# Theoretical Economics Volume 17, Number 2 (2022) is online

Theoretical Economics
Volume 17, Number 2 (2022)
https://econtheory.org/ojs/index.php/te/issue/view/55

Articles
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Pages: 507-519

Authors: Itzhak Gilboa, Larry Samuelson

Abstract: Decision theory can be used to test the logic of decision making---one may ask whether a given set of decisions can be justified by a decision-theoretic model. Indeed, in principal-agent settings, such justifications may be required---a manager of an investment fund may be asked what beliefs she used when valuing assets and a government may be asked whether a portfolio of rules and regulations is coherent. In this paper we ask which collections of uncertain-act evaluations can be simultaneously justified under the maxmin expected utility criterion by a single set of probabilities. We draw connections to the the Fundamental Theorem of Finance (for the special case of a Bayesian agent) and revealed-preference results.

Keywords: Decision theory, revealed preference, coherence, maxmin expected utility

JEL classification: D8

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Pages: 521-537

Authors: Sean Horan, Yves Sprumont

Abstract: We propose a class of decisive collective choice rules that rely on a linear ordering to partition the majority relation into two acyclic relations. The first of these relations is used to pare down the set of the feasible alternatives into a shortlist while the second is used to make a final choice from the shortlist.

Rules in this class are characterized by four properties: two classical rationality requirements (Sen's expansion consistency and Manzini and Mariotti's weak WARP); and adaptations of two classical collective choice requirements (Arrow's independence of irrelevant alternatives and Saari and Barney's no preference reversal bias). These rules also satisfy some other desirable properties, including an adaptation of May's positive responsiveness.

Keywords: Majority rule, decisiveness, IIA, monotonicity, rational shortlist methods

JEL classification: D71, D72

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Pages: 539-559

Authors: Sebastian Gryglewicz, Aaron Kolb

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.

Keywords: Dynamic signaling, reputation building, history dependence, exit dynamics

JEL classification: C73, D82, D83

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Pages: 561-585

Authors: Anton Kolotilin, Timofiy Mylovanov, Andriy Zapechelnyuk

Abstract: We consider a Bayesian persuasion problem where a sender's utility depends only on the expected state. We show that upper censorship that pools the states above a cutoff and reveals the states below the cutoff is optimal for all prior distributions of the state if and only if the sender's marginal utility is quasi-concave. Moreover, we show that it is optimal to reveal less information if the sender becomes more risk averse or the sender's utility shifts to the left. Finally, we apply our results to the problem of media censorship by a government.

Keywords: Bayesian persuasion, information design, censorship, media

JEL classification: D82, D83, L82

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Pages: 587-615

Authors: Alfredo Di Tillio, Ehud Lehrer, Dov Samet

Abstract: The main purpose of this paper is to provide a simple criterion enabling to conclude that two agents do not share a common prior. The criterion is simple, as it does not require information about the agents'
knowledge and beliefs, but rather only the record of a dialogue between the agents. In each stage of the dialogue the agents tell each other the probability they ascribe to a fixed event and update their beliefs about the event. To characterize dialogues consistent with a common prior, we first study monologues, which are sequences of probabilities assigned by a single agent to a given event in an exogenous learning process. A dialogue is consistent with a common prior if and only if each selection sequence from the two monologues comprising the dialogue is itself a monologue.

Keywords: Learning processes, Bayesian dialogue, Bayesian monologue, Ratio variation, Joint fluctuation, Agreement

JEL classification: D83

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Pages: 617-650

Authors: Begum Guney, Michael Richter

Abstract: We introduce a game-theoretic model with switching costs and endogenous references.  An agent endogenizes his reference strategy and then, taking switching costs into account, he selects a strategy from which there is no profitable deviation. We axiomatically characterize this selection procedure in one-player games. We then extend this procedure to multi-player simultaneous games by defining a Switching Cost Nash Equilibrium (SNE) notion, and prove that (i) an SNE always exists; (ii) there are sets of SNE which can never be a set of Nash Equilibrium for any standard game;  and  (iii) SNE with a specific cost structure exactly characterizes the Nash Equilibrium of nearby games,  in contrast to Radner's
(1980) $\varepsilon$-equilibrium. Subsequently, we apply our SNE notion to a product differentiation model, and reach the opposite conclusion of Radner
(1980): switching costs for firms may benefit consumers.  Finally, we compare our model with  others, especially K\"{o}szegi and Rabin's (2006) personal equilibrium.

Keywords: Switching cost Nash equilibrium, choice, endogenous reference, switching costs, epsilon equilibrium

JEL classification: D00, D01, D03, C72

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Pages: 651-686

Authors: Efe A. Ok, Gerelt Tserenjigmid

Abstract: Among the reasons behind the choice behavior of an individual taking a stochastic form are her potential indifference or indecisiveness between certain alternatives, and/or her willingness to experiment in the sense of occasionally deviating from choosing a best alternative in order to give a try to other options. We introduce methods of identifying if, and when, a stochastic choice model may be thought of as arising due to any one of these three reasons. Each of these methods furnishes a natural way of making deterministic welfare comparisons within any model that is rationalized as such.
In turn, we apply these methods, and characterize the associated welfare orderings, in the case of several well-known classes of stochastic choice models.

Keywords: Stochastic choice, indifference, incomplete preferences, experimentation, the general Luce model, random utility, additive perturbed utility, individual welfare

JEL classification: D01, D11, D81, D91

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Pages: 687-724

Authors: Laura Doval

Abstract: I introduce a stability notion, dynamic stability, for two-sided dynamic matching markets where (i) matching opportunities arrive over time,
(ii) matching is one-to-one, and (iii) matching is irreversible. The definition addresses two conceptual issues. First, since not all agents are available to match at the same time, one must establish which agents are allowed to form blocking pairs. Second, dynamic matching markets exhibit a form of externality that is not present in static markets: an agent’s payoff from remaining unmatched cannot be defined independently of what other contemporaneous agents’ outcomes are. Dynamically stable matchings always exist. Dynamic stability is a necessary condition to ensure timely participation in the economy by ensuring that agents do not strategically delay the time at which they are available to match.

Keywords: Dynamic stability, dynamic matching, stable matching, non-transferable utility, externalities, credibility, market design, dynamic arrivals, aftermarkets

JEL classification: D47, C78

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Pages: 725-762

Authors: Lukasz Balbus, Pawel Dziewulski, Kevin Reffett, Lukasz Wozny

Abstract: We present a new approach to studying equilibrium dynamics in a class of stochastic games with a continuum of players with private types and strategic complementarities. We introduce a suitable equilibrium concept, called Markov Stationary Nash Distributional Equilibrium (MSNDE), prove its existence, and determine comparative statics of equilibrium paths and the steady state invariant distributions to which they converge. Finally, we provide numerous applications of our results including: dynamic models of growth with status concerns, social distance, and paternalistic bequests with endogenous preferences for consumption.

Keywords: Large games, distributional equilibria, supermodular games, comparative dynamics, non-aggregative games, social interactions

JEL classification: C62, C72, C73

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Pages: 763-800

Authors: Rahul Deb, Matthew Mitchell, Mallesh M. Pai

Abstract: Motivated by markets for expertise,'' we study a bandit model where a principal chooses between a safe and risky arm. A strategic agent controls the risky arm and privately knows whether its type is high or low.
Irrespective of type, the agent wants to maximize duration of experimentation with the risky arm. However, only the high type arm can generate value for the principal. Our main insight is that reputational incentives can be exceedingly strong unless both players coordinate on maximally inefficient strategies on path. We discuss implications for online content markets, term limits for politicians and experts in organizations.
for politicians and experts in organizations.

JEL classification: D82, D86

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Pages: 801-839

Authors: Jan Christoph Schlegel

Abstract: Several structural results for the set of competitive equilibria in trading networks with frictions are established: The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, and a group-incentive-compatibility result hold with imperfectly transferable utility and in the presence of frictions. While our results are developed in a trading network model, they also imply analogous (and new) results for exchange economies with combinatorial demand and for two-sided matching markets with transfers.

Keywords: Trading Networks, Full Substitutability, Imperfectly Transferable Utility, Competitive Equilibrium, Indivisible Goods, Frictions, Lattice, Rural Hospitals

JEL classification: C78, D47, D52, L14

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Pages: 841-881

Authors: Stephan Lauermann, Asher Wolinsky

Abstract: This paper analyzes a common-value, first-price auction with state-dependent participation. The number of bidders, which is unobservable to them, depends on the true value. For participation patterns with many bidders in each state, the bidding equilibrium may be of a "pooling"
type---with high probability, the winning bid is the same across states and is below the ex-ante expected value---or of a "partially revealing"
type---with no significant atoms in the winning bid distribution and an expected winning bid increasing in the true value. Which of these forms will arise is determined by the likelihood ratio at the top of the signal distribution and the participation across states. We fully characterize this relation and show how the participation pattern determines the extent of information aggregation by the price.

Keywords: Auction theory, bargaining, competition

JEL classification: D44, D82

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Title: Long information design

Pages: 883-927

Authors: Frederic Koessler, Marie Laclau, Jérôme Renault, Tristan Tomala

Abstract: We analyze information design games between two designers with opposite preferences and a single agent.  Before  the agent makes a decision, designers repeatedly disclose public information about persistent state parameters. Disclosure continues until no designer wishes to reveal further information. We consider environments with general constraints on feasible information disclosure policies. Our main results characterize equilibrium payoffs and strategies of this long information design game and compare them with the equilibrium outcomes of games where designers  move only at a single predetermined period. When information disclosure policies are unconstrained, we show that at equilibrium in the long game, information is revealed right away in a single period; otherwise, the number of periods in which information is disclosed might be unbounded. As an application, we study a competition in product demonstration and show that more  information is revealed if each designer could disclose information at a predetermined period. The format that provides the buyer with  most information is the sequential game where  the last mover is the ex-ante favorite seller.

Keywords: Bayesian persuasion, concavification, convexification, information design, Mertens-Zamir solution, product demonstration, splitting games, statistical experiments, stochastic games

JEL classification: C72, D82

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Pages: 929-942

Authors: Abhigyan Bose, Souvik Roy

Abstract: Theorem 1 in Bhargava, Mohit et al. (2015) provides a necessary condition for a social choice function to be LOBIC with respect to a belief system satisfying top-set (TS) correlation. In this paper, we provide a counter example to that theorem and consequently provide a new necessary condition for the same in terms of sequential ordinal nondomination.

Keywords: Ordinal Bayesian incentive compatibility, correlated beliefs, sequential ordinal nondomination property

JEL classification: D71, D82

Publication Date:
Wednesday, May 25, 2022