scholarly journals Social Learning Equilibria

Econometrica ◽  
2020 ◽  
Vol 88 (3) ◽  
pp. 1235-1267 ◽  
Author(s):  
Elchanan Mossel ◽  
Manuel Mueller-Frank ◽  
Allan Sly ◽  
Omer Tamuz
Keyword(s):  
Social Learning ◽  
Information Aggregation ◽  
Equilibrium Concept ◽  
Extensive Form ◽  
Equilibrium Behavior ◽  
Dynamic Setting ◽  
Private Signals ◽  
The Given ◽  
Asymptotic Equilibrium ◽  
General Dynamic

We consider a large class of social learning models in which a group of agents face uncertainty regarding a state of the world, share the same utility function, observe private signals, and interact in a general dynamic setting. We introduce social learning equilibria, a static equilibrium concept that abstracts away from the details of the given extensive form, but nevertheless captures the corresponding asymptotic equilibrium behavior. We establish general conditions for agreement, herding, and information aggregation in equilibrium, highlighting a connection between agreement and information aggregation.

scholarly journals Misinterpreting Others and the Fragility of Social Learning

Econometrica ◽  
2020 ◽  
Vol 88 (6) ◽  
pp. 2281-2328 ◽  
Author(s):  
Mira Frick ◽  
Ryota Iijima ◽  
Yuhta Ishii
Keyword(s):  
Social Learning ◽  
Negative Impact ◽  
Information Aggregation ◽  
The State ◽  
Type Distribution ◽  
Long Run ◽  
Private Signals ◽  
The World ◽  
True State ◽  
Over Time

We exhibit a natural environment, social learning among heterogeneous agents, where even slight misperceptions can have a large negative impact on long‐run learning outcomes. We consider a population of agents who obtain information about the state of the world both from initial private signals and by observing a random sample of other agents' actions over time, where agents' actions depend not only on their beliefs about the state but also on their idiosyncratic types (e.g., tastes or risk attitudes). When agents are correct about the type distribution in the population, they learn the true state in the long run. By contrast, we show, first, that even arbitrarily small amounts of misperception about the type distribution can generate extreme breakdowns of information aggregation, where in the long run all agents incorrectly assign probability 1 to some fixed state of the world, regardless of the true underlying state. Second, any misperception of the type distribution leads long‐run beliefs and behavior to vary only coarsely with the state, and we provide systematic predictions for how the nature of misperception shapes these coarse long‐run outcomes. Third, we show that how fragile information aggregation is against misperception depends on the richness of agents' payoff‐relevant uncertainty; a design implication is that information aggregation can be improved by simplifying agents' learning environment. The key feature behind our findings is that agents' belief‐updating becomes “decoupled” from the true state over time. We point to other environments where this feature is present and leads to similar fragility results.

A General Analysis of Sequential Social Learning

2021 ◽  
Author(s):  
Itai Arieli ◽  
Manuel Mueller-Frank
Keyword(s):  
Social Learning ◽  
Utility Function ◽  
Posterior Probability ◽  
General Analysis ◽  
Sufficient Condition ◽  
Important Class ◽  
General Utility ◽  
Learning Game ◽  
Necessary And Sufficient ◽  
The Given

This paper analyzes a sequential social learning game with a general utility function, state, and action space. We show that asymptotic learning holds for every utility function if and only if signals are totally unbounded, that is, the support of the private posterior probability of every event contains both zero and one. For the case of finitely many actions, we provide a sufficient condition for asymptotic learning depending on the given utility function. Finally, we establish that for the important class of simple utility functions with finitely many actions and states, pairwise unbounded signals, which generally are a strictly weaker notion than unbounded signals, are necessary and sufficient for asymptotic learning.

scholarly journals Learning from prices: information aggregation and accumulation in an asset market

2020 ◽  
Author(s):  
Michele Berardi
Keyword(s):  
Private Information ◽  
Dynamic Properties ◽  
Public Information ◽  
Information Aggregation ◽  
Time Varying ◽  
Private Signals ◽  
Private And Public ◽  
Fundamental Value ◽  
Over Time

Abstract Can prices convey information about the fundamental value of an asset? This paper considers this problem in relation to the dynamic properties of the fundamental (whether it is constant or time-varying) and the structure of information available to agents. Risk-averse traders receive two potential signals each period: one exogenous and private and the other, prices, endogenous and public. Prices aggregate private information but include aggregate noise. Information can accumulate over time both through endogenous and exogenous signals. With a constant fundamental, the precision of both private and public cumulative information increases over time but agents put progressively more weight on the endogenous signals, asymptotically disregarding private ones. If the fundamental is time-varying, the use of past private signals complicates the role of prices as a source of information, since it introduces endogenous serial correlation in the price signal and cross-correlation between it and innovations in the fundamental. A modified version of the Kalman filter can still be used to extract information from prices and results show that the precision of the endogenous signals converges to a constant, with both private and public information used at all times.

scholarly journals Quasi-Perfect Stackelberg Equilibrium

2019 ◽  
Vol 33 ◽  
pp. 2117-2124 ◽  
Author(s):  
Alberto Marchesi ◽  
Gabriele Farina ◽  
Christian Kroer ◽  
Nicola Gatti ◽  
Tuomas Sandholm
Keyword(s):  
Broad Class ◽  
Stackelberg Equilibrium ◽  
Correlated Equilibrium ◽  
Equilibrium Concept ◽  
Extensive Form ◽  
Tree Form ◽  
Axiomatic Definition ◽  
Security Games ◽  
Definition Of ◽  
Perfect Equilibria

Equilibrium refinements are important in extensive-form (i.e., tree-form) games, where they amend weaknesses of the Nash equilibrium concept by requiring sequential rationality and other beneficial properties. One of the most attractive refinement concepts is quasi-perfect equilibrium. While quasiperfection has been studied in extensive-form games, it is poorly understood in Stackelberg settings—that is, settings where a leader can commit to a strategy—which are important for modeling, for example, security games. In this paper, we introduce the axiomatic definition of quasi-perfect Stackelberg equilibrium. We develop a broad class of game perturbation schemes that lead to them in the limit. Our class of perturbation schemes strictly generalizes prior perturbation schemes introduced for the computation of (non-Stackelberg) quasi-perfect equilibria. Based on our perturbation schemes, we develop a branch-and-bound algorithm for computing a quasi-perfect Stackelberg equilibrium. It leverages a perturbed variant of the linear program for computing a Stackelberg extensive-form correlated equilibrium. Experiments show that our algorithm can be used to find an approximate quasi-perfect Stackelberg equilibrium in games with thousands of nodes.

On the Efficiency of Social Learning

Econometrica ◽  
2019 ◽  
Vol 87 (6) ◽  
pp. 2141-2168 ◽  
Author(s):  
Dinah Rosenberg ◽  
Nicolas Vieille
Keyword(s):  
Social Learning ◽  
Simple Condition ◽  
Learning Models ◽  
Binary Decision ◽  
Learning Efficiency ◽  
Private Signals ◽  
Entire Sequence ◽  
Necessary And Sufficient

We revisit prominent learning models in which a sequence of agents make a binary decision on the basis of both a private signal and information related to past choices. We analyze the efficiency of learning in these models, measured in terms of the expected welfare. We show that, irrespective of the distribution of private signals, learning efficiency is the same whether each agent observes the entire sequence of earlier decisions or only the previous decision. In addition, we provide a simple condition on the signal distributions that is necessary and sufficient for learning efficiency. This condition fails to hold in many cases of interest. We discuss a number of extensions and variants.

scholarly journals Rational Groupthink*

2020 ◽  
Vol 136 (1) ◽  
pp. 621-668 ◽  
Author(s):  
Matan Harel ◽  
Elchanan Mossel ◽  
Philipp Strack ◽  
Omer Tamuz
Keyword(s):  
Information Aggregation ◽  
Rational Agents ◽  
Private Signals

Abstract We study how long-lived rational agents learn from repeatedly observing a private signal and each others’ actions. With normal signals, a group of any size learns more slowly than just four agents who directly observe each others’ private signals in each period. Similar results apply to general signal structures. We identify rational groupthink—in which agents ignore their private signals and choose the same action for long periods of time—as the cause of this failure of information aggregation.

scholarly journals LOGARITHMIC MARKETS CORING RULES FOR MODULAR COMBINATORIAL INFORMATION AGGREGATION

2012 ◽  
Vol 1 (1) ◽  
pp. 3-15 ◽  
Author(s):  
Robin Hanson
Keyword(s):  
Conditional Independence ◽  
Information Aggregation ◽  
Scoring Rules ◽  
Conditional Probabilities ◽  
Probability Estimates ◽  
Or Groups ◽  
Betting Markets ◽  
The Given ◽  
Independence Relations

In practice, scoring rules elicit good probability estimates from individuals, while betting markets elicit good consensus estimates from groups. Market scoring rules combine these features, eliciting estimates from individuals or groups, with groups costing no more than individuals. Regarding a bet on one event given another event, only logarithmic versions preserve the probability of the given event. Logarithmic versions also preserve the conditional probabilities of other events, and so preserve conditional independence relations. Given logarithmic rules that elicit relative probabilities of base event pairs, it costs no more to elicit estimates on all combinations of these base events.

Complementary Information and Learning Traps*

2019 ◽  
Vol 135 (1) ◽  
pp. 389-448 ◽  
Author(s):  
Annie Liang ◽  
Xiaosheng Mu
Keyword(s):  
Social Learning ◽  
Information Sources ◽  
Information Aggregation ◽  
Large Set ◽  
Complementary Information ◽  
Simple Property ◽  
Unknown State ◽  
Long Run ◽  
Efficient Information ◽  
Correlated Information

Abstract We develop a model of social learning from complementary information: short-lived agents sequentially choose from a large set of flexibly correlated information sources for prediction of an unknown state, and information is passed down across periods. Will the community collectively acquire the best kinds of information? Long-run outcomes fall into one of two cases: (i) efficient information aggregation, where the community eventually learns as fast as possible; (ii) “learning traps,” where the community gets stuck observing suboptimal sources and information aggregation is inefficient. Our main results identify a simple property of the underlying informational complementarities that determines which occurs. In both regimes, we characterize which sources are observed in the long run and how often.

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