Template-Type: ReDIF-Paper 1.0 Author-Name: Anqi Li Author-Workplace-Name: Department of Economics, University of Waterloo, Canada Title: A Rational Inattention Theory of Echo Chamber Abstract: We develop a rational inattention theory of echo chamber, whereby players gather information about an uncertain state by allocating limited attention capacities across biased primary sources and the other players. The resulting Poisson attention network transmits information from the primary source to a player either directly or indirectly through the other players. Rational inattention generates heterogeneous demands for information among players who are initially biased towards different decisions. In an echo chamber equilibrium, each player restricts attention to his own-biased source and like-minded friends, as the latter attend to the same primary source as his, and so could serve as secondary sources in case the information transmission from the primary source to him is disrupted. We provide sufficient conditions that give rise to echo chamber equilibria, characterize the attention networks within echo chambers, and use our results to inform the design and regulation of information platforms. Length: 60 pages Creation-Date: 2023-07 Revision-Date: File-URL: https://uwaterloo.ca/economics/sites/default/files/uploads/documents/a-rational-inattention-theory-of-echo-chamber.pdf File-Format: Application/pdf Number: 23001 Classification-JEL: D83, D85 Handle: RePEc:wat:wpaper:23001 Template-Type: ReDIF-Paper 1.0 Author-Name: Clemens Possnig Author-Workplace-Name: Department of Economics, University of Waterloo, Canada Title: Reinforcement Learning and Collusion Abstract: This paper presents an analytical characterization of the long run policies learned by algorithms that interact repeatedly. These algorithms update policies which are maps from observed states to actions. I show that the long run policies correspond to equilibria that are stable points of a tractable differential equation. As a running example, I consider a repeated Cournot game of quantity competition, for which learning the stage game Nash equilibrium serves as non-collusive benchmark. I give necessary and sufficient conditions for this Nash equilibrium not to be learned. These conditions are requirements on the state variables algorithms use to determine their actions, and on the stage game. When algorithms determine actions based only on the past period's price, the Nash equilibrium can be learned. However, agents may condition their actions on richer types of information beyond the past period's price. In that case, I give sufficient conditions such that the policies converge with positive probability to a collusive equilibrium, while never converging to the Nash equilibrium. Length: 72 pages Creation-Date: 2023-07 Revision-Date: File-URL: https://uwaterloo.ca/economics/sites/default/files/uploads/documents/reinforcement-learning-and-collusion.pdf File-Format: Application/pdf Number: 23002 Classification-JEL: C73, D43, D83 Handle: RePEc:wat:wpaper:23002 Template-Type: ReDIF-Paper 1.0 Author-Name: Clemens Possnig Author-Workplace-Name: Department of Economics, University of Waterloo, Canada Title: Learning to Best Reply: On the Consistency of Multi-Agent Batch Reinforcement Learning Abstract: This paper provides asymptotic results for a class of model-free actor-critic batch - reinforcement learning algorithms in the multi-agent setting. At each period, each agent faces an estimation problem (the critic, e.g. a value function), and a policy updating problem. The estimation step is done by parametric function estimation based on a batch of past observations. Agents have no knowledge of each others incentives and policies. I provide sufficient conditions for each agent's parametric function estimator to be consistent in the multi-agent environment, which enables agents to learn to best respond despite the non-stationarity inherent in multi-agent systems. The conditions depend on the environment, batch size, and policy step size. These sufficient conditions are useful in the asymptotic analysis of multi-agent learning, e.g. in the application of long-run characterisations using stochastic approximation techniques. Length: 22 pages Creation-Date: 2023-08 Revision-Date: File-URL: https://uwaterloo.ca/economics/sites/default/files/uploads/documents/learning-to-best-reply-on-the-consistency-of-multi-agent-reinforcement-learning.pdf File-Format: Application/pdf Number: 23003 Classification-JEL: Handle: RePEc:wat:wpaper:23003 Template-Type: ReDIF-Paper 1.0 Author-Name: Clemens Possnig Author-Workplace-Name: Department of Economics, University of Waterloo, Canada Author-Name: Andreea Rotarescu Author-Workplace-Name: Department of Economics, Wake Forest University, Winston-Salem, USA Author-Name: Kyungchul Song Author-Workplace-Name: Vancouver School of Economics, University of British Columbia, Vancouver, Canada Title: Estimating Dynamic Spillover Effects Along Multiple Networks in a Linear Panel Model Abstract: Spillover of economic outcomes often arises over multiple networks, and distinguishing their separate roles is important in empirical research. For example, the direction of spillover between two groups (such as banks and industrial sectors linked in a bipartite graph)has important economic implications, and a researcher may want to learn which direction is supported in the data. For this, we need to have an empirical methodology that allows for both directions of spillover simultaneously. In this paper, we develop a dynamic linear panel model and asymptotic inference with large n and small T, where both directions of spillover are accommodated through multiple networks. Using the methodology developed here, we perform an empirical study of spillovers between bank weakness and zombie-firm congestion in industrial sectors, using firm-bank matched data from Spain between 2005 and 2012. Overall, we find that there is positive spillover in both directions between banks and sectors Length: 59 pages Creation-Date: 2022-11 Revision-Date: File-URL: https://uwaterloo.ca/economics/sites/default/files/uploads/documents/estimating-dynamic-spillover-effects-along-multiple-networks-in-a-linear-panel-model.pdf File-Format: Application/pdf Number: 22007 Classification-JEL: C12, C21, C31, E44, G21, G32 Handle: RePEc:wat:wpaper:22007 Template-Type: ReDIF-Paper 1.0 Author-Name: Anqi Li Author-Workplace-Name: Department of Economics, University of Waterloo, Canada Author-Name: Federico Echenique Author-Workplace-Name: Department of Economics, University of California, Berkeley, United States Title: Rationally Inattentive Statistical Discrimination: Arrow Meets Phelps Abstract: WWhen information acquisition is costly but flexible, a principal may rationally acquire information that favors “majorities†over “minorities†unless the latter are strictly more productive than the former. Majorities therefore face incentives to invest in becoming productive, whereas minorities are discouraged from such investments. The principal, in turn, focuses scarce attentional resources on majorities precisely because they are likely to invest. We give conditions under which the resulting discriminatory equilibrium is most preferred by the principal, despite that all groups are ex-ante identical. Our results add to the discussions of affirmative action, implicit bias, and occupational segregation and stereotypes. Length: 60 pages Creation-Date: 2022-12 Revision-Date: 2023-08 File-URL: https://uwaterloo.ca/economics/sites/default/files/uploads/documents/rationally-inattentive-statistical-discrimination-arrow-meets-phelps_0.pdf File-Format: Application/pdf Number: 23004 Classification-JEL: D82, D86, D31, J71 Handle: RePEc:wat:wpaper:23004 Template-Type: ReDIF-Paper 1.0 Author-Name: Lin Hu Author-Workplace-Name: Research School of Finance, Actuarial Studies and Statistics, Australian National University Author-Name: Matthew Kovach Author-Workplace-Name: Department of Economics, Purdue University Author-Name: Anqi Li Author-Workplace-Name: Department of Economics, University of Waterloo, Canada Title: Learning News Bias: Misspecifications and Consequences Abstract: We study how a decision maker (DM) learns about the bias of unfamiliar news sources. Absent any frictions, a rational DM uses known sources as a yardstick to discern the true bias of a source. If a DM has misspecified beliefs, this process fails. We derive long-run beliefs, behavior, welfare, and corresponding comparative statics, when the DM has dogmatic, incorrect beliefs about the bias of known sources. The distortion due to misspecified learning is succinctly captured by a single-dimensional metric we introduce. Our model generates the hostile media effect and false polarization, and has implications for fact-checking and misperception recalibration. Length: 40 pages Creation-Date: 2023-09 File-URL: https://uwaterloo.ca/economics/sites/default/files/uploads/documents/learning-news-bias-misspecifications-and-consequences.pdf File-Format: Application/pdf Number: 23005 Classification-JEL: Handle: RePEc:wat:wpaper:23005