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on Microeconomics |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Francisco Castro (Graduate School of Business, Columbia University); Gabriel Weintraub (Graduate School of Business, Stanford University) |
| Abstract: | We study the classic sequential screening problem in the presence of buyers’ ex-post participation constraints. A leading example is the online display advertising market, in which publishers frequently do not use up-front fees and instead use transaction-contingent fees. We establish conditions under which the optimal selling mechanism is static and buyers are not screened with respect to their interim type, or sequential and the buyers are screened with respect to their interim type. In particular, we provide an intuitive necessary and su?icient condition under which the static contract is optimal for general distributions of ex-post values. Further, we completely characterize the optimal sequential contract with binary interim types and continuum of ex-post values when this condition fails. Importantly, the latter contract randomizes the allocation of the low type buyer while giving a deterministic allocation to the high type. We also provide partial results for the case of multiple interim types. |
| Keywords: | Sequential screening, Ex-post participation constraints, Static contract, Sequential contract |
| JEL: | C72 D82 D83 |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2078r2&r=mic |
| By: | Pablo Amorós (Department of Economics, University of Málaga) |
| Abstract: | The honest opinions of a group of experts must be aggregated to determine the deserving winner of a competition. The aggregation procedure is majoritarian if, whenever a majority of experts honestly believe that a contestant is the best one, then that contestant is considered the deserving winner. The fact that an expert believes that a contestant is the best one does not necessarily imply that she wants this contestant to win as, for example, she might be biased in favor of some other contestant. Then, we have to design a mechanism that implements the deserving winner. We show that, if the aggregation procedure is majoritarian, such a mechanism exists only if the experts are totally impartial. This impossibility result is very strong as it does not depend on the equilibrium concept considered. |
| Keywords: | mechanism design; social choice; aggregation of experts'? opinions; jury |
| JEL: | C72 D71 D78 |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:mal:wpaper:2018-3&r=mic |
| By: | Francisco Espinosa; Debraj Ray |
| Abstract: | Agents signal their type in a principal-agent model; the principal seeks to retain good agents. Types are signaled with some ambient noise. Agents can choose to add or remove additional noise at a cost. It is shown that monotone retention strategies, in which the principal keeps the agent if the signal crosses some threshold, are generically never equilibria. The main result identifies an equilibrium with a bounded retention zone, in which the principal is wary of both excessively good and excessively bad signals: she retains the agent if the signal is “moderate” and replaces him otherwise. The equilibria we uncover are robust to various extensions: non-normal signal structures, non-binary types, interacting agents, costly mean-shifting, or dynamics with term limits. We discuss applications to risky portfolio management, fake news and noisy government statistics. |
| JEL: | D72 D82 D86 |
| Date: | 2018–05 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:24627&r=mic |
| By: | Hebert, Benjamin (Stanford University); Woodford, Michael (Columbia University) |
| Abstract: | We propose a new principle for measuring the cost of information structures in rational inattention problems, based on the cost of generating the information used to make a decision through a dynamic evidence accumulation process. We introduce a continuous-time model of sequential information sampling, and show that, in a broad class of cases, the choice frequencies resulting from optimal information accumulation are the same as those implied by a static rational inattention problem with a particular static information-cost function. Among the static cost functions that can be justified in this way is the mutual information cost function proposed by Sims [2010], but we show that other cost functions can be justified in this way as well. We introduce a class of "neighborhood-based" cost functions, which also summarize the results of dynamic evidence accumulation, and (unlike mutual information) incorporate a conception of the similarity of states to one another, making it more costly to undertake experiments that can produce different results in similar but non-identical states. With this alternative cost function, optimal information accumulation results in choice frequencies that are similar in similar states; in a continuous-state extension of the model, optimality implies choice frequencies that vary continuously with the state, even when the choice payoffs jump discontinuously with variation in the state. This feature of our version of the rational inattention model conforms with evidence from perceptual discrimination experiments. |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:repec:ecl:stabus:3457&r=mic |
| By: | Hoffmann, Eric; Sabarwal, Tarun |
| Abstract: | We extend the global games method to finite player, finite action, monotone games. These games include games with strategic complements, games with strategic substitutes, and arbitrary combinations of the two. Our result is based on common order properties present in both strategic complements and substitutes, the notion of p-dominance, and the use of dominance solvability as the solution concept. In addition to being closer to the original arguments in Carlsson and van Damme (1993), our approach requires fewer additional assumptions. In particular, we require only one dominance region, and no assumptions on state monotonicity, or aggregative structure, or overlapping dominance regions. As expected, the p-dominance condition becomes more restrictive as the number of players increases. In cases where the probabilistic burden in belief formation may be reduced, the p-dominance condition may be relaxed as well. We present some examples that are not covered by existing results. |
| Keywords: | Global games, strategic complements, strategic substitutes, monotone games, equilibrium selection |
| JEL: | C70 C72 |
| Date: | 2018–05–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:86943&r=mic |
| By: | Bergemann, Dirk; Brooks, Benjamin A; Morris, Stephen |
| Abstract: | We revisit the revenue comparison of standard auction formats, including first-price, second-price, and English auctions. We rank auctions according to their revenue guarantees, i.e., the greatest lower bound of revenue across all informational environments, where we hold fixed the distribution of bidders' values. We conclude that if we restrict attention to the symmetric affiliated models of Milgrom and Weber (1982) and monotonic pure-strategy equilibria, first-price, second-price, and English auctions all have the same revenue guarantee, which is equal to that of the first-price auction as characterized by Bergemann, Brooks and Morris (2017). If we consider all equilibria or if we allow more general models of information, then first-price auctions have a greater revenue guarantee than all other auctions considered. |
| Keywords: | affiliated values; common values; English auction; First-price auction; revenue equivalence; Revenue guarantee; revenue ranking; second-price auction |
| JEL: | C72 D44 D82 D83 |
| Date: | 2018–05 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:12964&r=mic |
| By: | Anton Kolotilin (School of Economics, UNSW Business School, UNSW Sydney); Andriy Zapechelnyuk (School of Economics and Finance, University of St Andrews) |
| Abstract: | There are two common ways for a principal to influence the decision making of an agent. One is to manipulate the agent's information (persuasion problem). Another is to limit the agent's decisions (delegation problem). We show that, under general assumptions, these two problems are equivalent; so solving one problem solves the other. We illustrate how the methods developed in the persuasion literature can be applied to address unsolved delegation problems by considering monopoly regulation with a participation constraint. |
| Keywords: | persuasion, delegation, regulation |
| JEL: | D82 D83 L43 |
| Date: | 2018–04 |
| URL: | http://d.repec.org/n?u=RePEc:swe:wpaper:2018-06&r=mic |
| By: | Lionel DE BOISDEFFRE |
| Abstract: | We consider a pure exchange economy, where agents, typically asymmetrically informed, exchange securities, on financial markets, and commodities, on spot markets. Consumers have private characteristics, anticipations and beliefs, and no model to forecast prices. They are dispensed with rational expectation and bounded rationality assumptions, such as Radner's (1972, 1979), Kurz' (1994) or Koutsougeras-Yannelis' (1999). We show that they face an incompressible uncertainty, represented by a so-called "minimum uncertainty set". This uncertainty typically adds to the exogenous one, on the state of nature, an 'endogenous uncertainty' over future spot prices. At equilibrium, all agents expect the 'true' price on every spot market as a possible outcome, and elect optimal strategies, ex ante, which clear on all markets, ex post. We show this sequential equilibrium exists whenever agents' prior anticipations embed the minimum uncertainty set. This outcome differs from the standard generic existence results of Hart (1975), Radner (1979), and Duffie-Shaffer (1985), among others, based on the rational expectations of prices. |
| Keywords: | Sequential equilibrium, Temporary equilibrium, Perfect foresight, Existence, Rational expectations, Financial markets, Asymmetric Information, Arbitrage |
| JEL: | D52 |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:tac:wpaper:2017-2018_8&r=mic |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Juuso Valimaki (Aalto School of Economics) |
| Abstract: | We provide an introduction to the recent developments in dynamic mechanism design, with a primary focus on the quasilinear case. First, we describe socially optimal (or e?icient) dynamic mechanisms. These mechanisms extend the well-known Vickrey-Clark-Groves and D’Aspremont-Gérard-Varet mechanisms to a dynamic environment. Second, we discuss revenue optimal mechanisms. We cover models of sequential screening and revenue maximizing auctions with dynamically changing bidder types. We also discuss models of information management where the mechanism designer can control (at least partially) the stochastic process governing the agents’ types. Third, we consider models with changing populations of agents over time. After discussing related models with risk-averse agents and limited liability, we conclude with a number of open questions and challenges that remain for the theory of dynamic mechanism design. |
| Keywords: | Dynamic Mechanism Design, Sequential Screening, Dynamic Pivot Mechanism, Bandit Auctions, Information Management, Dynamic Pricing |
| JEL: | D44 D82 D83 |
| Date: | 2017–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2102r&r=mic |
| By: | Romanyuk, Gleb; Smolin, Alexey |
| Abstract: | Short-lived buyers arrive to a platform over time and randomly match with sellers. The sellers stay at the platform and sequentially decide whether to accept incoming requests. The platform designs what buyer information the sellers observe before deciding to form a match. We show full information disclosure leads to a market failure because of excessive rejections by the sellers. If sellers are homogeneous, then coarse information policies are able to restore efficiency. If sellers are heterogeneous, then simple censorship policies are often constrained efficient as shown by a novel method of calculus of variations. |
| Keywords: | cream skimming, matching markets, market failure, information design, calculus of variations |
| JEL: | C73 C78 D82 D83 |
| Date: | 2018–05–14 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:86713&r=mic |
| By: | Volker Nocke; Nicolas Schutz |
| Abstract: | Using an aggregative games approach, we analyze horizontal mergers in a model of multiproduct-firm price competition with nested CES or nested logit demands. We show that the Herfindahl index provides an adequate measure of the welfare distortions introduced by market power, and that the induced change in the naively-computed Herfindahl index is a good approximation for the market power effect of a merger. We also provide conditions under which a merger raises consumer surplus, and conditions under which a myopic, consumer-surplus-based merger approval policy is dynamically optimal. Finally, we study the aggregate surplus and external effects of a merger. |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_024_2018&r=mic |
| By: | Montez, João; Schutz, Nicolas |
| Abstract: | We study a class of games where stores source unobservable inventories in advance, and then simultaneously set prices. Our framework allows for firm asymmetries, heterogeneity in consumer tastes, endogenous consumer information through advertising, and salvage values for unsold units. The payoff structure relates to a complete-information all-pay contest with outside options, non-monotonic winning and losing functions, and conditional investments. In the generically unique equilibrium, stores randomize their price choice and, conditional on that choice, serve all their targeted demand---thus, some inventories may remain unsold. As inventory costs become fully recoverable, the equilibrium price distribution converges to an equilibrium of the associated Bertrand game (where firms first choose prices and then produce to order). This suggests that with production in advance, the choice between a Cournot analysis and a Bertrand-type analysis, as properly generalized in this paper, should depend on whether or not stores observe rivals' inventories before setting prices. |
| Keywords: | all-pay contests; Bertrand convergence.; inventories; oligopoly; production in advance |
| JEL: | L13 |
| Date: | 2018–05 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:12963&r=mic |
| By: | Antill, Samuel (Stanford University); Grenadier, Steven (Stanford University) |
| Abstract: | We model a firm's optimal capital structure decision in a framework in which it may later choose to enter either Chapter 11 reorganization or Chapter 7 liquidation. Creditors anticipate equityholders' ex-post reorganization incentives and price them into the ex-ante credit spreads. Using a realistic dynamic bargaining model of reorganization, the implied capital structure results in both higher credit spreads and dramatically lower leverage than existing models. If reorganization is less efficient than liquidation, the added option of reorganization can actually make equityholders worse off ex-ante, even when they liquidate on the equilibrium path. |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:repec:ecl:stabus:3582&r=mic |
| By: | Haraguchi, Junichi; Matsumura, Toshihiro |
| Abstract: | We investigate a free-entry mixed oligopoly with constant marginal costs. A privatization policy is implemented after private firms enter the market. We find that both full privatization and full nationalization are equilibrium policies, and the former is the worst privatization policy for welfare. |
| Keywords: | entry-then-privatization, constant marginal costs, profit-enhancing entry, two polar equilibrium privatization policies |
| JEL: | D43 H44 L33 |
| Date: | 2018–05–14 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:86704&r=mic |