Payoff-relevant Information Research Articles

Preference Externality Estimators: A Comparison of Border Approaches and IVs

This paper compares two estimators—the Border Approach and an Instrumental Variable (IV) estimator—using a unified framework where identifying variation arises from “preference externalities,” following the intuition in Waldfogel (2003) . We highlight two dimensions in favor of the IV approach. First, an econometric model of the data-generating process reveals that the border approach requires a set of identification assumptions that are not easily satisfied in practice: the ignorance of some payoff-relevant information and conflicting spatial correlation assumptions. The IV approach, in contrast, exhibits greater internal validity because it is derived from the model that generates the data. Second, the border approach suffers from representative issues when the true effect sizes are different between border and off-border regions. We use a common political advertising example to evaluate these estimators and suggest ways to evaluate or limit the above concerns, such as excluding localities that are a large share of the policy making region and evaluating spatial correlations of observables. We find the border approach’s representative issue to be substantial when the ignorance assumption is most plausible and observe that spatial correlations do not reflect those needed in the unobservables for consistency of the estimator. The IV, in contrast, does not exhibit concerns related to local average treatment effects. We also derive the specific conditions when the border approach can reduce bias relative to OLS. This paper was accepted by Raphael Thomadsen, marketing. Funding: This work was supported by National Natural Science Foundation of China (NSFC) [72072004, 72131001]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2023.4977 .

Selling information in competitive environments

Data buyers compete in a game of incomplete information about which a single data seller owns some payoff-relevant information. The seller faces a joint information- and mechanism-design problem: deciding which information to sell, while eliciting the buyers' types and imposing payments. We derive the welfare- and revenue-optimal mechanisms for a class of games with binary actions and states. Our results highlight the critical properties of selling information in competitive environments: (i) the negative externalities arising from buyer competition increase the profitability of recommending the correct action to one buyer exclusively; (ii) for the buyers to follow the seller's recommendations, the degree of exclusivity must be limited; (iii) the buyers' obedience constraints also reduce the distortions in the allocation of information introduced by a monopolist; (iv) as competition becomes fiercer, these limitations become more severe, weakening the impact of market power on the optimal allocation of information.

A Network Solution to Robust Implementation: The Case of Identical but Unknown Distributions

Abstract We study robust mechanism design in environments in which agents commonly believe that others’ types are identically distributed, but we do not assume that the actual distribution is common knowledge, nor that it is known to the designer. First, we characterize all incentive compatible transfers under these assumptions. Second, we characterize the conditions under which full implementation is possible via direct mechanisms, that only elicit payoff relevant information, and the transfer schemes which achieve it whenever possible. The full implementation results obtain from showing that the problem can be transformed into one of designing a network of strategic externalities, subject to suitable constraints which are dictated by the incentive compatibility requirements.

Delegated Learning and Non-Credible Communication

We consider a setting in which an impatient agent acquires payoff-relevant information about the true state of the world. The agent endogenously chooses when to stop learning, at which point an uninformed principal takes an action to maximize her own expected payoff. The agent's preferences are biased relative to the principal's, generating misalignment of expected payoffs. When communication is non-credible, the principal can only rely upon the agent's endogenous stopping rule when strategically specifying her course of action. In the no-communication equilibrium, the agent adopts a one-sided stopping rule as a function of her posterior belief that is consistent with the principal's pre-specified course of action at the time of stopping. When the principal has commitment power, relative to the full-communication equilibrium, the agent is always worse off; for intermediate values of prior beliefs, the principal is better off. The one-sided equilibrium stopping rule (and associated action) can switch discretely as a function of prior beliefs, generating dramatic regime changes for arbitrarily small changes in beliefs. When learning is initiated in the no-communication equilibrium there is a non-zero probability of indefinite delay, in which the agent never ceases learning and the principal never takes an action.

Cognitive Limits and Preferences for Information

The structure of uncertainty underlying certain decision problems may be so complex as to elude decision-makers’ full understanding, curtailing their willingness to pay for payoff-relevant information — a puzzle manifesting itself in, for instance, low stock-market participation rates. I present a decision-theoretic method that enables an analyst to identify decision-makers’ information-processing abilities from observing their preferences for information. A decision-maker who is capable of understanding only those events that either almost always or almost never happen fails to attach instrumental value to any information source. On the other hand, non-trivial preferences for information allow perfect identification of the decision-maker’s mental capacity.

Efficiency With(out) Intermediation in Repeated Bilateral Trade

This paper analyzes repeated version of the bilateral trade model where the independent payoff relevant private information of the buyer and the seller is correlated across time. Using this setup it makes the following five contributions. First, it derives necessary and sufficient conditions on the primitives of the model as to when efficiency can be attained under ex post budget balance and participation constraints. Second, in doing so, it introduces an intermediate notion of budget balance called interim budget balance that allows for the extension of liquidity but with participation constraints for the issuing authority, interpreted here as an intermediary). Third, it pins down the class of all possible mechanisms that can implement the efficient allocation with and without an intermediary. Fourth, it provides a foundation for the role of an intermediary in a dynamic mechanism design model under informational constraints. And, fifth, it argues for a careful interpretation of the folk proposition that less information is better for efficiency in dynamic mechanisms under ex post budget balance and observability of transfers.

Reputation and Screening in a Noisy Environment with Irreversible Actions

We introduce a class of two-player dynamic games to study the effectiveness of screening in a principal-agent problem. In every period, the principal chooses either to irreversibly stop the game or to continue, and the agent chooses an action if the principal chooses to continue. The agent’s type is his private information, and his actions are imperfectly observed. Players’ flow payoffs depend on the agent’s action, and players’ lump-sum payoffs when the game stops depends on the agent’s type. Both players are long-lived and share a common discount factor. We study the limit of the equilibrium outcomes as both players get arbitrarily patient. Nash equilibrium payoff vectors converge to the unique Nash equilibrium payoff vector of an auxiliary, two-stage game with observed mixed actions. The principal learns some but not all information about the agent’s type. Any payoff-relevant information revelation takes place at the beginning of the game. We calculate the probability that the principal eventually stops the game, against each type of the agent.

Failure of common knowledge of language in common-interest communication games

This paper explores higher-order uncertainty about message availability in communication games with perfectly aligned preferences. It can be impossible to achieve ex post efficiency in equilibrium even when it is mutual knowledge that the size of the set of available messages would be sufficient to convey all payoff-relevant information. There are equilibria that achieve ex post efficiency whenever a rich language condition is satisfied: the set of available messages is large relative to the sender's assessment of the number of information sets of the sender the receiver considers possible. Weaker conditions suffice if one adopts an ex ante perspective.

Selective Sampling with Information-Storage Constraints

A decision-maker acquires payoff-relevant information until she reaches her storing capacity, at which point she either terminates the decision-making and chooses an action, or discards some information. By conditioning the probability of termination on the information collected, she controls the correlation between the payoff state and her terminal action. We provide an optimality condition for the emerging stochastic choice. The condition highlights the benefits of selective memory applied to the extracted signals. The constrained-optimal choice rule exhibits (i) confirmation bias, (ii) speed-accuracy complementarity, (iii) overweighting of rare events, and (iv) salience effect.

The Allocation of Future Business: Dynamic Relational Contracts with Multiple Agents

We consider how a firm dynamically allocates business among several suppliers to motivate them in a relational contract. The firm chooses one supplier who exerts private effort. Output is non-contractible, and each supplier observes only his own relationship with the principal. In this setting, allocation decisions constrain the transfers that can be promised to suppliers in equilibrium. Consequently, optimal allocation decisions condition on payoff-irrelevant past performance to make strong incentives credible. We construct a dynamic allocation rule that attains first-best whenever any allocation rule does. This allocation rule performs strictly better than any rule that depends only on payoff-relevant information. (JEL D21, D82, L14, L24)

Should we regulate financial information?

Regulations that require asset issuers to disclose payoff-relevant information to potential buyers are often called “investor protection.” But even when they improve real economic efficiency, such regulations may still harm investors. By making payoffs less uncertain, information reduces risk and therefore reduces return. Similarly, real efficiency gains benefit only asset issuers, who can always choose to disclose. Providing information improves investors' welfare only when 1) issuers strategically manipulate the asset supply to obfuscate information, or 2) the information induces firms to take on riskier investments. Using a portfolio choice model with information markets, the paper explores which types of assets might warrant investor protection.

Informational Robustness and Solution Concepts

We discuss four solution concepts for games with incomplete information. We show how each solution concept can be viewed as encoding informational robustness. For a given type space, we consider expansions of the type space that provide players with additional signals. We distinguish between expansions along two dimensions. First, the signals can either convey payoff relevant information or only payoff irrelevant information. Second, the signals can be generated from a common (prior) distribution or not. We establish the equivalence between Bayes Nash equilibrium behavior under the resulting expansion of the type space and a corresponding more permissive solution concept under the original type space. This approach unifies some existing literature and, in the case of an expansion without a common prior and allowing for payoff relevant signals, leads us to a new solution concept that we dub belief-free rationalizability.

Handing Out Guns at a Knife Fight: Behavioral Limitations of Subgame-Perfect Implementation

The assumption that payoff-relevant information is observable but not verifiable is important for many core results in contract, organizational and institutional economics. However, subgame-perfect implementation (SPI) mechanisms - which are based on off-equilibrium arbitration clauses that impose fines for lying and the inappropriate use of arbitration - can be used to render payoff-relevant observable information verifiable. Thus, if SPI mechanisms work as predicted they undermine the foundations of important economic results based on the observable but non-verifiable assumption. Empirical evidence on the effectiveness of SPI mechanisms is, however, scarce. In this paper we show experimentally that SPI mechanisms have severe behavioral limitations. They induce retaliation against legitimate uses of arbitration and thus make the parties reluctant to trigger arbitration. The inconsistent use of arbitration eliminates the incentives to take first-best actions and leads to costly disagreements such that individuals - if given the choice - opt out of the mechanism in the majority of the cases. Incentive compatible redesigns of the mechanism solve some of these problems but generate new ones such that the overall performance of the redesigned mechanisms remains low. Our results indicate that there is little hope for SPI mechanisms to solve verifiability problems unless they are made retaliation-proof and, more generally, robust to other-regarding preferences.

Challenges to a Policy Treatment of Speculative Trading Motivated by Differences in Beliefs

This paper discusses some of the challenges faced by a policy treatment of speculative trading that is motivated by differences in beliefs. The first challenge is philosophical. Suppose two investors prefer to speculate with each other, under the common knowledge that they are motivated to trade purely by a difference in beliefs (unconditional probability assessments). In the absence of third-party costs, are there conditions under which society should try to prevent them from doing so? The second challenge is the existence of a rationale for a policy based on beliefs, as distinct from other determinants of risk preferences. The third challenge is the ability of enforcement agencies to monitor the distinction between belief-motivated trade and trade motivated by more obvious welfare-enhancing activities, such as hedging, liquidity provision, or acquiring payoff-relevant information.

Better Access to Information Can Decrease Price Efficiency

No. A common regulatory response to high market uncertainty is to increase transparency by making access to fundamental, payoff-relevant information cheaper. We study the impact of such policies on how informative prices are about fundamentals in a setting where investors can endogenously choose to learn about asset fundamentals and liquidity trading by others. When liquidity demand is price-dependent (e.g., due to forced deleveraging), we show that higher transparency, even if exclusively targeting fundamentals, can make prices less informative. As such, regulatory changes which make learning easier may exacerbate the very problems they are intended to address.

Handing Out Guns at a Knife Fight: Behavioral Limitations of Subgame-Perfect Implementation

The assumption that payoff-relevant information is observable but not verifiable is important for many core results in contract, organizational and institutional economics. However, subgame-perfect implementation (SPI) mechanisms - which are based on off-equilibrium arbitration clauses that impose fines for lying and the inappropriate use of arbitration - can be used to render payoff-relevant observable information verifiable. Thus, if SPI mechanisms work as predicted they undermine the foundations of important economic results based on the observable but non-verifiable assumption. Empirical evidence on the effectiveness of SPI mechanisms is, however, scarce. In this paper we show experimentally that SPI mechanisms have severe behavioral limitations. They induce retaliation against legitimate uses of arbitration and thus make the parties reluctant to trigger arbitration. The inconsistent use of arbitration eliminates the incentives to take first-best actions and leads to costly disagreements such that individuals - if given the choice - opt out of the mechanism in the majority of the cases. Incentive compatible redesigns of the mechanism solve some of these problems but generate new ones such that the overall performance of the redesigned mechanisms remains low. Our results indicate that there is little hope for SPI mechanisms to solve verifiability problems unless they are made retaliation-proof and, more generally, robust to other-regarding preferences.

Beautiful or White? Discrimination in Group Formation

We explore the importance of appearance in the endogenous formation of groups using a series of experiments. Participants get to choose who they want in their group, and we manipulate the amount of payoff-relevant information on behavior, thereby making it costly to discriminate based on appearance. We draw participants from a representative sample of a demographically and economically diverse population. This allows broader applicability of our results. We find that beauty predicts desirability as a group member, yet it might mask racial preferences. Payoff-relevant information reduces discrimination a great deal, yet discrimination based on appearance remains. Although their behavior is the same, unattractive participants have a one in ten chance of making it to the most preferred group, whereas attractive participants have a one in three chance. Our results are most consistent with taste-based, rather than statistical, discrimination.

A Framework for Dynamic Oligopoly in Concentrated Industries

We consider dynamic oligopoly models in the spirit of Ericson and Pakes (1995). We introduce a new computationally tractable model for industries with a few dominant firms and many fringe firms, in which firms keep track of the detailed state of dominant firms and of few moments of the distribution that describes the states of fringe firms. Based on this idea we introduce a new equilibrium concept that we call moment-based Markov equilibrium (MME). MME is behaviorally appealing and computationally tractable. However, because moments may not summarize all payoff relevant information, MME strategies may not be optimal. We propose different approaches to overcome this difficulty with varying degrees of restrictions on the model primitives and strategies. We illustrate our methods with computational experiments and show that they work well in empirically relevant models, and significantly extend the class of dynamic oligopoly models that can be studied computationally. In addition, our methods can also be used to improve approximations in other settings such as dynamic industry models with a continuum of firms and an aggregate shock and stochastic growth models.

Discrimination in the lab: Does information trump appearance?

Using a laboratory experiment, we find evidence consistent with statistical discrimination in a public good and group formation game. In the game, payoff relevant information is presented to subjects, thereby making it costly to discriminate when choosing group members. We find that behavior is correlated with race and people use race to predict behavior. However, race only matters when information on behavior is absent. These results are further confirmed when incentives are in place to encourage behavior that is counter to stereotypes. Not all subjects discriminate in the same way, suggesting unfamiliarity and some in-group, out-group bias. Overall, the evidence points to a lack of information rather than discriminatory preferences.

Contextual Inference in Markets: On the Informational Content of Product Lines

Context can influence decisions. This malleability of choice is usually invoked as evidence that people do not maximize stable preference orderings. In a market equilibrium, however, context conveys payoff-relevant information to consumers. Consequently, these consumers rationally violate naïve formulations of standard choice theoretic principles. I identify informational asymmetries under which apparently anomalous behaviors, namely the compromise effect and choice overload, arise as market equilibria. Firms respond to consumers' contextual inference; in case of the compromise effect, a firm may introduce premium loss leaders (expensive goods of overly high quality that increase the demand for other goods). (JEL D11, D83, M31)