Social Learning in a Changing World

Econometrica, 2021

This paper proposes a tractable model of Bayesian learning on large random networks where agents choose whether to adopt an innovation. We study the impact of the network structure on learning dynamics and product diffusion. In directed networks, all direct and indirect links contribute to agents' learning. In comparison, learning and welfare are lower in undirected networks and networks with cliques. In a rich class of networks, behavior is described by a small number of differential equations, making the model useful for empirical work.

2015

We theoretically and empirically study an incomplete information model of social learning. Agents initially guess the binary state of the world after observing a private signal. In subsequent rounds, agents observe their network neighbors' previous guesses before guessing again. Types are drawn from a mixture of learning models-Bayesian, where agents face incomplete information about others' types, and DeGroot, where agents follow the majority of their neighbors' previous period guesses. We study (1) learning features of both types in our incomplete information model; (2) what network structures lead to failures of asymptotic learning; (3) whether realistic networks exhibit such structures. We conducted lab experiments with 665 subjects in Indian villages, and 350 students from ITAM in Mexico. We conduct a reduced form analysis and then structurally estimate the mixing parameter, finding the share of Bayesian agents to be 10% and 50% in the village and student samples, respectively.

We study models of learning in games where agents with limited memory use social information to decide when and how to change their play. When agents only observe the aggregate distribution of payoffs and only recall information from the last period, we show that aggregate play comes close to Nash equilibrium behavior for (generic) games, and that pure equilibria are generally more stable than mixed equilibria. When agents observe not only the payoff distribution of other agents but also the actions that led to those payoffs, and can remember this for some time, the length of memory plays a key role. When agents' memory is short, aggregate play may not come close to Nash equilibrium, but it does so if the game satisfies a acyclicity condition. When agents have sufficiently long memory their behavior comes close to Nash equilibrium for generic games. However, unlike in the model where social information is solely about how well other agents are doing, mixed equilibria can be favored over pure ones.

I present a model of social learning over an exogenous, directed network that may be readily nested within broader macroeconomic models with dispersed information and combines the attributes that agents (a) act repeatedly and simultaneously; (b) are Bayes-rational; and (c) have strategic interaction in their decision rules. To overcome the challenges imposed by these requirements, I suppose that the network is opaque: agents do not know the full structure of the network, but do know the link distribution. I derive a specific law of motion for the hierarchy of aggregate expectations, which includes a role for network shocks (weighted sums of agents' idiosyncratic shocks). The network causes agents' beliefs to exhibit increased persistence, so that average expectations overshoot the truth following an aggregate shock. When the network is sufficiently (and plausibly) irregular, transitory idiosyncratic shocks cause persistent aggregate effects, even when agents are identically sized and do not trade.

This paper analyzes a model of social learning in a social network. Agents decide whether or not to adopt a new technology with unknown payoffs based on their prior beliefs and the experiences of their neighbors in the network. Using a mean-field approximation, we prove that the diffusion process always has at least one stable equilibrium, and we examine the dependance of the set of equilibria on the model parameters and the structure of the network. In particular, we show how first and second order stochastic dominance shifts in the degree distribution of the network impact diffusion. We find that the relationship between equilibrium diffusion levels and network structure depends on the distribution of payoffs to adoption and the distribution of agents’ prior beliefs regarding those payoffs, and we derive the precise conditions characterizing those relationships.

PloS one, 2016

This paper advances theories of social learning through an empirical examination of how social networks change over time. Social networks are important for learning because they constrain individuals' access to information about the behaviors and cognitions of other people. Using data on a large social network of mobile device users over a one-month time period, we test three hypotheses: 1) attraction homophily causes individuals to form ties on the basis of attribute similarity, 2) aversion homophily causes individuals to delete existing ties on the basis of attribute dissimilarity, and 3) social influence causes individuals to adopt the attributes of others they share direct ties with. Statistical models offer varied degrees of support for all three hypotheses and show that these mechanisms are more complex than assumed in prior work. Although homophily is normally thought of as a process of attraction, people also avoid relationships with others who are different. These mecha...

Decision and Control, 2008 …, 2008

We study the problem of dynamic learning by a social network of agents. Each agent receives a signal about an underlying state and communicates with a subset of agents (his neighbors) in each period. The network is connected. In contrast to the majority of existing learning models, we focus on the case where the underlying state is time-varying. We consider the following class of rule of thumb learning rules: at each period, each agent constructs his posterior as a weighted average of his prior, his signal and the information he receives from neighbors. The weights given to signals can vary over time and the weights given to neighbors can vary across agents. We distinguish between two subclasses: (1) constant weight rules;

2010

IEEE Transactions on Control of Network Systems, 2022

We study non-Bayesian social learning on random directed graphs and show that under mild assumptions on the connectivity of the network, all the agents almost surely learn the true state of the world asymptotically in time if the sequence of the associated weighted adjacency matrices belongs to Class P* (a broad class of stochastic chains that subsumes uniformly strongly connected chains). We show that though uniform strong connectivity is not necessary for asymptotic learning, it helps ensure that all the agents' beliefs converge to a consensus almost surely even when the true state is not identifiable. We then show how our main result applies to a few variants of the original model such as inertial non-Bayesian learning and learning in the presence of link failures. Besides, we show that our main result is an extension of a few known results that pertain to learning on time-varying graphs. We also show by proof and an example that if the network of influences is balanced in a ...

Physica A-statistical Mechanics and Its Applications, 2008

We consider a social system of interacting heterogeneous agents with learning abilities, a model close to Random Field Ising Models, where the random field corresponds to the idiosyncratic willingness to pay. Given a fixed price, agents decide repeatedly whether to buy or not a unit of a good, so as to maximize their expected utilities. We show that the equilibrium reached by the system depends on the nature of the information agents use to estimate their expected utilities.