Theoretical Economics January 2018 is now online
TABLE OF CONTENTS, Volume 13, Number 1 (January 2018)
Full Issue
Articles
Title: Ranking by rating
Pages: 1-18
Authors: Yves Sprumont
Abstract: Ranking by Rating consists in evaluating the performances of items using exogenous rating functions, and ranking these items according to their performance ratings. Any such method is separable: the ordering of two items does not depend on the performances of the remaining items. When performances belong to a finite set, ranking by rating is characterized by separability and a property of consistency; this characterization generalizes to the infinite case under a continuity axiom. Consistency follows from separability and symmetry, or from monotonicity alone. When performances are vectors in R₊^{m}, a separable, symmetric, monotonic, continuous, and invariant method must rank items according to a weighted geometric mean of their performances along the m dimensions.
Keywords: Ranking methods, separability
JEL classification: D71, D89
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Title: The limit of discounted utilitarianism
Pages: 19-38
Authors: Adam Jonsson, Mark Voorneveld
Abstract: This paper presents an infinite-horizon version of intergenerational utilitarianism. By studying discounted utilitarianism as the discount factor tends to one, we obtain a new welfare criterion:
limit-discounted utilitarianism (LDU). We show that LDU meets standard assumptions of efficiency, equity, and interpersonal comparability, but allows us to compare more pairs of utility streams than commonly-used utilitarian criteria, including the overtaking criterion and the catching-up criterion. We also introduce a principle of compensation for postponements of utility streams and use it to characterize the LDU criterion on a restricted domain.
Keywords: Utilitarianism, intergenerational equity, time preference
JEL classification: D63, D70, D90
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Title: Inequality reducing properties of progressive income tax schedules:
the case of endogenous income
Pages: 39-60
Authors: Oriol Carbonell-Nicolau, Humberto Llavador
Abstract: The case for progressive income taxation is often based on the classic result of Jakobsson (1976) and Fellman (1976), according to which progressive and only progressive income taxes---in the sense of increasing average tax rates on income---ensure a reduction in income inequality. This result has been criticized on the ground that it ignores the possible disincentive effect of taxation on work effort, and the resolution of this critique has been a long-standing problem in public finance. This paper provides a normative rationale for progressivity that takes into account the effect of an income tax on labor supply. It shows that a tax schedule is inequality reducing only if it is progressive---in the sense of increasing marginal tax rates on income---and identifies a necessary and sufficient condition on primitives under which progressive and only progressive taxes are inequality reducing.
Keywords: Progressive taxation, income inequality, incentive effects of taxation
JEL classification: D63, D71
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Title: On path independent stochastic choice
Pages: 61-86
Authors: David S. Ahn, Federico Echenique, Kota Saito
Abstract: We investigate stochastic choice when only the average and not the entire distribution of choices is observable, focusing attention on the popular Luce model. Choice is path independent if it is recursive, in the sense that choosing from a menu can be broken up into choosing from smaller submenus. While an important property, path independence is known to be incompatible with continuous choice. The main result of our paper is that a natural modification of path independence, that we call partial path independence, is not only compatible with continuity but ends up characterizing the ubiquitous Luce (or
Logit) rule.
Keywords: Luce model, stochastic choice, logit model, path independence
JEL classification: D01,D11
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Title: High frequency repeated games with costly monitoring
Pages: 87-114
Authors: Ehud Lehrer, Eilon Solan
Abstract: We study two-player discounted repeated games in which a player cannot monitor the other unless he pays a fixed amount. It is well known that in such a model the folk theorem holds when the monitoring cost is of the order of magnitude of the stage payoff. We analyze high frequency games in which the monitoring cost is small but still significantly higher than the stage payoff. We characterize the limit set of public perfect equilibrium payoffs as the monitoring cost tends to 0. It turns out that this set is typically a strict subset of the set of feasible and individually rational payoffs. In particular, there might be efficient and individually rational payoffs that cannot be sustained in equilibrium. We also make an interesting connection between games with costly monitoring and games played between long-lived and short-lived players. Finally, we show that the limit set of public perfect equilibrium payoffs coincides with the limit set of Nash equilibrium payoffs. This implies that our characterization applies also to sequential equilibria.
Keywords: High frequency repeated games, costly monitoring, Nash equilibrium, public perfect equilibrium, no folk theorem, characterization
JEL classification: C72, C73
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Title: Dynamic project selection
Pages: 115-144
Authors: Arina Nikandrova, Romans Pancs
Abstract: We study a normative model of an internal capital market that a company uses to choose between its two divisions’ projects. Each project's value is initially unknown to all, but can be dynamically learned by the corresponding division. Learning can be suspended or resumed at any time and is costly. We characterize an internal capital market that maximizes the company’s expected cash flow.
Keywords: Internal capital market, irreversible project selection
JEL classification: D82, D83, G320, G310
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Title: Temptation with uncertain normative preference
Pages: 145-174
Authors: John E. Stovall
Abstract: We model a decision maker who anticipates being tempted but is also uncertain about what is normatively best. Our model is an extended version of Gul and Pesendorfer's (2001) with three time periods: in the ex ante period the agent chooses a set of menus, in the interim period she chooses a menu from this set, and in the final period she chooses from the menu. We posit axioms from the ex ante perspective. Our main axioms on preference state that the agent prefers flexibility in the ex ante period and the option to commit in the interim period. Our representation is a generalization of Dekel et al.'s (2009)and identifies the agent's multiple normative preferences and multiple temptations. We also characterize the uncertain normative preference analogue to the representation of Stovall (2010). Finally, we characterize the special case where normative preference is not uncertain. This special case allows us to uniquely identify all components of the representations of Dekel et al. (2009) and Stovall (2010).
Keywords: Temptation, uncertain normative preference, interim preference for commitment
JEL classification: D01, D11
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Title: Robust contracting under common value uncertainty
Pages: 175-204
Authors: Sarah Auster
Abstract: A buyer makes an offer to a privately informed seller for a good of uncertain quality. Quality determines both the seller's valuation and the buyer's valuation and the buyer evaluates each contract according to its worst-case performance over a set of probability distributions. The paper demonstrates that the contract that maximizes the minimum payoff over all possible probability distributions of quality is a screening menu that separates all types, whereas the optimal contract for any given probability distribution is a posted price, which induces bunching. Using the ϵ-contamination model, according to which the buyer's utility is a weighted average of his single prior expected utility and the worst-case scenario, the analysis further shows that for intermediate degrees of confidence the optimal mechanism combines features of both of these contracts.
Keywords: Ambiguity aversion, optimal contracting, lemons problem
JEL classification: D81, D82, D86
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Title: On asymmetric reserve prices
Pages: 205-238
Authors: Maciej H. Kotowski
Abstract: We investigate equilibrium bidding in first-price auctions with asymmetric reserve prices. For example, the auctioneer may set a low reserve price for one subset of bidders and a high reserve price for others. When used to pursue a distributional objective, lowering the reserve price for some bidders channels benefits toward marginal agents in the favored group and does not adversely impact non-favored bidders whose reserve price is unchanged. Even in symmetric environments, when the valuation distribution is not regular, introducing asymmetric reserve prices can increase the auctioneer's revenue compared to an optimal common reserve price.
Implications for auction design are considered.
Keywords: First-price auction, asymmetric auctions, reserve price, mechanism design, affirmative action, procurement
JEL classification: D44
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Title: Payoff equivalence of efficient mechanisms in large matching markets
Pages: 239-272
Authors: Yeon-Koo Che, Olivier Tercieux
Abstract: We study Pareto efficient mechanisms in matching markets when the number of agents is large and individual preferences are randomly drawn from a class of distributions, allowing for both common and idiosyncratic shocks.
We provide a broad set of circumstances under which, as the market grows large, all Pareto efficient mechanisms---including top trading cycles (with an arbitrary ownership structure), serial dictatorship (with an arbitrary serial order), and their randomized variants---produce a distribution of agent utilities that in the limit coincides with the utilitarian upper bound. This implies that Pareto efficient mechanisms are uniformly asymptotically payoff equivalent ``up to the renaming of agents.'' Hence, when the conditions of our model are met, policy makers need not discriminate among Pareto efficient mechanisms based on the aggregate payoff distribution of participants.
Keywords: Large matching markets, pareto efficiency, payoff equivalence
JEL classification: C70,D47,D61,D63
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Title: Inefficient rushes in auctions
Pages: 273-306
Authors: Angel Hernando-Veciana, Fabio Michelucci
Abstract: We analyze a setting common in privatizations, public tenders and takeovers in which the ex post efficient allocation, i.e. the first best, is not implementable. Our first main result is that the open ascending auction is not second best because it is prone to rushes, i.e. all active bidders quitting simultaneously, that undermine its efficiency. Our second main result is that the second best can be implemented with a two-round auction used in real-life privatizations. We also show how this result generalizes using a survival auction with a novel tie-breaking rule.
Keywords: Privatization, efficiency, auctions, mechanism design, multi-round mechanisms
JEL classification: D44, D82
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Title: Collusion constrained equilibrium
Pages: 307-340
Authors: Rohan Dutta, David Knudsen Levine, Salvatore Modica
Abstract: We study collusion within groups in non-cooperative games. The primitives are the preferences of the players, their assignment to non-overlapping groups and the goals of the groups. Our notion of collusion is that a group coordinates the play of its members among different incentive compatible plans to best achieve its goals.
Unfortunately,
equilibria that meet this requirement need not exist. We instead introduce the weaker notion of collusion constrained equilibrium. This allows groups to put positive probability on alternatives that are suboptimal for the group in certain razor's edge cases where the set of incentive compatible plans changes discontinuously. These collusion constrained equilibria exist and are a subset of the correlated equilibria of the underlying game. We examine four perturbations of the underlying game. In each case we show that equilibria in which groups choose the best alternative exist and that limits of these equilibria lead to collusion constrained equilibria. We also show that for a sufficiently broad class of perturbations every collusion constrained equilibrium arises as such a limit. We give an application to a voter participation game showing how collusion constraints may be socially costly.
Keywords: Collusion, group
JEL classification: C72, D70
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Title: Who goes first? Strategic delay under information asymmetry
Pages: 341-376
Authors: Peter A. Wagner
Abstract: This paper considers a timing game in which heterogeneously informed agents have the option to delay an investment strategically to learn about its uncertain return from the experience of others. I study the effects of information exchange through strategic delay on long-run beliefs and outcomes. Investment decisions are delayed when the information structure prohibits informational cascades. When there is only moderate inequality in the distribution of information, equilibrium beliefs converge in the long-run, and there is an insufficient aggregate investment relative to the efficient benchmark. When the distribution of information is more skewed, there can be a persistent wedge in posterior beliefs between well and poorly informed agents, because the poorly informed tend to ``drive out'' the well-informed.
Keywords: Strategic delay, social learning
JEL classification: D83, C73
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Title: Matching information
Pages: 377-414
Authors: Hector Chade, Jan Eeckhout
Abstract: We analyze the optimal allocation of experts to teams, where experts differ in the precision of their information, and study the assortative matching properties of the resulting assignment. The main insight is that in general it is optimal to diversify the composition of the teams, ruling out positive assortative matching. This diversification leads to negative assortative matching when teams consist of pairs of experts. And when experts' signals are conditionally independent, all teams have similar precision. We also show that if we allow experts to join multiple teams, then it is optimal to allocate them equally across all teams. Finally, we analyze how to endogenize the size of the teams, and we extend the model by introducing heterogeneous firms in which the teams operate.
Keywords: Assortative matching, teams, diversification, correlation
JEL classification: C78, D83
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Title: Robust multiplicity with a grain of naiveté
Pages: 415-465
Authors: Aviad Heifetz, Willemien Kets
Abstract: Rationalizability is a central concept in game theory. Since there may be many rationalizable strategies, applications commonly use refinements to obtain sharp predictions. In an important paper, Weinstein and Yildiz [2007] show that no refinement is robust to perturbations of high-order beliefs. We show that robust refinements do exist if we relax the assumption that all players are unlimited in their reasoning ability. In particular, for a class of models, every strict Bayesian-Nash equilibrium is robust. In these environments, a researcher interested in making sharp predictions can use refinements to select among the strict equilibria of the game, and these predictions will be robust.
Keywords: Robustness, games with incomplete information, rationalizability, finite depth of reasoning, higher-order beliefs, level-k models, global games, refinements
JEL classification: C72, D8
