Theoretical Economics: Recent Articles
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Articles recently published or accepted for publicationSun, 15 Sep 2024 03:05:00 EDTen-usAdoption epidemics and viral marketing
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5886/40138/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5886/40138/1Mon, 09 Sep 2024 00:00:00 EDTby <b>David McAdams and Yangbo Song</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on September 9, 2024<p>Abstract: An innovation (e.g., new product or idea) spreads like a virus, transmitted by those who have previously adopted it. Agents update their beliefs about innovation quality based on private signals and when they hear about the innovation. We characterize equilibrium adoption dynamics and the resulting lifecycle of virally-spread innovations. Herding on adoption can occur but only early in the innovation lifecycle, and adoption eventually ceases for all virally-spread innovations. A producer capable of advertising directly to consumers finds it optimal to wait and allow awareness to grow virally initially after launch.Adversarial coordination and public information design
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5768/40137/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5768/40137/1Mon, 09 Sep 2024 00:00:00 EDTby <b>Nicolas A. Inostroza and Alessandro Pavan</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on September 9, 2024<p>Abstract: We study flexible public information design in global games. In addition to receiving public information from the designer, agents are endowed with exogenous private information and must decide between two actions (invest and not invest), the profitability of which depends on unknown fundamentals and the agents’ aggregate action. The designer does not trust the agents to play favorably to her and evaluates any policy under the “worst-case scenario.” First, we show that the optimal policy removes any strategic uncertainty by inducing all agents to take the same action, but without permitting them to perfectly learn the fundamentals and/or the beliefs that rationalize other agents’ actions. Second, we identify conditions under which the optimal policy is a simple “pass/fail” test. Finally, we show that when the designer cares only about the probability the aggregate investment is successful, the optimal policy need not be monotone in fundamentals but then identify conditions on payoffs and exogenous beliefs under which the optimal policy is monotone.Expected balanced uncertain utility
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5404/40039/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5404/40039/1Fri, 23 Aug 2024 00:00:00 EDTby <b>Simon Grant, Berend Roorda, and Jingni Yang</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on August 23, 2024<p>Abstract: We introduce and analyze expected balanced uncertain utility (EBUU) theory. A prior and a balanced outcome-set utility characterize an EBUU decision maker. Conditional on a reference or ``balancing value'', the latter assigns a utility to each outcome-set. The decision maker associates with each act, its envelope, the minimal measurable mapping from states to outcome-sets that contains the act. She then (implicitly) ranks an act according to the balancing value at which the expected balanced utility of its associated envelope is zero. As a consequence her risk preferences need only exhibit betweenness allowing or behavior that can accommodate Allais-type paradoxes.Dynamic economics with quantile preferences
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5454/40031/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5454/40031/1Thu, 22 Aug 2024 00:00:00 EDTby <b>Luciano I. de Castro, Antonio F. Galvao, and Daniel da Siva Nunes</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on August 22, 2024<p>Abstract: This paper studies a dynamic quantile model for intertemporal decisions under uncertainty, in which the decision maker maximizes the $\tau$-quantile of the stream of future utilities, for $\tau\in (0,1)$.
We present two sets of contributions.
First, we generalize existing results in directions that are important for applications.
In particular, the sets of choices and random shocks are general metric spaces, either connected or finite.
Moreover, the future state is not exclusively determined by agent's choice, but can also be influenced by shocks.
Under these generalizations, we establish the Principle of Optimality, show that the corresponding dynamic problem yields a value function and, under suitable assumptions, this value function is concave and differentiable.
Additionally, we derive the corresponding Euler equation.
Second, we illustrate the usefulness of this approach by studying two prominent dynamic economics models.
The first deals with intertemporal consumption with one asset.
We obtain closed form expressions for the value function, the optimal asset allocation and consumption, as well as for the consumption path.
These closed form solutions allow us to obtain useful comparative statics that shed light on how consumption and savings respond to increase in risk aversion, impatience and interest rates.
For the second model, we discuss a quantile-based version of the job-search model with uncertainty.Gradual learning from incremental actions
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5452/39960/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5452/39960/1Thu, 15 Aug 2024 00:00:00 EDTby <b>Tuomas Laiho, Pauli Murto, and Julia Salmi</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on August 15, 2024<p>Abstract: We introduce a collective experimentation problem where a continuum of agents choose the timing of irreversible actions under uncertainty and where public feedback from the actions arrives gradually over time. The leading application is the adoption of new technologies. The socially optimal expansion path entails an informational trade-off where acting today speeds up learning but postponing capitalizes on the option value of waiting. We contrast the social optimum to the decentralized equilibrium where agents ignore the social value of information they generate. We show that the equilibrium can be obtained by assuming that agents ignore the future actions of other agents, which lets us recast the complicated two-dimensional problem as a series of one-dimensional problems.Repeated trade with imperfect information about previous transactions
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5694/39945/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5694/39945/1Wed, 14 Aug 2024 00:00:00 EDTby <b>Francesc Dilme</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on August 14, 2024<p>Abstract: This paper studies repeated bargaining with noisy information about previous transactions. A buyer has private information about his willingness to pay, which is either low or high, and buys goods from different sellers over time. Each seller observes a noisy history of signals about the buyer's previous purchases and sets a price. We compare the cases where previous prices are observable to sellers with the case where they are not. We show that more signal precision is counterbalanced by two equilibrium mechanisms that slow learning and keep incentives in balance: (1) sellers offer discounted prices more often, and (2) the buyer rejects high prices with a higher probability. The effect of making prices observable depends on the signal precision: When the signal is imprecise, making prices public strengthens the discounting mechanism, improving efficiency and buyer welfare; when the signal is precise, making prices public activates the rejection mechanism, and efficiency and buyer welfare may decrease. Independently of the price observability, the buyer tends to benefit from a more precise signal about previous purchases.To infinity and beyond: a general framework for scaling economic theories
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5878/39867/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5878/39867/1Wed, 07 Aug 2024 00:00:00 EDTby <b>Yannai A. Gonczarowski, Scott Duke Kominers, and Ran I. Shorrer</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on August 7, 2024<p>Abstract: Many economic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. We provide a principled framework for scaling results from such models by removing these finiteness assumptions. Our sufficient conditions are on the theorem statement only, and not on its proof. This results in short proofs, and even allows us to use the same argument to scale similar theorems that were proven using distinctly different tools. We demonstrate the versatility of our approach via an array of examples from revealed-preference theory.Randomized collective choices based on a fractional tournament
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5589/39854/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5589/39854/1Mon, 05 Aug 2024 00:00:00 EDTby <b>Yves Sprumont</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on August 5, 2024<p>Abstract: An extension rule assigns to each fractional tournament x (specifying, for every pair of social alternatives a and b, the proportion x_{ab} of voters who prefer a to b) a random choice function y (specifying a collective choice probability distribution for each subset of alternatives) which chooses a from {a,b} with probability x_{ab}.
There exist multiple neutral and stochastically rationalizable extension rules. Both Linearity (requiring that y be an affine function of x) and Independence of Irrelevant Comparisons (asking that the probability distribution on a subset of alternatives depend only on the restriction of the fractional tournament to that subset) are incompatible with very weak properties implied by Stochastic Rationalizability.
We identify a class of maximal domains, which we call sequentially binary, guaranteeing that every fractional tournament arising from a population of voters with preferences in such a domain has a unique admissible stochastically rationalizable extension.On the limitations of data-based price discrimination
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5916/39806/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5916/39806/1Tue, 30 Jul 2024 00:00:00 EDTby <b>Haitian Xie, Ying Zhu, and Denis Shishkin</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on July 30, 2024<p>Abstract: The classic third degree price discrimination (3PD) model requires the knowledge of the distribution of buyer valuations and the covariate to set the price conditioned on the covariate.
In terms of generating revenue, the classic result shows that 3PD is at least as good as uniform pricing. What if the seller has to set a price based only on a sample of observations from the underlying distribution? Is it still obvious that the seller should engage in 3PD? This paper sheds light on these fundamental questions. In particular, the comparison of the revenue performance between 3PD and uniform pricing is ambiguous overall when prices are set based on samples.
This finding is in the nature of statistical learning under uncertainty: a curse of dimensionality, but also other small sample complications.Bayesian social aggregation with almost-objective uncertainty
http://econtheory.org/ojs/index.php/te/article/viewArticle/20241351
http://econtheory.org/ojs/index.php/te/article/viewArticle/20241351Wed, 24 Jul 2024 00:00:00 EDTby <b>Marcus Pivato and Tchouante Ngamo Elise Flore</b><p>Published in Theoretical Economics 19 (3), 1351–1398 (July 24, 2024)<p>Abstract: We consider collective decisions under uncertainty, when agents have generalized Hurwicz preferences, a broad class allowing many different ambiguity attitudes, including subjective expected utility preferences. We consider sequences of acts that are “almost-objectively uncertain” in the sense that asymptotically, all agents almost-agree about the probabilities of the underlying events. We introduce a Pareto axiom which applies only to asymptotic preferences along such almost-objective sequences. This axiom implies that the social welfare function is utilitarian, but it does not impose any constraint on collective beliefs. Next, we show that a Pareto axiom restricted to two-valued acts implies that collective beliefs are contained in the closed convex hull of individual beliefs, but imposes no constraints on the social welfare function. Neither axiom entails any link between individual and collective ambiguity attitudes.Buying voters with uncertain instrumental preferences
http://econtheory.org/ojs/index.php/te/article/viewArticle/20241305
http://econtheory.org/ojs/index.php/te/article/viewArticle/20241305Wed, 24 Jul 2024 00:00:00 EDTby <b>Charles Louis-Sidois and Leon Andreas Musolff</b><p>Published in Theoretical Economics 19 (3), 1305–1349 (July 24, 2024)<p>Abstract: We analyze a vote-buying model where the members of a committee vote on a proposal important to a vote buyer. Each member incurs a privately-drawn disutility if the proposal passes. We characterize the cheapest combination of bribes that guarantees the proposal passes in all equilibria. When members vote simultaneously, the number of bribes is at least 50% larger than the number of votes required to pass the proposal (vote threshold). The number of bribes increases with the dispersion of the disutility distribution and all members are bribed with sufficient dispersion. A proportional increase in the number of members and the vote threshold leads to a less-than-proportional increase in capture cost, and the cost may increase with the vote threshold. With sequential voting and disutility distribution $U[0,1]$, all members are bribed and bribes are equal. Finally, sequential voting increases capture cost in small committees and decreases it in large committees.Stable matching in large markets with occupational choice
http://econtheory.org/ojs/index.php/te/article/viewArticle/20241261
http://econtheory.org/ojs/index.php/te/article/viewArticle/20241261Wed, 24 Jul 2024 00:00:00 EDTby <b>Guilherme Carmona and Krittanai Laohakunakorn</b><p>Published in Theoretical Economics 19 (3), 1261–1304 (July 24, 2024)<p>Abstract: We introduce a model of large many-to-one matching markets with occupational choice where each individual can choose which side of the market to belong to. We show that stable matchings exist under mild assumptions; in particular, both complementarities and externalities can be accommodated. Our model generalizes Greinecker and Kah (2021), which focuses on one-to-one matching and did not allow for occupational choice. Applications include the roommate problem with non-atomic participants, explaining the size and distribution of firms and wage inequality.Existence and uniqueness of solutions to the Bellman equation in stochastic dynamic programming
http://econtheory.org/ojs/index.php/te/article/viewArticle/20241223
http://econtheory.org/ojs/index.php/te/article/viewArticle/20241223Wed, 24 Jul 2024 00:00:00 EDTby <b>Juan Pablo Rincón-Zapatero</b><p>Published in Theoretical Economics 19 (3), 1223–1260 (July 24, 2024)<p>Abstract: In this paper we develop a framework to analyze stochastic dynamic optimization problems in discrete time. We obtain new results about the existence and uniqueness of solutions to the Bellman equation through a notion of Banach contractions that generalizes known results for Banach and local contractions. We apply the results obtained to an endogenous growth model and compare our approach with other well known methods, such as the weighted contraction method, countable local contractions and the Q-transform.A theory of fair random allocation under priorities
http://econtheory.org/ojs/index.php/te/article/viewArticle/20241185
http://econtheory.org/ojs/index.php/te/article/viewArticle/20241185Wed, 24 Jul 2024 00:00:00 EDTby <b>Xiang Han</b><p>Published in Theoretical Economics 19 (3), 1185–1221 (July 24, 2024)<p>Abstract: In the allocation of indivisible objects under weak priorities, a common practice is to break the ties using a lottery and randomize over deterministic mechanisms. Such randomizations usually lead to unfairness and inefficiency ex-ante. We propose and study the concept of ex-ante fairness for random allocations, extending some key results in the one-sided and two-sided matching markets. It is shown that the set of ex-ante fair random allocations forms a complete and distributive lattice under first-order stochastic dominance relations, and the agent-optimal ex-ante fair mechanism includes both the deferred acceptance algorithm and the probabilistic serial mechanism as special cases. Instead of randomizing over deterministic mechanisms, our mechanism is constructed using the division method, a new general way of constructing random mechanisms from deterministic mechanisms. As additional applications, we demonstrate that several previous extensions of the probabilistic serial mechanism have their foundations in existing deterministic mechanisms.Robust performance evaluation of independent agents
http://econtheory.org/ojs/index.php/te/article/viewArticle/20241151
http://econtheory.org/ojs/index.php/te/article/viewArticle/20241151Wed, 24 Jul 2024 00:00:00 EDTby <b>Ashwin Kambhampati</b><p>Published in Theoretical Economics 19 (3), 1151–1184 (July 24, 2024)<p>Abstract: A principal provides incentives for independent agents. The principal cannot observe the agents' actions, nor does she know the entire set of actions available to them. It is shown that an anti-informativeness principle holds: very generally, robustly optimal contracts must link the incentive pay of the agents. In symmetric and binary environments, they must exhibit joint performance evaluation — each agent's pay is increasing in the performance of the other.