Network Formation with Heterogeneous Nodes and Stochasticity

ed information set of each scientist (i.e., information about how many of each type of experiment each scientist has done), while they take as random the actual realizations of these random variables. So these probabilities reflect the assessment that a third-party observer would make before any connections are formed, knowing the experiments that each scientist has done, but not the outcomes of these experiments. The decision procedures scientists follow may be arbitrarily good or bad (relative to the unspecified decision problem). In this section I will only give some minimal constraints on δC i . These minimal behavioral assumptions turn out to be sufficient for the main result, theorem 13. In a slight abuse of notation, I use δC i to denote both i’s decision procedure and the total number of connections that i makes. The latter is a random variable, taking values in the non-negative integers, because it depends (in general) on the information obtained through the process. Let δC i,[A] denote the number of scientists with abstracted information set [A] that i connects to. Obviously, δC i,[A] is also a random variable and δC i,[A] is related to δC i :