"Detecting Robust Personal Equilibrium Effects in Misspecified Causal Models", with John Nachbar. Journal of Mathematical Economics, vol 118, 2025.
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Abstract Following the work of Spiegler (2016), we use directed acyclical graphs (DAGs) to model a decision maker (DM) who is boundedly rational in the sense of having a misspecified causal model. Spiegler (2016) shows that certain misspecifications can lead to personal equilibrium effects: the DM calculates conditional probabilities of the relevant state variables incorrectly, and the DM’s action influences her interpretation of the data in ways that exacerbate this issue. We show that these personal equilibrium effects are robust, i.e., they do not depend on the details of the underlying distribution. We provide an exact characterization of when robust personal equilibrium effects arise, which is formulated in terms of structural conditional independence assertions of the DM’s misspecified DAG. Examples demonstrate how sensitive robust PE effects are to the structural details of the subjective DAG that, in most cases, are the DM’s private information. We consider detecting robust personal equilibrium effects under partial knowledge of the DM’s misspecified causal model.
"Mind the Revenue Gap: On the Performance of Approximation Mechanisms under Budget Constraints", with Ahuva Mu'alem. Proceedings SAGT 2024 Conference (Lecture Notes in Computer Science vol 15156).
Download full-version: Mind-Rev-Gap
Abstract We consider a buyer–seller interaction, where the seller has one object to allocate and the buyer has private valuations and private budgets, to study the revenue performance of approximation mechanisms. Approximation mechanisms are obtained from the set of incentive compatible, individually rational, and budget feasible mechanisms, denoted M, in two different ways: (i) by imposing additional constraints, thus restricting M to a subclass N; or (ii) by relaxing some of the original constraints, thus expanding M to a superclass N'. We measure the performance of a restricted class N using the guaranteed fraction of optimal revenue ratio introduced by Hart and Nisan (2017). To evaluate the performance of a relaxation class N' we introduce a related ratio, which we call the maximal value of relaxation. We focus on a restricted class of simple mechanisms, consisting of those whose associated menus have a small number of entries. We also pay attention to a restricted class of mechanisms that involves stronger incentive constraints and that has received attention in the literature for its computational tractability. Finally, we consider a class of relaxed mechanisms where the seller can costlessly prevent the buyer from over-reporting the budget. In one case, we obtain arbitrarily good approximation results. In others, the revenue gap between optimal mechanisms and optimal approximation mechanisms is exceedingly large. Overall, our research highlights the limitations of using approximation mechanisms in settings with private values and private budgets.
"Cause and Effect in Political Polarization: A Dynamic Analysis", with Steve Callander. Journal of Political Economy, vol 130, 2022.
Download: Behavioral-Voters
Download the working paper version with online appendix: Behavioral-Voters-WP
Abstract Polarization is both a description of the current state of politics and a dynamic path that has rippled across the political domain over decades. We provide a simple model that explains why polarization appears incrementally and why it was elites who polarized first and more dramatically, whereas mass polarization came later and has been less pronounced. We incorporate an ostensibly unrelated finding about how voters form preferences into a dynamic model of elections. This change, when combined with the response of strategic candidates, creates a feedback loop that can replicate many features of the data. We explore the model’s implications for other aspects of politics and trace what it predicts for the future of polarization.
"Selling Mechanisms for a Financially Constrained Buyer", with Ahuva Mu'alem. Games & Economic Behavior, vol 124, 2020.
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Abstract Financial constraints are central to many economic transactions, yet relatively little is understood about the design of auctions and selling mechanisms in their presence. This paper studies implementability and revenue equivalence for selling mechanisms in a model where a seller has multiple (possibly infinite) items to allocate, and a buyer has private valuations and private budgets. We provide necessary and sufficient conditions for selling mechanisms to be incentive compatible and ex-post budget feasible for the buyer. In addition, we employ these conditions to derive the revenue equivalence principle in the presence of private budgets. Our conditions are based on a novel network approach to incentive compatibility that also takes care of budget feasibility. This approach exploits the subtle difference between unrestricted incremental values —the minimal value difference between an item assigned to the buyer by the seller and another alternative— and restricted incremental values —the minimal value difference between the assigned item and the alternative when the buyer can actually afford the alternative, given her financial disposition. We derive important properties of incentive compatible, budget feasible prices, and illustrate our approach in a multi-item allocation problem with a convex type space.
"Monotonicity and Revenue Equivalence Domains by Monotonic Transformations in Differences", with Rudolf Müller. Journal of Mathematical Economics, vol 70, 2017.
Download: MTP-app
Abstract In a mechanism design setting with quasilinear preferences, a domain of admissible valuations of an agent is called a monotonicity domain if every 2-cycle monotone allocation rule is truthfully implementable (in dominant strategies). The domain is called a revenue equivalence domain if every implementable allocation rule satisfies revenue equivalence. Carbajal and Müller (2015) introduced the notions of monotonic transformations in differences and showed that if the domain admits these transformations then it is a revenue equivalence and monotonicity domain. Here, we show that various economic domains, with countable or uncountable allocation sets, admit monotonic transformations in differences. Our applications include public and private supply of divisible public goods, multi-unit auction-like environments with increasing valuations, and allocation problems with externalities. Single-peaked domains admit only a modified version of monotonic transformations in differences. We show that this property implies too that single-peaked domains are revenue and monotonicity domains.
"A Model of Price Discrimination under Loss Aversion and State Contingent Reference Points", with Jeffrey Ely. Theoretical Economics, vol 11, 2016.
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Abstract We study optimal price discrimination when a monopolist faces a continuum of consumers with reference-dependent preferences. A consumer’s valuation for product quality consists of an intrinsic valuation affected by a private state signal (type) and a gain–loss valuation that depends on deviations of purchased quality from a reference point. Following Kőszegi and Rabin (2006), we consider loss-averse buyers who evaluate gains and losses in terms of changes in the consumption valuation, but in our model each buyer evaluates consumption outcomes relative to his own state-contingent reference quality level. We capture the process by which reference qualities are formed via a reference consumption plan, and use a generalization of the Mirrlees representation of the indirect utility to fully characterize optimal contracts for loss-averse consumers. We find that, depending on the reference plan, optimal price discrimination may exhibit (i) downward distortions beyond the standard downward distortions due to screening, (ii) efficiency gains relative to second-best contracts without loss aversion, and (iii) upward distortions above first-best quality levels without loss aversion. We consider ex ante and ex post consistent contracts in which quality offers by the firm coincide, in expectations or at every state realization, respectively, with the reference quality levels. We find the firm’s unique preferred ex ante and ex post consistent contract menu and specify conditions under which, for the second case, it also constitutes the consumers’ preferred menu.
"Implementability under Monotonic Transformations in Differences", with Rudolf Müller. Journal of Economic Theory, vol 160, 2015.
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Abstract In a social choice setting with quasilinear preferences and monetary transfers, a domain of admissible valuations is called a monotonicity domain if every 2-cycle monotone allocation rule is truthfully implementable (in dominant strategies). The domain is called a revenue equivalence domain if every implementable allocation rule satisfies the revenue equivalence property. We introduce the notions of monotonic transformations in differences, which can be interpreted as extensions of Maskin’s monotonic transformations to quasilinear environments, and show that if the domain admits these transformations then it is a monotonicity and revenue equivalence domain. Our proofs are elementary and do not rely on strenuous additional machinery. We illustrate monotonic transformations in differences for settings with finite and infinite allocation sets.
"Truthful Implementation and Preference Aggregation in Restricted Domains", with Andrew McLennan and Rabee Tourky. Journal of Economic Theory, vol 148, 2013.
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Abstract In a setting where agents have quasi-linear utilities over social alternatives and a transferable commodity, we consider three properties that a social choice function may possess: truthful implementation (in dominant strategies); monotonicity in differences; and lexicographic affine maximization. We introduce the notion of a flexible domain of preferences that allows elevation of pairs and study which of these conditions implies which others in such domain. We provide a generalization of the theorem of Roberts (1979) in restricted valuation domains. Flexibility holds (and the theorem is not vacuous) if the domain of valuation profiles is restricted to the space of continuous functions defined on a compact metric space, or the space of piecewise linear functions defined on an affine space, or the space of smooth functions defined on a compact differentiable manifold. We provide applications of our results to public goods allocation settings, with finite and infinite alternative sets.
"Mechanism Design without Revenue Equivalence", with Jeff Ely. Journal of Economic Theory, vol 148, 2013.
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Abstract We study mechanism design problems in quasi-linear environments where the envelope theorem and revenue equivalence principle fail due to non-convex and non-differentiable valuations. We obtain a characterization of incentive compatibility based on the Mirrlees representation of the indirect utility and a monotonicity condition on the allocation rule, which pin down the range of possible payoffs as a function of the allocation rule. To illustrate our approach we derive the optimal selling mechanism in a buyer–seller situation where the buyer is loss-averse; we find a budget-balanced, efficient mechanism in a public goods location model; and we consider a principal–agent model with ex post non-contractible actions available to the agent.
"On the Uniqueness of Groves Mechanisms and the Payoff Equivalence Principle". Games & Economic Behavior, vol 68, 2010.
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Abstract Consider a standard mechanism design setting with quasi-linear preferences and private valuations. From Holmström (1979), we know that if the valuations are smooth with respect to types then any efficient, dominant strategy mechanism is in the class of Groves mechanisms. Here I show that, given regular assumptions on the primitives of the design problem, a weaker condition that includes the case of non-smooth valuations is sufficient and necessary for the uniqueness of Groves mechanisms among all efficient, dominant strategy mechanisms. This condition, which imposes a restriction on the behavior of the one-sided directional derivatives of the valuation functions with respect to individual types, is also shown to be sufficient and necessary to obtain the Payoff Equivalence principle for dominant strategy mechanisms whose choice rules are affine maximizers.