How do states distribute the burdens of collective defense? This paper develops a network theory of burden sharing. We focus on bilateral defense cooperation agreements (DCAs), which promote cooperation in a variety of defense, military, and security issue areas. Using a computational model, we show that DCA partners’ defense spending depends on the network structure of their agreements. In bilateral terms, DCAs increase defense spending by committing states to defense activities and allowing partners to reciprocally punish free riding. However, as a state's local network of defense partnerships grows more densely connected, with many transitive “friend of a friend” relations, DCAs have the countervailing effect of reducing defense spending. The more deeply integrated states are in bilateral defense networks, the less they spend on defense. We distinguish two potential mechanisms behind this effect—one based on efficiency improvements, the other on free riding. An empirical analysis using multilevel inferential network models points more to efficiency than to free riding. Defense networks reduce defense spending, and they do so by allowing countries to produce security more efficiently.

We consider the specification of effects of numerical actor attributes, having an interval level of measurement, in statistical models for directed social networks. A fundamental mechanism is homophily or assortativity, where actors have a higher likelihood to be tied with others having similar values of the variable under study. But there are other mechanisms that may also play a role in how the attribute values of two actors influence the likelihood of a tie between them. We discuss three additional mechanisms: aspiration, the tendency to send more ties to others having high values; attachment conformity, sending more ties to others whose values are close to the “social norm”; and sociability, where those having higher values will tend to send more ties generally. These mechanisms may operate jointly, and then their effects will be confounded. We present a specification representing these effects simultaneously by a four-parameter quadratic function of the values of sender and receiver. Flexibility can be increased by a five-parameter extension. We argue that for numerical actor attributes having important effects on directed networks, these specifications may provide an improvement. An illustration is given of dependence of advice ties on academic grades, analyzed by the Stochastic Actor-oriented Model.

The temporal exponential random graph model (TERGM) and the stochastic actor-oriented model (SAOM, e.g., SIENA) are popular models for longitudinal network analysis. We compare these models theoretically, via simulation, and through a real-data example in order to assess their relative strengths and weaknesses. Though we do not aim to make a general claim about either being superior to the other across all specifications, we highlight several theoretical differences the analyst might consider and find that with some specifications, the two models behave very similarly, while each model out-predicts the other one the more the specific assumptions of the respective model are met.