Theoretical Economics Volume 16, Number 2 (May 2021) is now online
Theoretical Economics
Volume 16, Number 2 (May 2021)
Table of contents
https://econtheory.org/ojs/index.php/te/issue/view/51
Articles
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Title: Bounded rationality and limited datasets
Pages: 359-380
Authors: Geoffroy de Clippel, Kareen Rozen
Abstract: Bounded rationality theories are typically characterized over exhaustive data sets. We develop a methodology to understand the empirical content of such theories with limited data, adapting the classic, revealed-preference approach to new forms of revealed information. We apply our approach to an array of theories, illustrating its versatility. We identify theories and datasets testable in the same elegant way as Rationality, and theories and datasets where testing is more challenging. We show that previous attempts to test consistency of limited data with bounded rationality theories are subject to a conceptual pitfall that may lead to false conclusions that the data is consistent with the theory.
Keywords: Bounded rationality, revealed preference, limited data
JEL classification: D9
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Title: On selecting the right agent
Pages: 381-402
Authors: Geoffroy de Clippel, Kfir Eliaz, Daniel Fershtman, Kareen Rozen
Abstract: Each period, a principal must assign one of two agents to a new task. Profit is stochastically higher when the agent is qualified for the task, but the principal cannot observe qualification. Her only decision is which of the two agents to assign, if any, given the public history of selections and profits, but she cannot commit to any rule. While she maximizes expected discounted profits, each agent maximizes his expected discounted selection probabilities. We fully characterize when the principal's first-best payoff is attainable in equilibrium, and identify a simple, belief-free, strategy profile achieving this first-best whenever feasible. Addionally, we provide a partial characterization of the case with many agents and discuss how our analysis extends to other variations of the game.
Keywords: Dynamic mechanism design without commitment, dynamic mechanism design without transfers
JEL classification: C73, D23
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Title: Evolution, heritable risk and skewness loving
Pages: 403-424
Authors: Yuval Heller, Arthur J. Robson
Abstract: Our understanding of risk preferences can be sharpened by considering their evolutionary basis. The existing literature has focused on two sources of risk: idiosyncratic risk and aggregate risk. We introduce a new source of risk, heritable risk, in which there is a positive correlation between the fitness of a newborn agent and the fitness of her parent.
Heritable risk was plausibly common in our evolutionary past and it leads to a strictly higher growth rate than the other sources of risk. We show that the presence of heritable risk in the evolutionary past may explain the tendency of people to exhibit skewness loving today.
Keywords: Evolution of preferences, risk attitude, risk interdependence, long-run growth rate, fertility rate
JEL classification: D81, D91
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Title: Local agency costs of political centralization
Pages: 425-448
Authors: Roger B. Myerson
Abstract: We analyze a model of moral hazard in local public services which could be efficiently managed by officials under local democratic accountability, but not by officials who are appointed by the ruler of a centralized autocracy. The ruler might prefer to retain an official who diverted resources from public services but contributed part to benefit the ruler. The autocratic ruler would value better public services only when residents reduce taxable investments which become unprofitable without good public services. For local government to benefit local residents, they must have some decentralized power to punish an official who serves them badly even while serving the ruler well
Keywords: Local public goods, moral hazard, decentralized democracy, centralized autocracy
JEL classification: D72, H41, H70
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Title: Trust and betrayals: reputational payoffs and behaviors without commitment
Pages: 449-475
Authors: Harry Pei
Abstract: I study a repeated game in which a patient player wants to win the trust of some myopic opponents but can strictly benefit from betraying them.
His benefit from betrayal is strictly positive and is his persistent private information. I characterize every type of patient player's highest equilibrium payoff and construct equilibria that attain this payoff. Since the patient player's Stackelberg action is mixed and motivating the lowest-benefit type to play mixed actions is costly, every type's highest equilibrium payoff is strictly lower than his Stackelberg payoff. In every equilibrium where the patient player approximately attains his highest equilibrium payoff, no type of the patient player plays stationary strategies or completely mixed strategies.
Keywords: Reputation, no commitment type, equilibrium payoff, equilibrium behavior
JEL classification: C73, D82, D83
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Title: Costly miscalibration
Pages: 477-506
Authors: Yingni Guo, Eran Shmaya
Abstract: We consider a platform which provides probabilistic forecasts to a customer using some algorithm. We introduce a concept of miscalibration, which measures the discrepancy between the forecast and the truth. We characterize the platform's optimal equilibrium when it incurs some cost for miscalibration, and show how this equilibrium depends on the miscalibration
cost: when the miscalibration cost is low, the platform uses more distant forecasts and the customer is less responsive to the platform's forecast; when the miscalibration cost is high, the platform can achieve its commitment payoff in an equilibrium, and the only extensive-form rationalizable strategy of the platform is its strategy in the commitment solution. Our results show that miscalibration cost is a proxy for the degree of the platform's commitment power, and thus provide a microfoundation for the commitment solution.
Keywords: Calibration, miscalibration, cheap talk, commitment, Bayesian persuasion, e-commerce platform
JEL classification: D81, D82, D83
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Title: Constrained preference elicitation
Pages: 507-538
Authors: Yaron Azrieli, Christopher P. Chambers, Paul J. Healy
Abstract: A planner wants to elicit information about an agent's preference relation, but not the entire ordering. Specifically, preferences are grouped into ``types,'' and the planner only wants to elicit the agent's type. We first assume beliefs about randomization are subjective, and show that a space of types is elicitable if and only if each type is defined by what the agent would choose from some list of menus. If beliefs are objective then additional type spaces can be elicited, though a convexity condition must be satisfied. These results remain unchanged when we consider a setting with multiple agents.
Keywords: Elicitation, incentive compatibility, random mechanisms
JEL classification: D8,C7
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Title: Random ambiguity
Pages: 539-570
Authors: Jay Lu
Abstract: We introduce a model of random ambiguity aversion. Choice is stochastic due to unobserved shocks to both information and ambiguity aversion. This is modeled as a random set of beliefs in the maxmin expected utility model of Gilboa and Schmeidler (1989). We characterize the model and show that the distribution of ambiguity aversion can be uniquely identified using binary choices. A novel stochastic order on random sets is introduced that characterizes greater uncertainty aversion under stochastic choice. If the set of priors is the Aumann expectation of the random set, then choices satisfy dynamic consistency. This corresponds to an agent who knows the distribution of signals but is uncertain about how to interpret signal realizations. More broadly, the analysis of stochastic properties of random ambiguity attitudes provides a theoretical foundation for the study of models of random non-linear utility.
Keywords: Stochastic choice, ambiguity, random utility, updating
JEL classification: D81, D83
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Title: Delegating learning
Pages: 571-603
Authors: Juan F. Escobar, Qiaoxi Zhang
Abstract: Learning is crucial to organizational decision making but often needs to be delegated. We examine a dynamic delegation problem where a principal decides on a project with uncertain profitability. A biased agent, who is initially as uninformed as the principal, privately learns the profitability over time and communicates to the principal. We formulate learning delegation as a dynamic mechanism design problem and characterize the optimal delegation scheme. We show that private learning gives rise to the tradeoff between how much information to acquire and how promptly it is reflected in the decision. We discuss implications on learning delegation for distinct organizations.
Keywords: Private learning, delegation, delays, deadlines, commitment, cheap talk
JEL classification: D82, D83
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Title: Communication with forgetful liars
Pages: 605-638
Authors: Philippe Jehiel
Abstract: I consider multi-round cheap talk communication environments in which, after a lie, the informed party has no memory of the content of the lie. I characterize the equilibria with forgetful liars in such settings assuming that a liar's expectation about his past lie coincides with the equilibrium distribution of lies aggregated over all possible realizations of the states. The approach is used to shed light on when the full truth is almost surely elicited, and when multiple lies can arise in equilibrium. Elaborations are proposed to shed light on why non-trivial communication protocols are used in criminal investigations.
Keywords: Forgetful liars, lie detection, analogy-based expectations, cheap talk
JEL classification: C72, D82
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Title: Sequential persuasion
Pages: 639-675
Authors: Fei Li, Peter Norman
Abstract: This paper studies sequential Bayesian persuasion games with multiple senders. We provide a tractable characterization of equilibrium outcomes. We apply the model to study how the structure of consultations affects information revelation. Adding a sender who moves first cannot reduce informativeness in equilibrium, and results in a more informative equilibrium in the case of two states. Moreover, with the exception of the first sender, it is without loss of generality to let each sender move only once. Sequential persuasion cannot generate a more informative equilibrium than simultaneous persuasion and is always less informative when there are only two states.
Keywords: Bayesian persuasion, communication, competition in persuasion, multiple senders, sequential persuasion
JEL classification: D82,D83
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Title: The implementation of stabilization policy
Pages: 677-716
Authors: Olivier Loisel
Abstract: In locally linearized dynamic stochastic rational-expectations models, I introduce the concepts of feasible paths (paths on which the policy instrument can be expressed as a function of the policymaker's observation set) and implementable paths (paths that can be obtained, in a minimally robust way, as the unique local equilibrium under a policy-instrument rule consistent with the policymaker's observation set). I show that, for relevant observation sets, the optimal feasible path under monetary policy can be non-implementable in the New Keynesian model, while constant-debt feasible paths under tax policy are always implementable in the Real Business Cycle model. The first result sounds a note of caution about one of the main lessons of the New Keynesian literature, namely the importance for central banks to track some key unobserved exogenous rates of interest, while the second one restores to some extent the role of income or labor-income taxes in safely stabilizing public debt. For any given implementable path, I show how to design arithmetically a policy-instrument rule consistent with the policymaker's observation set and implementing this path as the robustly unique local equilibrium.
Keywords: Stabilization policy, local-equilibrium determinacy, observation set, feasible path, implementable path, optimal monetary policy, debt-stabilizing tax policy
JEL classification: E32, E52
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Title: Equilibrium in misspecified Markov decision processes
Pages: 717-757
Authors: Ignacio Esponda, Demian Pouzo
Abstract: We provide an equilibrium framework for modeling the behavior of an agent who holds a simplified view of a dynamic optimization problem. The agent faces a Markov Decision Process, where a transition probability function determines the evolution of a state variable as a function of the previous state and the agent’s action. The agent is uncertain about the true transition function and has a prior over a set of possible transition functions; this set reflects the agent’s (possibly simplified) view of her environment and may not contain the true function. We define an equilibrium concept and provide conditions under which it characterizes steady-state behavior when the agent updates her beliefs using Bayes’ rule.
Keywords: Misspecified model, Markov decision process, equilibrium
JEL classification: C61, D83
