Networks, decisions, and outcomes : coordination with local information and the value of temporal data for learning influence networks

Abstract

We study decision making by networked entities and the interplay between networks and outcomes under two different contexts: in the first part of the thesis, we study how strategic agents that share local information coordinate; in the second part of the thesis, we quantify the gain of having access to temporally richer data for learning of influence networks. In the first part of the thesis, we study the role of local information channels in enabling coordination among strategic agents. Building on the standard finite-player global games framework, we show that the set of equilibria of a coordination game is highly sensitive to how information is locally shared among agents. In particular, we show that the coordination game has multiple equilibria if there exists a collection of agents such that (i) they do not share a common signal with any agent outside of that collection; and (ii) their information sets form an increasing sequence of nested sets, referred to as a filtration. Our characterization thus extends the results on the uniqueness and multiplicity of equilibria in global games beyond the well-known case in which agents have access to purely private or public signals. We then provide a characterization of how the extent of equilibrium multiplicity is determined by the extent to which subsets of agents have access to common information: we show that the size of the set of equilibrium strategies is increasing with the extent of variability in the size of the subsets of agents who observe the same signal. We study the set of equilibria in large coordination games, showing that as the number of agents grows, the game exhibits multiple equilibria if and only if a non-vanishing fraction of the agents have access to the same signal. We finally consider an application of our framework in which the noisy signals are interpreted to be the idiosyncratic signals of the agents, which are exchanged through a communication network. In the second part of the thesis, we quantify the gain in the speed of learning of parametric models of influence, due to having access to richer temporal information. We infer local influence relations between networked entities from data on outcomes and assess the value of temporal data by characterizing the speed of learning under three different types of available data: knowing the set of entities who take a particular action; knowing the order in which the entities take an action; and knowing the times of the actions. We propose a parametric model of influence which captures directed pairwise interactions and formulate different variations of the learning problem. We use the Fisher information, the Kullback-Leibler (KL) divergence, and sample complexity as measures for the speed of learning. We provide theoretical guarantees on the sample complexity for correct learning based on sets, sequences, and times. The asymptotic gain of having access to richer temporal data for the speed of learning is thus quantified in terms of the gap between the derived asymptotic requirements under different data modes. We also evaluate the practical value of learning with richer temporal data, by comparing learning with sets, sequences, and times given actual observational data. Experiments on both synthetic and real data, including data on mobile app installation behavior, and EEG data from epileptic seizure events, quantify the improvement in learning due to richer temporal data, and show that the proposed methodology recovers the underlying network well.