A general analysis of boundedly rational learning in social networks

Abstract

We analyze boundedly rational learning in social networks within binary action environments. We establish how learning outcomes depend on the environment (i.e., informational structure, utility function), the axioms imposed on the updating behavior, and the network structure. In particular, we provide a normative foundation for quasi‐Bayesian updating, where a quasi‐Bayesian agent treats others' actions as if they were based only on their private signal. Quasi‐Bayesian updating induces learning (i.e., convergence to the optimal action for every agent in every connected network) only in highly asymmetric environments. In all other environments, learning fails in networks with a diameter larger than 4. Finally, we consider a richer class of updating behavior that allows for nonstationarity and differential treatment of neighbors' actions depending on their position in the network. We show that within this class there exist updating systems that induce learning for most networks.

A Structural Model for Network Games with Incomplete Information

“…In econometric studies on the identification and structural estimation of social network formation models, there is still room for researchers to (Ballester et al, 2006;Cohen-Cole et al, 2018;De Paula et al, 2018;Elhorst et al, 2012;Graham, 2017;Huang et al, 2020;Leung, 2020;Sheng, 2020). The main issues of social and economic interaction networks are to establish the emergence of social learning and bounded rational learning (Acemoglu et al, 2011;Mueller-Frank and Neri, 2021), exchange of information (Acemoglu et al, 2014;Leung, 2020) and, development and stability of structural groups within the network itself (Sheng, 2020;Stadtfeld et al, 2020). 5 This is due to several reasons.…”

“…Of course, in situations of uncertainty, when players have partial information, observational learning is a crucial component of interaction. Among the many possible mechanisms by which players learn from each other, observational learning describes the process by which a player draws inferences about the information held by other players based on observation of their behavior (Mueller-Frank and Neri, 2021).…”

Bayesian Decision Making in Groups is Hard

“…In contrast, we think of our model as relevant to situations where, as is often the case, it is not practical to exhaustively list all of one's evidence and reasoning instead of stating or summarizing one's opinion. A popular approach to study bounded rationality is by replacing Bayesian actions with heuristic (non-Bayesian) rules (Arieli et al 2019a,b, Bala and Goyal 1998, DeGroot 1974, Golub and Jackson 2010, Jadbabaie et al 2012, Li and Tan 2018, Molavi et al 2018, Mueller-Frank and Neri 2017. These rules are often rooted in empirically observed behavioral and cognitive biases.…”

Sequential Naive Learning

“…Under quasi-Bayesian prior formation, which was first introduced by Eyster and Rabin [19] 6 each observed action is treated as if it were a Bayesian best response to only the private signal of the agent taking the action. 7 For experimental findings supporting the quasi-Bayesian updating heuristic see Eyster, Rabin, and Weizsacker [20], Mueller-Frank and Neri [40] and Dasaratha and He [14]. Since agents observe only the unordered set of past actions, the identities of the agents taking a given action are not observed.…”

“…Eyster and Rabin[19] refer to this as best response trailing naive inference 7. Further studies of this heuristic include Mueller-Frank and Neri[40], Levy and Razin[34], Dasaratha and He[15], and Arieli, Babichenko, and Shlomov[3] 8. Unless agents have a distribution over the order with which actions are taken.…”