No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Social Learning and Costly Information Acquisition
Abstract
Short-lived agents want to predict a random variable and have to decide how much effort to devote to collect private information and consequently how much to rely on public information. The latter is just a noisy average of past predictions. It is shown that costly information acquisition prevents an unbounded accumulation of public information if (and only if) the marginal cost to acquire information is positive at zero . When public precision at period n, , tends to infinity with n but the rate of convergence of public information to is slowed down with respect to the exogenous information case. At the market outcome agents acquire too little private information. This happens either with respect to a (decentralized) first best benchmark or, for n large, with respect to a (decentralized) second best benchmark. For high discount factors the limit point of market public precision always falls short of the welfare benchmarks whenever . In the extreme, as the discount factor tends to one public precision tends to infinity in the welfare-optimal programs while it remains bounded at the market solution. Otherwise, if public precision accumulates in an unbounded way both at the first and second best solutions. More public information may hurt at either the market or second best solutions.
... The main ideas of an early contribution on costly signal acquisition by Burguet and Vives (2000) can be seen in a simplified model with unbounded signals and continuous actions and states. Agents seek to choose an action as close as possible to the value of a continuous state θ. ...
... Thus, the consistent message from Burguet and Vives (2000), Mueller-Frank and Pai (2016), and Ali (2018a) is that asymptotic learning is not robust to introducing costs of acquiring (or processing) private information. ...
... The information acquisition cost function is C(q) = C(T/ζ) and it is the time cost. If each member needs to pay c for each unit of time, we have C (0) = c > 0. However, if the time cost is C(T) = T 2 , we have C (0) = 0. 8 The conclusions in Proposition 6 are very similar to the ones in Burguet & Vives [25]: in one social learning model with information acquisition, Burguet & Vives [25] show that the aggregate information gathered over time tends to infinity if and only if the marginal cost at zero information acquisition is zero; in our model, the aggregate information is changing in the committee size but not the time. 9 To see the convexity of the marginal value, note that there is ...
... The information acquisition cost function is C(q) = C(T/ζ) and it is the time cost. If each member needs to pay c for each unit of time, we have C (0) = c > 0. However, if the time cost is C(T) = T 2 , we have C (0) = 0. 8 The conclusions in Proposition 6 are very similar to the ones in Burguet & Vives [25]: in one social learning model with information acquisition, Burguet & Vives [25] show that the aggregate information gathered over time tends to infinity if and only if the marginal cost at zero information acquisition is zero; in our model, the aggregate information is changing in the committee size but not the time. 9 To see the convexity of the marginal value, note that there is ...
We analyze a committee decision in which individuals with common preferences are uncertain which of two alternatives is better for them. Members can acquire costly information. Private signals and information choice are both continuous. As is consistent with Down’s rational ignorance hypothesis, each member acquires less information in a larger committee and tends to acquire zero information when the committee size goes to infinity. However, with more members, a larger committee can gather more aggregate information in equilibrium. The aggregate information is infinite with the size going to infinity if and only if marginal cost at “zero information acquisition” is zero. When the marginal cost at “zero information acquisition” is positive, the probability of making an appropriate decision tends to be less than one.
... So only a few individuals end up acquiring private signals. This is a version of the "Law of the Few" (see Galeotti and Goyal (2010) The main ideas of an early contribution on costly signal acquisition by Burguet and Vives (2000) can be seen in a simplified model with unbounded signals and continuous actions and states. Agents seek to choose an action as close as possible to the value of a continuous state θ. ...
... Owing to normality, ρ n−1 is equal to sum of the initial ρ 0 and the precisions of signals of predecessors. Thus, the consistent message from Burguet and Vives (2000), Mueller-Frank and Pai (2016), and Ali (2018a) is that asymptotic learning is not robust to introducing costs of acquiring (or processing) private information. ...
We review the theory of information cascades and social learning. Our goal is to describe in a relatively integrated and accessible way the more important themes, insights and applications of the literature as it has developed over the last thirty years. We also highlight open questions and promising directions for further theoretical and empirical exploration.
... So only a few individuals end up acquiring private signals. This is a version of the "Law of the Few" (see Galeotti and Goyal (2010) The main ideas of an early contribution on costly signal acquisition by Burguet and Vives (2000) can be seen in a simplified model with unbounded signals and continuous actions and states. Agents seek to choose an action as close as possible to the value of a continuous state θ. ...
... Owing to normality, ρ n−1 is equal to sum of the initial ρ 0 and the precisions of signals of predecessors. Thus, the consistent message from Burguet and Vives (2000), Mueller-Frank and Pai (2016), and Ali (2018a) is that asymptotic learning is not robust to introducing costs of acquiring (or processing) private information. ...
We review the theory of information cascades and social learning. Our goal is to describe in a relatively integrated and accessible way the more important themes, insights and applications of the literature as it has developed over the last thirty years. We also highlight open questions and promising directions for further theoretical and empirical exploration.
... Burguet and Vives [15] relax the assumption that the precision of private signals is exogenous. ...
... For example, an increase in product quality makes consumers more likely to purchase and search but it is not difficult to construct examples in which the likelihood of paths ending in the cascade set for N is higher. Pastine and Pastine [33] obtain similar " perverse " results when they study the effect of changing the accuracy of signals on the probability of incorrect herds, and Burguet and Vives [15] find that increasing the noise in public information can improve welfare. By restricting the likelihood ratio to lie within the learning region, we are able to obtain a closed form solution for the probability of a bad herd. ...
We develop a model of herds in which consumers observe only the aggregate purchase history, not the complete ordered history of search actions. We show that the purchasing information changes the conditions under which herds can occur for both low- and high-quality products. Inferior products are certain to be ignored; high quality products may be ignored, but complete learning may also occur. We obtain closed form solutions for the probabilities of these events and conduct comparative statics. We test the model's predictions using data from an online music market created by Salganik, Dodds, and Watts (2006).
... However, to the best of our knowledge, none of these papers has explained how consumers obtain the private signal in the first place except that consumers are somehow endowed with it and the question faced by consumers is to what extent they should rely on their private signal or the predecessors' actions. One exception is Burguet and Vives (2000) where they formally model the cost to acquire information and draw implications of this cost for the accumulation of public information. However, their model abstracts away the endogeneity in pricing decisions that a firm could use to affect the information acquisition. ...
... By contrast, we show that welfare is typically bounded away from efficiency when the state may change, even with an arbitrarily small probability. As is the case in our paper, Burguet and Vives (2000) and Ali (2018) consider a setup in which private signals are costly. Again, our focus on nonpersistent states shifts the focus away from the question of asymptotic learning that is central in their papers. ...
We consider social learning in a changing world. Society can remain responsive to state changes only if agents regularly act upon fresh information, which limits the value of social learning. When the state is close to persistent, a consensus whereby most agents choose the same action typically emerges. The consensus action is not perfectly correlated with the state though, because the society exhibits inertia following state changes. Phases of inertia may be longer when signals are more precise, even if agents draw large samples of past actions, as actions then become too correlated within samples, thereby reducing informativeness and welfare.
... Our setting with choice of information connects to Burguet and Vives (2000), Mueller-Frank and Pai (2016), and Ali (2018), which introduced endogenous information acquisition to social learning. Relative to this work, our paper considers choice from a fixed set of information sources (with a capacity constraint), in contrast to choice from a flexible set of information sources (with a cost on precision). ...
We develop a model of social learning from overabundant information: Agents have access to many sources of information, and observation of all sources is not necessary in order to learn the payoff-relevant state. Short-lived agents sequentially choose to acquire a signal realization from the best source for them. All signal realizations are public. Our main results characterize two starkly different possible long-run outcomes, and the conditions under which each obtains: (1) efficient information aggregation, where the community eventually achieves the highest possible speed of learning; (2) "learning traps," where the community gets stuck using a suboptimal set of sources and learns inefficiently slowly. A simple property of the correlation structure separates these two possibilities. In both regimes, we characterize which sources are observed in the long run and how often.
... The approach in the present paper stands in a certain contrast to behaviorally inspired models on herding and informational cascades such as in Burguet and Vives (2000), Lee (1998), Banerjee (1992), or Bikhchandani, Hirshleifer, and Welch (1992). I do not want to suggest, however, that the rational expectations equilibrium in the present model describes the behavior of investors exhaustively or even correctly. ...
In order to explore the incentives for information acquisition in nan- cial markets, a model of the joint information and portfolio choice is developed. Investors are allowed to acquire a number of signals that inform about a risky asset's dividend, and \informational e- ciency" is dened as a social planner's preferred signal allocation. If prices are fully revealing, a complete rational expectations equilibrium exists|contrary to a wide-held conjecture. The equilibrium entails no information acquisition and is informationally ecient. The reason is that the transmission of information through price to other investors brings market expectations closer to each investor's own expectations. This reduces the dierence between expected payos and the asset price, a negative eect of more information. When prices are only partly informative, some investors start acquiring information as long as markets are suciently small so that prices reveal little informa- tion to others. However, the acquisition of more information inflicts a negative externality on uninformed investors who rationally extract information from price. Thus, markets are likely to be informationally inecient as informed investors tend to acquire too much information. JEL: G14, D81
... The trouble is not that microcredit is a bad idea, it is that there are other ideas that do not get adequately tested simply because they lack an initial impetus. In recent theoretical work Burguet and Vives (2000) show that there are cases when keeping quiet about new ideas – taking the opposite approach from the Knowledge Bank – can improve welfare. This is because keeping quiet limits the chances that an " inefficient " fad will emerge and gives a wider variety of ideas a fighting chance. ...
... There are antecedent prediction-learning models in finance. Burguet and Vives (2000) posit a learning model in an economy where agents learn through private signals about a payoff related parameter θ. In the Burguet and Vives (2000) model, each agent forms an estimate b θ t of θ, based on an information set with a level of precision δ t . ...
There have been many theoretical representations of learning in financial markets, but few empirical realizations. In this paper, we establish an empirical learning framework which emphasizes the ordering of history, the similarity of events, the importance of memory and the importance of parameter variation in learning. The methodology proposed transforms the standard event study into a dynamic event study with learning. We construct a test for learning and investigate its properties using a Monte Carlo simulation. To illustrate the method, we consider a long-period study of IPOs on the NYSE, AMEX and NASDAQ from 1980 to 1996.
We consider social learning in a changing world. With changing states, societies can be responsive only if agents regularly act upon fresh information, which significantly limits the value of observational learning. When the state is close to persistent, a consensus whereby most agents choose the same action typically emerges. However, the consensus action is not perfectly correlated with the state, because societies exhibit inertia following state changes. When signals are precise enough, learning is incomplete, even if agents draw large samples of past actions, as actions then become too correlated within samples, thereby reducing informativeness and welfare.
Social learning is the updating of beliefs based on observation of others. Such observation can lead to efficient aggregation of information, but also to inaccurate decisions, fragility of mass behaviors, and, in the case of information cascades, to complete blockage of learning. We review the theory of information cascades and social learning and discuss important themes, insights, and applications of this literature as it has developed over the last 30 years. We also highlight open questions and promising directions for further theoretical and empirical exploration. (JEL D71, D82, D83, D91, Z13)
We study the optimal disclosure policy in a sender–receiver communication game where the receiver's morale, defined as his expected state of the world, affects his performance. The sender observes the state and chooses whether to disclose it to the receiver, who then decides whether to participate in a task. The receiver wins if his performance in the task meets a target. No disclosure is optimal if the receiver wins with average morale in each state. Otherwise, in the threshold disclosure equilibrium that Pareto‐dominates full disclosure, the receiver quits as the sender discloses the worst states and wins as the sender withholds the rest. The receiver wins in more states in the Pareto‐optimal equilibrium as the sender chooses a non‐monotonic disclosure policy. Our theory reveals a trade‐off between transparency and efficiency when morale affects performance. It has applications in a broad range of areas including military, family, education and business. Nous étudions la politique de divulgation optimale dans un jeu de communication émetteur‐récepteur où le moral du récepteur, défini comme son état attendu du monde, affecte ses performances. L'expéditeur observe l'état et choisit de le divulguer au destinataire, qui décide alors de participer ou non à une tâche. Le receveur gagne si sa performance dans la tâche atteint un objectif. Aucune divulgation n'est optimale si le receveur gagne avec un moral moyen dans chaque état. Sinon, dans l'équilibre de divulgation de seuil qui domine la divulgation complète de Pareto, le récepteur quitte lorsque l'expéditeur divulgue les pires états et gagne lorsque l'expéditeur retient le reste. Le récepteur gagne dans plus d'états dans l'équilibre optimal de Pareto lorsque l'expéditeur choisit une politique de divulgation non monotone. Notre théorie révèle un compromis entre transparence et efficacité lorsque le moral affecte la performance. Il a des applications dans un large éventail de domaines, notamment l'armée, la famille, l'éducation et les affaires.
We analyze a social learning model where the agents' utility depends on a common component and an idiosyncratic component. Each agent splits a learning budget between the two components. We show that information about the common component is fully aggregated if and only if agents do not have to sacrifice learning about their idiosyncratic component in order to learn marginally about the common component. If agents vary in how much they value their idiosyncratic component, then the order of agents can strictly impact how much information is aggregated.
We consider a sequential investment process that is characteristic of crowdfunding platforms, among other contexts. Investors wish to avoid the cost of information acquisition and thus prefer to rely on information acquired by previous investors. This may lead to a phenomenon similar to an information cascade. We characterize the optimal policy that balances between the incentive to acquire information and the optimal investment decision. The policy is based on time-varying transparency levels such that it may be worthwhile to conceal some information in some periods.
This paper was accepted by Joshua Gans, business strategy.
This paper incorporates costly information into a model of observational learning. Individuals would like to avoid the cost of buying information and free-ride on the public history. The paper characterizes when learning is nevertheless complete. Necessary and sufficient conditions for complete learning follow from an elementary principle: a player purchases information only if it can influence her action. With a “coarse” action space, learning is complete if and only if for every cost c>0, a positive measure of types can acquire, at cost less than c, an experiment that can overturn the public history. With a “rich” action space, learning is complete if and only if for every cost c>0, a positive measure of types can acquire any informative signal at cost weakly less than c. The results are applied to financial markets to evaluate when markets are informationally efficient despite information being costly.
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.
We formalize the idea that house price changes may drive rational waves of optimism and pessimism in the economy. In our model, a house price increase caused by aggregate disturbances may be misinterpreted as a sign of higher local permanent income, leading households to demand more consumption and housing. Higher demand reinforces the initial price increase in an amplification loop that drives comovement in output, labor, residential investment, land prices, and house prices even in response to aggregate supply shocks. The qualitative implications of our otherwise frictionless model are consistent with observed business cycles and it can explain the economic impact of apparently autonomous changes in sentiment without resorting to non-fundamental shocks or nominal rigidity.
We consider the implementability and welfare effects of a partial announcement policy using a beauty contest model in which agents’ actions are strategic complements and their decisions on public information acquisition are endogenous. We obtain the following results: (i) if a social planner sells public information at a constant price, then multiple equilibria emerge and the partial announcement equilibrium becomes unstable; (ii) there exist pricing rules that ensure a unique and stable equilibrium partial publicity level, which indicates that a partial announcement policy can be implemented; and (iii) as the precision of public information increases, the optimal price rises due to higher optimal publicity level. To realize the higher optimal publicity level in equilibrium, the social planner must reset the pricing rules to lower the price of public information for each publicity level.
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.
This paper studies information acquisition and use in network games. The network structure incorporates both strategic complements (positive links) and substitutes (negative links). An information-use game played on a correlation-adjusted network is derived. Equilibrium inefficiencies in both acquisition and use of information are characterized. Inefficient bunching obtains in information acquisition, where the spread in equilibrium signal precisions is below that prescribed by the planner. The welfare analysis offers a policy intervention publicizing players' information investments. The more linked a player is, positively or negatively, the more strongly they respond to the policy to influence others' information acquisition and use.
We study informational freeriding in a model where agents privately acquire information and then decide when to reveal it by taking an action. Examples of such freeriding are prevalent in financial markets, e.g., the timing of initial public offerings, analysts’ forecasts, and mutual funds’ investment decisions. The main results show that, in large populations, few agents provide significant information while the vast majority of agents freeride. We highlight the role of uncertainty and market size in shaping the dynamics of price discovery. Among other results, we find that heightened uncertainty over the underlying state enhances information production, yet weakens the precision and speed of information aggregation in the market.
This paper presents novel evidence on the pattern of voting in referenda and develops a spatial learning model that helps explain such behavior. In particular, we shed light on the determinants of voters’ choices over nuclear power using data on two Italian referenda. Exploiting the panel structure of the data, we document that voting against nuclear power increases, whenever the distance from the closest nuclear plant decreases. However, we detect a different voting behavior between municipalities close to existing reactors and those close to proposed ones. A possible explanation is that many citizens hold more precise information on nuclear safety because they have experienced the presence of a reactor in their vicinity for many years. Therefore, we propose a model of voting with endogenous information acquisition interacting both proximity and learning effects, whose results are compatible with the empirical findings. Citizens receive public and private signals and revise their beliefs on the risk of living close to a plant. Such revision process is nested into a spatial voting model establishing conditions for a similar or different voting behavior of the electorate based on the proximity from the reactor.
While the central bank observes market activity to assess economic fundamentals, it shapes the market outcome through the conduct of monetary policy. A dilemma arises from this dual role because the more the central bank shapes the market, the more it influences the informational content of market outcomes. This paper analyzes how accounting for the endogeneity of information affects optimal monetary policy. By reducing the accuracy of central bank information, endogenous information calls for a higher degree of opacity, weakens accommodation policy to shocks, and broadens the range of parameters for which taking a signaling action is detrimental to welfare.
The performance of prediction markets depends crucially on the quality of user contribution. A social-media-based prediction market can utilize aspects of social effects to improve users’ contribution quality. In this study, we examine the causal effect of social audience size and online endorsement on prediction market participants’ prediction accuracy through a randomized field experiment. By conducting a comprehensive treatment effect analysis, we estimate both the average treatment effect (ATE) and the quantile treatment effect using the difference-in-differences method. Our empirical results on ATE show that an increase in audience size leads to an improvement in prediction accuracy, and that a higher level of online endorsement also leads to prediction improvements. Interestingly, we find that the quantile treatment effects are heterogeneous: users of intermediate prediction ability respond most positively to an increase in social audience size and online endorsement. These findings suggest that prediction markets can target people of intermediate abilities to obtain the most significant prediction improvement.
The online appendix is available at https://doi.org/10.1287/isre.2016.0679.
This paper explores incomplete and endogenous information in network games. Each player either privately or publicly acquires costly information regarding a global, payoff-relevant state prior to simultaneous play. Strategic complements and substitutes are incorporated into the network structure. The unique information-response equilibrium, played on a correlation-adjusted network, is characterized. Measures of marginal strategic values to information and informational externalities as functions of network position are derived, and the welfare implications of the model are explored. A blueprint for efficient policy design is developed. Policies that certify players' information investments target players with both high strategic values and high informational externalities. Numerical estimations are used to assess the relative accuracies of previously studied centrality measures when identifying optimal targets.
This article performs a welfare analysis of markets with private information in which agents condition on prices in the rational expectations tradition. Price-contingent strategies introduce two externalities in the use of private information: a pecuniary externality and a learning externality. The pecuniary externality induces agents to put too much weight on private information and in the standard case, when the allocation role of the price prevails over its informational role, overwhelms the learning externality which impinges in the opposite way. The price may be very informative but at the cost of an excessive dispersion of the actions of agents. The welfare loss at the market solution may be increasing in the precision of private information. The analysis provides insights into optimal business cycle policy and a rationale for a Tobin-like tax for financial transactions.
When a decision maker is a member of multiple social groups, her actions may cause information to “spill over” from one group to another. We study the nature of these spillovers in an observational learning game where two groups interact via a common player, and where conventions emerge when players follow the decisions of the members of their own groups rather than their own private information. We show that: (i) if a convention develops in one group but not the other group, then the convention spills over via the common player; (ii) when conventions disagree, then the common player’s decision breaks the convention in one group; and (iii) when no convention has developed, then the common player’s decision triggers the same convention in both groups. We also show that information spillovers may reduce welfare, and we investigate the surplus-maximizing timing of spillovers.
This chapter studies how incomplete information helps accommodate frictions in coordination, leading to novel insights on the joint determination of expectations and macroeconomic outcomes. We review and synthesize recent work on global games, beauty contests, and their applications. We elaborate on the distinct effects of strategic uncertainty relative to fundamental uncertainty. We demonstrate the potential fragility of workhorse macroeconomic models to relaxations of common knowledge; the possibility of operationalizing the notions of “coordination failure” and “animal spirits” in a manner that unifies unique- and multiple-equilibrium models; and the ability of incomplete information to offer a parsimonious explanation of important empirical regularities. We provide a general treatment of these ideas, as well as specific applications in the context of business cycles, financial crises, and asset pricing.
We study a sequential social learning model where agents privately acquire information by costly search. Search costs of agents are private, and are independently and identically distributed. We show that asymptotic learning occurs if and only if search costs are not bounded away from zero. We explicitly characterize equilibria for the case of two actions, and show that the probability of late moving agents taking the suboptimal action vanishes at a linear rate. Social welfare converges to the social optimum as the discount rate converges to one if and only if search costs are not bounded away from zero.
When an agent has the opportunity to access public information, whether or not to acquire costly private information is a strategic decision. In this case, to study the informativeness of the revealed information, it is essential to consider the processes of both information acquisition and revelation together. Using a model in which two agents sequentially forecast the true state of a forthcoming period, this paper studies an agent’s strategic behavior in acquiring and revealing costly private information in the presence of the payoff externality due to their competition. If the penalty for an incorrect forecast is greater than the reward for being right, the forecast cannot be informative because there is no investment in private information. Otherwise, costly private information is acquired as long as the information quality is moderate. Hence, the payoff structure under which the reward is greater than the penalty is a necessary condition for the investment in costly private information. Moreover, the acquired information is always revealed truthfully without herding or anti-herding. That is, the introduction of endogenous costly information raises the issue of "free-riding" rather than the issue of "herding or anti-herding".
Environmentally-friendly (“green”) products face a unique set of market barriers. I develop a dynamic model of observational learning and costly search wherein a green consumer product enters a market to challenge an established “dirty” product. Purchase decisions depend on price and quality differences, consumers’ willingness-to-pay to protect the environment, and the cost of obtaining information. Using both theoretical analyses and simulations, I solve for the long-term market performance of the green product. Conditions are provided for when it is socially optimal to encourage green purchases with public policy. Comparative statics predict the effectiveness of various policy tools used to improve market performance. Permanent financial incentives are shown to be more effective than informational campaigns at encouraging green purchases if the green product is inferior to the dirty substitute. Temporary financial incentives are shown to be an ineffective tool to encourage the long-term market success of any green product. Numerical market simulations are used to test and supplement the theory.
We study the diffusion of dispersed private information in a large economy, where agents learn from the actions of others through two channels: a public channel, such as equilibrium market prices, and a private channel, for example local interactions. We show that, when agents learn only from the public channel, an initial release of public information increases agentsʼ total knowledge at all times and increases welfare. When a private learning channel is present, this result is reversed: more initial public information reduces agents asymptotic knowledge by an amount in order of log(t) units of precision. When agents are sufficiently patient, this reduces welfare.
Penguins jumping off a cliff, economic forecasters and financial advisors speculating against a currency, and farmers using traditional methods in India are all practising social learning. Such learning from the behavior of others may and does lead to herds, crashes, and booms. These issues have become, over the last ten years, an exciting field of research in theoretical and applied economics, finance, and in other social sciences. This book provides both an informal introduction and in-depth insights into the most recent advances. Each chapter is devoted to a separate issue: individuals learn from the observations of actions, the outcomes of these actions, and from what others say. They may delay or make an immediate decision; they may compete against others or gain from cooperation; they make decisions about investment, crop choices, and financial investments. The book highlights the similarities and the differences between the various cases.
We calculate equilibria of dynamic double-auction markets in which agents are distinguished by their preferences and information. Over time, agents are privately informed by bids and offers. Investors are segmented into groups that differ with respect to characteristics determining information quality, including initial information precision as well as market “connectivity,” the expected frequency of their trading opportunities. Investors with superior information sources attain strictly higher expected profits, provided their counterparties are unable to observe the quality of those sources. If, however, the quality of bidders’ information sources are commonly observable, then, under conditions, investors with superior information sources have strictly lower expected profits.Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.
This paper performs a welfare analysis of economies with private information when public information is endogenously generated and agents can condition on noisy public statistics in the rational expectations tradition. We find that equilibrium is not (restricted) efficient even when feasible allocations share similar properties to the market context (e.g., linear in information). The reason is that the market in general does not internalize the informational externality when public statistics (e.g., prices) convey information. Under strategic substitutability, equilibrium prices will tend to convey too little information when the 'informational' role of prices prevails over its index of scarcity role and too much information in the opposite case. Under strategic complementarity, prices always convey too little information. These results extend to the internal efficiency benchmark (accounting only for the collective welfare of the active players). However, received results - on the relative weights placed by agents on private and public information when the latter is exogenous - may be overturned.
Existing models show that herding in decisions can cause significant information loss, inferior information aggregation, and impaired decision making. However, we show that in a multistage decision setting with endogenous information production, herding on the initial decision can actually result in superior aggregate information and improved decisions. This is because the possibility of herding by a follower incentivizes the leader to increase its ex ante information production to an extent that it can dominate the information loss from herding. Examples include decisions to enter new markets, fund R&D, and provide early-stage venture capital.
An informational cascade occurs when it is optimal for an individual, having observed the actions of those ahead of him, to follow the behavior of the preceding individual with regard to his own information. The authors argue that localized conformity of behavior and the fragility of mass behaviors can be explained by informational cascades. Copyright 1992 by University of Chicago Press.
The Introduction of laboratory experimentation
in economics was motivated
by theories of industrial organization
and market performance. The first
published market experiments were those
of Edward H. Chamberlin (1948). He explored
the behavioral characteristics of
markets he described as being "purely"
but not "perfectly" competitive and he
thought that the principles of monopolistic
competition would be more useful than
the textbook theory of demand and supply
in explaining the observed behavior. Austin
C. Hoggatt (1959) and Heinz Sauermann
and Reinhard Selten (1959) both focused
on markets with three competitors
and independently provided the first experimental
evidence that the Cournot
model might be a reasonably accurate description
of oligopolistic behavior. Oligopoly
and bilateral monopoly motivated
the classic work of Lawrence E. Fouraker
and Sidney Siegel (1963) which introduced
several of the techniques still used
today. Vernon L. Smith's (1962) sensitivity
to the organization of the U.S. security industry
led him to the fundamental discovery
that the law of competitive demand
and supply can be observed operating in
an experimental environment. The field
of experimental economics has experienced
substantial evolution during the intervening
twenty years. This paper is an
attempt to provide an introduction to the
methods and an assessment of available
results which might now be useful to the
students of industrial organization.
In economies where agents bear some risk, the analysis would often be facilitated by the assumption that the risks are i.i.d. and disappear in the aggregate. A formal appeal to the law of large numbers requires the consideration of a sequence of finite economies. In an economy with a continuum of agents there are countable families of sets for which it is impossible for a law of large numbers to be valid. With countably many agents and a finitely additive measure, independence is compatible with the law of large numbers.
We investigate the use of standard statistical models for quantal choice in a game theoretic setting. Players choose strategies based on relative expected utility and assume other players do so as well. We define a quantal response equilibrium (ORE) as a fixed point of this process and establish existence. For a logit specification of the error structure, we show that as the error goes to zero, QRE approaches a subset of Nash equilibria and also implies a unique selection from the set of Nash equilibria in generic games. We fit the model to a variety of experimental data sets by using maximum likelihood estimation. Journal of Economic Literature Classification Numbers: C19, C44, C72, C92.
In a game of a finite number of repetitions of a Cournot-type model of an industry, if firms are satisfied to get close to (but not necessarily achieve) their optimal responses to other firms' sequential strategies, then in the resulting noncooperative “equilibria” of the sequential market game, (1) if the lifetime of the industry is large compared to the number of firms, there are equilibria corresponding to any given duration of the cartel, whereas (2) if the number of firms is large compared to the industry's lifetime, all equilibria will be close (in some sense) to the competitive equilibrium.
Just like economists, voters have conflicting views about redistributive taxation because they estimate its incentive costs differently. We model rational agents as trying to learn from their dynastic income mobility experience the relative importance of effort and predetermined factors in the generation of income inequality and therefore the magnitude of these incentive costs. In the long run 'left-wing dynasties' believing less in individual effort and voting for more redistribution coexist with 'right-wing dynasties.' This allows us to explain why individual mobility experience and not only current income matters for political attitudes and how persistent differences in perceptions about social mobility can generate persistent differences in redistribution across countries. Copyright 1995, the President and Fellows of Harvard College and the Massachusetts Institute of Technology.
The author analyzes a sequential decision model in which each decisionmaker looks at the decisions made by previous decisionmakers in taking her own decision. This is rational for her because these other decisionmakers may have some information that is important for her. The author then shows that the decision rules that are chosen by optimizing individuals will be characterized by herd behavior; i.e., people will be doing what others are doing rather than using their information. The author then shows that the resulting equilibrium is inefficient. Copyright 1992, the President and Fellows of Harvard College and the Massachusetts Institute of Technology.
We formulate an infinite-horizon Bayesian learning model in which the planner faces a cost from switching actions that does not approach zero as the size of the change vanishes. We recast the model as a dynamic programming problem which will always have a continuous value function and an optimal policy. We show that the planner's beliefs will converge eventually to some stochastic limit belief which, however, is not necessarily a point mass on the "truth." The planner's actions will also converge, although not necessarily to an optimal action given the truth. A key implication of adjustment costs is that the planner will change her action only finitely many times. We present a simple example illustrating how adjustment costs can lead the planner to settle in the long run on an action that is far away from the optimal action given the "truth" and which yields a reward significantly below that of the optimal action.
This primer rigorously introduces the auction model of "risk neutral bidders with independent private values". The model is central to auction theory, and its structure is the same as a many models used in information economics. Results are derived regarding the nature of equilibria, the effects of entry fess and reserve prices, revenue equilivalence, and the design of optimal auctions. Widely applicable concepts are emphasized, such as revealed preference logic, the single-crossing property, and the Revelation Principle. Intended readers are economics graduate and advanced undergraduate students, and all economists who want to examine auction theory in detail.
We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. This version, called cumulative prospect theory, applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses. Two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting functions. A review of the experimental evidence and the results of a new experiment confirm a distinctive fourfold pattern of risk: risk aversion for gains and risk seeking for losses of high probability; risk seeking for gains and risk aversion for losses of low probability. Copyright 1992 by Kluwer Academic Publishers
Recent experimental evidence appears to reject simple Nash equilibrium models of bidding behavior in first-price auctions. The author presents a methodological critique of this evidence. Existing tests have concentrated on deviations of subjects from predictions in the message space of the action: bid deviations. The author suggests that it is more natural to evaluate subject behavior in expected payoff space. He concludes that the evidence against the simple models is not significant enough to warrant their rejection. Copyright 1989 by American Economic Association.
The problem of controlling a stochastic process, with unknown parameters over an infinite horizon, with discounting is considered. Agents express beliefs about unknown parameters in terms of distributions. Under general conditions, the sequence of beliefs converges to a limit distribution. The limit distribution may or may not be concentrated at the true parameter value. In some cases, complete learning is optimal; in others, the optimal strategy does not imply complete learning. The paper concludes with examination of some special cases and a discussion of a procedure for generating examples in which incomplete learning is optimal. Copyright 1988 by The Econometric Society.
This paper considers a problem of optimal learning by experimentation by a single decision maker. Most of the analysis is
concerned with the characterisation of limit beliefs and actions. We take a two-stage approach to this problem: first, understand
the case where the agent's payoff function is deterministic; then, address the additional issues arising when noise is present.
Our analysis indicates that local properties of the payoff function (such as smoothness) are crucial in determining whether
the agent eventually attains the true maximum payoff or not. The paper also makes a limited attempt at characterising optimal
experimentation strategies.
A model of competitive bidding is developed in which the winning bidder's payoff may depend upon his personal preferences, the preferences of others, and the intrinsic qualities of the object being sold. In this model, the English (ascending) auction generates higher average prices than does the second-price auction. Also, when bidders are risk-neutral, the second-price auction generates higher average prices than the Dutch and first-price auctions. In all of these auctions, the seller can raise the expected price by adopting a policy of providing expert appraisals of the quality of the objects he sells.
Analysis of decision making under risk has been dominated by expected utility theory, which generally accounts for people's actions. Presents a critique of expected utility theory as a descriptive model of decision making under risk, and argues that common forms of utility theory are not adequate, and proposes an alternative theory of choice under risk called prospect theory. In expected utility theory, utilities of outcomes are weighted by their probabilities. Considers results of responses to various hypothetical decision situations under risk and shows results that violate the tenets of expected utility theory. People overweight outcomes considered certain, relative to outcomes that are merely probable, a situation called the "certainty effect." This effect contributes to risk aversion in choices involving sure gains, and to risk seeking in choices involving sure losses. In choices where gains are replaced by losses, the pattern is called the "reflection effect." People discard components shared by all prospects under consideration, a tendency called the "isolation effect." Also shows that in choice situations, preferences may be altered by different representations of probabilities. Develops an alternative theory of individual decision making under risk, called prospect theory, developed for simple prospects with monetary outcomes and stated probabilities, in which value is given to gains and losses (i.e., changes in wealth or welfare) rather than to final assets, and probabilities are replaced by decision weights. The theory has two phases. The editing phase organizes and reformulates the options to simplify later evaluation and choice. The edited prospects are evaluated and the highest value prospect chosen. Discusses and models this theory, and offers directions for extending prospect theory are offered. (TNM)
A competitive, dynamic model of entry into a new industry is set up and both its positive and normative aspects are studied.
The main assumptions are that entry is sequential, that it occurs under imperfect information on the size of the market and
that better information becomes available as time goes on. The gradual improvement in information is due to the fact that
later waves of entrants are able to observe the profitability of earlier entrants. The major results reported here (under
suitable restrictions) are that the equilibrium rate of entry is monotonically decreasing over time, and that—at any given
point in time—it is smaller than the socially optimal one.
This paper studies a class of information transmission processes called rumors. The distinctive features of these processes are that the information transmission takes place in such a way that the recipient does not quite know whether or not to believe the information and that the probability that someone receives the information depends on how many people already have it. Counter-intuitive comparative statics results are obtained. For example, more information and higher productivity may reduce welfare, while changing the speed with which the rumor spreads has no welfare effect. Copyright 1993 by The Review of Economic Studies Limited.
Although economics is not commonly thought to be an experimental science, laboratory methods are being increasingly used as economic theories become more sophisticated. It is often possible to structure payoffs and procedures so that a theory is tested on its domain, with all structural assumptions satisfied. If the theory fails, individual components can be tested; if the theory works, it can be stressed with procedures that violate the structural assumptions in carefully chosen directions. Applications of this experimental method have been motivated by three distinct sets of issues: the relative efficiencies of alternative market institutions, the predictions and applications of game theory, and the behavioral validity of expected utility theory. This paper presents specific examples from each of these areas to highlight the usefulness of experimentation. Common objections to this methodology are also discussed, as are some of the principal lessons that have been learned, both about economic behavior, and about how to evaluate theoretic propositions in the laboratory.