nothing more often than individuals do (and are even more likely to do so when the responder is another group). Groups and individuals in the role of responder return on average the same fraction of the amount sent. Hence, we conclude that groups are less trusting than individuals, but just as trustworthy.     

Closeness centrality via the Condorcet principle

We provide a characterization of closeness centrality in the class of distance-based centralities. To this end, we introduce a natural property, called majority comparison, that states that out of two adjacent nodes the one closer to more nodes is more central. We prove that any distance-based centrality that satisfies this property gives the same ranking in every graph as closeness centrality. The axiom is inspired by the interpretation of the graph as an election in which nodes are both voters and candidates and their preferences are determined by the distances to the other nodes.     

Motivations for self-assembling into project teams

This study investigates the self-assembly mechanisms of ad hoc project teams using a bipartite network perspective. Individuals and projects are modeled as two types of nodes and team membership as relations between them. This approach enables us to investigate factors that impact voluntary team assembly at the individual, dyadic, and team levels simultaneously. Using Exponential Random Graph Models (ERGM/p*), we study players’ combat teams in a Massively Multiplayer Online Role-Playing Game (MMORPG) as a case of self-assembled project teams. Empirical results show that individuals are motivated to join ad hoc teams to complete difficult projects but not projects with long durations. We also found that individuals tend to collaborate with specific teammates who have complementary skills, those who have similar age or skill level, and those who are affiliated with the same organizational entity.