#### Abstract

Scholars have increasingly become aware that actors’ self-selection into networks (e.g., homophily) is an important determinant of network-tie formation. Such self-selection adds methodological complexity to the empirical evaluation of the effects of network ties on individual behavior. Moreover, the endogenous network formation implies that network-tie structures and actors’ behavior “coevolve” over time. Therefore, in longitudinal network studies, it is very crucial for scholars to understand the nature of coevolutionary dynamics in the data, in order to explain the network-formation and the behavioral-decision-making mechanisms accurately. In this project, we claim that one of the most important aspects of the coevolutionary dynamic is its connection with history dependence. By history dependence, we primarily focus on what Page (2006) defines as “phat” and path dependence. We first establish theoretically that systems with coevolution can easily generate multiple equilibria (i.e., the steady states of the system), using a simple Markov type-interaction model that allows for endogenous tie formation. The potential of multiple equilibria posits an important and very difficult empirical question--how sensitive are equilibrium distributions (over types) to the past states? More simply put, to what extent does history matter? What is at stake in this question is not trivial. If history matters for an equilibrium attained in the society, then we can also analyze the potential policy interventions that could change the path of the social process such that it would lead to a socially optimal equilibrium. As for the empirical strategy, we start with developing a discrete-time Markov model, combining a spatial-logit and p-star model to evaluate the empirical significance of coevolutionary dynamics in the data. The strength of this empirical approach is in its direct connection with the theoretical Markov interaction model, and can provide a foundation for developing statistical tests for history dependence generated by coevolution.