Theoretical Economics: Recent Articles
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Articles recently published or accepted for publicationSat, 12 Jun 2021 17:05:00 EDTen-usDynamic signaling with stochastic stakes
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/3710/31000/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/3710/31000/1Tue, 08 Jun 2021 00:00:00 EDTby <b>Sebastian Gryglewicz and Aaron Kolb</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on June 8, 2021<p>Abstract: We study dynamic signaling in a game of stochastic stakes. Each period, a privately informed agent of binary type chooses whether to continue receiving a return that is an increasing function of both her reputation and an exogenous public stakes variable or to irreversibly exit the game. A strong type has a dominant strategy to continue. In the unique perfect Bayesian equilibrium, the weak type plays a mixed strategy that depends only on current stakes and their historical minimum, and she builds a reputation by continuing when the stakes reach a new minimum. We discuss applications to corporate reputation management, online vendor reputation, and limit pricing with stochastic demand.Bayesian comparative statics
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/4345/30893/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/4345/30893/1Fri, 28 May 2021 00:00:00 EDTby <b>Teddy Mekonnen and René Leal Vizcaíno</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on May 28, 2021<p>Abstract: We study how changes to the informativeness of signals in Bayesian games and single-agent decision problems affect the distribution of equilibrium actions. Focusing on supermodular environments, we provide conditions under which a more precise private signal for one agent leads to an increasing-mean spread or a decreasing-mean spread of equilibrium actions for all agents. We apply our comparative statics to information disclosure games between a sender and many receivers and derive sufficient conditions on the primitive payoffs that lead to extremal disclosure of information.Equilibrium contracts and boundedly rational expectations
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/4231/30751/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/4231/30751/1Tue, 11 May 2021 00:00:00 EDTby <b>Heiner Schumacher and Heidi Christina Thysen</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on May 11, 2021<p>Abstract: We study a principal-agent framework in which the agent forms beliefs about the principal's project based on a misspecified subjective model. She fits this model to the objective probability distribution to predict output under alternative actions. Misspecifications in the subjective model may lead to biased beliefs. However, under mild restrictions, the agent has correct beliefs on the equilibrium path so that the optimal contract is non-exploitative. This allows for a behavioral version of the informativeness principle: The optimal contract conditions on an additional variable only if it is informative about the action according to the agent's subjective model. We further characterize when misspecifications affect the optimal contract. One implication of this characterization is that the scope for belief biases depends on the agent's job, e.g., her position in the hierarchy.Family ties: school assignment with siblings
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/4086/30750/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/4086/30750/1Tue, 11 May 2021 00:00:00 EDTby <b>Umut Dur, Thayer Morrill, and William Phan</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on May 11, 2021<p>Abstract: We introduce a generalization of the school choice problem motivated by the following observations: students are assigned to grades within schools, many students have siblings who are applying as well, and school districts commonly guarantee that siblings will attend the same school. This last condition disqualifies the standard approach of considering grades independently as it may separate siblings. We argue that the central criterion in school choice---elimination of justified envy---is now inadequate as it does not consider siblings. We propose a new solution concept, suitability, that addresses this concern, and we introduce a new family of strategy-proof mechanisms that satisfy it. Using data from the Wake County magnet school assignment, we demonstrate the impact on families of our proposed mechanism versus the ``naive'' assignment where sibling constraints are not taken into account.Choosing what to pay attention to
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/3850/30749/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/3850/30749/1Tue, 11 May 2021 00:00:00 EDTby <b>Chad Fulton</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on May 11, 2021<p>Abstract: This paper studies static rational inattention problems with multiple actions and multiple shocks. We solve for the optimal signals chosen by agents and provide tools to interpret information processing. By relaxing restrictive assumptions previously used to gain tractability, we allow agents more latitude to choose what to pay attention to. Our applications examine the pricing problem of a monopolist who sells in multiple markets and the portfolio problem of an investor who can invest in multiple assets. The more general models that our methods allow us to solve yield new results. We show conditions under which the multimarket monopolist would optimally choose a uniform pricing strategy, and we show how optimal information processing by rationally inattentive investors can be interpreted as learning about the Sharpe ratio of a diversified portfolio.Equilibrium securitization with diverse beliefs
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/4157/30713/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/4157/30713/1Fri, 07 May 2021 00:00:00 EDTby <b>Andrew Ellis, Michele Piccione, and Shengxing Zhang</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on May 7, 2021<p>Abstract: We study the effects of diverse beliefs on equilibrium securitization under risk neutrality. We provide a simple characterization of the optimal securities. Pooling and tranching of assets emerges in equilibrium as a consequence of the traders' diverse beliefs about asset returns. The issuer of securities tranches the asset pool, and traders sort among the tranches according to their beliefs. We show how the traders' disagreement about the correlation of asset returns is a key factor in determining which assets are pooled.Equilibrium in misspecified Markov decision processes
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210717
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210717Mon, 03 May 2021 00:00:00 EDTby <b>Ignacio Esponda and Demian Pouzo</b><p>Published in Theoretical Economics 16 (2), 717–757 (May 3, 2021)<p>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.The implementation of stabilization policy
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210677
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210677Mon, 03 May 2021 00:00:00 EDTby <b>Olivier Loisel</b><p>Published in Theoretical Economics 16 (2), 677–716 (May 3, 2021)<p>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.Sequential persuasion
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210639
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210639Mon, 03 May 2021 00:00:00 EDTby <b>Fei Li and Peter Norman</b><p>Published in Theoretical Economics 16 (2), 639–675 (May 3, 2021)<p>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.Communication with forgetful liars
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210605
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210605Mon, 03 May 2021 00:00:00 EDTby <b>Philippe Jehiel</b><p>Published in Theoretical Economics 16 (2), 605–638 (May 3, 2021)<p>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.Delegating learning
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210571
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210571Mon, 03 May 2021 00:00:00 EDTby <b>Juan F. Escobar and Qiaoxi Zhang</b><p>Published in Theoretical Economics 16 (2), 571–603 (May 3, 2021)<p>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.Random ambiguity
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210539
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210539Mon, 03 May 2021 00:00:00 EDTby <b>Jay Lu</b><p>Published in Theoretical Economics 16 (2), 539–570 (May 3, 2021)<p>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.Constrained preference elicitation
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210507
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210507Mon, 03 May 2021 00:00:00 EDTby <b>Yaron Azrieli, Christopher P. Chambers, and Paul J. Healy</b><p>Published in Theoretical Economics 16 (2), 507–538 (May 3, 2021)<p>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.Costly miscalibration
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210477
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210477Mon, 03 May 2021 00:00:00 EDTby <b>Yingni Guo and Eran Shmaya</b><p>Published in Theoretical Economics 16 (2), 477–506 (May 3, 2021)<p>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.Trust and betrayals: reputational payoffs and behaviors without commitment
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210449
http://econtheory.org/ojs/index.php/te/article/viewArticle/20210449Mon, 03 May 2021 00:00:00 EDTby <b>Harry Pei</b><p>Published in Theoretical Economics 16 (2), 449–475 (May 3, 2021)<p>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.