Theoretical Economics, Volume 15, Number 1 (January 2020) has just been published

Theoretical Economics

Volume 15, Number 1 (January 2020)

Table of contents




Title: Discriminatory price auctions with resale and optimal quantity caps

Pages: 1-28

Authors: Brian Baisa, Justin Burkett

Abstract: We present a model of a discriminatory price auction in which a large bidder competes against many small bidders, followed by a post-auction resale stage in which the large bidder is endogenously determined to be a buyer or a seller. We extend results on first-price auctions with resale to this setting and use these results to give a tractable characterization of equilibrium behavior. We use this characterization to study the policy of capping the amount that may be won by large bidders in the auction, a policy that has received little attention in the auction literature. Our analysis shows that the trade-offs involved when adjusting these quantity caps can be understood in terms familiar to students of asymmetric first-price single-unit auctions. Furthermore, whether one seeks to maximize welfare or revenue can have contradictory implications for the choice of cap.

Keywords: Multi-unit auctions, resale, quantity caps

JEL classification: D42, D44, D47, D82




Title: Learning by matching

Pages: 29-56

Authors: Yi-Chun Chen, Gaoji Hu

Abstract: This paper studies a stability notion and matching processes in the job market with incomplete information on the workers' side. Each worker is associated with a type, and each firm cares about the type of her employee under a match. Moreover, firms' information structure is described by partitions over possible worker type profiles. With this firm-specific information, we propose a stability notion which, in addition to requiring individual rationality and no blocking pairs, captures the idea that the absence of rematching conveys no further information. When an allocation is not stable under the status quo information structure, a new pair of an allocation and an information structure will be derived. We show that starting from an arbitrary allocation and an arbitrary information structure, the process of allowing randomly chosen blocking pairs to rematch, accompanied by information updating, will converge with probability one to an allocation that is stable under the updated information structure.

Our results are robust with respect to various alternative learning patterns.

Keywords: Two-sided matching, incomplete information, stability, learning-blocking path, convergence

JEL classification: C78, D83




Title: Performance-maximizing large contests

Pages: 57-88

Authors: Wojciech Olszewski, Ron Siegel

Abstract: Many sales, sports, and research contests are put in place to maximize contestants’ performance. We investigate and provide a complete characterization of the prize structures that achieve this objective in settings with many contestants. The contestants may be ex-ante asymmetric in their abilities and prize valuations, and there may be complete or incomplete information about these parameters. The prize valuations and performance costs may be linear, concave, or convex. A main novel takeaway is that awarding numerous different prizes whose values gradually decline with contestants’ ranking is optimal in the typical case of contestants with convex performance costs and concave prize valuations. This suggests that many real-world contests can be improved by increasing the number of prizes and making them more heterogeneous. The techniques we develop can also be used to formulate and solve other contest design questions that have so far proven intractable.

Keywords: Large contests, contest design, optimal contests, mechanism design

JEL classification: D44, D47, D82




Title: Uncertain rationality, depth of reasoning and robustness in games with incomplete information

Pages: 89-122

Authors: Fabrizio Germano, Jonathan Weinstein, Peio Zuazo-Garin

Abstract: Predictions under common knowledge of payoffs may differ from those under arbitrarily, but finitely, many orders of mutual knowledge; Rubinstein's (1989)Email game is a seminal example. Weinstein and Yildiz (2007) showed that the discontinuity in the example generalizes: for all types with multiple rationalizable (ICR) actions, there exist similar types with unique rationalizable action. This paper studies how a wide class of departures from common belief in rationality impact Weinstein and Yildiz's discontinuity. We weaken ICR to ICRλ, where λ is a sequence whose term λn is the probability players attach to (n- 1)th-order belief in rationality. We find that Weinstein and Yildiz's discontinuity remains when λn is above an appropriate threshold for all n, but fails when λn converges to 0. That is, if players' confidence in mutual rationality persists at high orders, the discontinuity persists, but if confidence vanishes at high orders, the discontinuity vanishes.

Keywords: Robustness, rationalizability, bounded rationality, incomplete information, belief hierarchies

JEL classification: C72, D82, D83




Title: Agency business cycles

Pages: 123-158

Authors: Mikhail Golosov, Guido Menzio

Abstract: We develop a theory of endogenous and stochastic fluctuations in economic activity. Individual firms choose to randomize over firing or keeping workers who performed poorly in the past to give them an ex-ante incentive to exert effort. Different firms choose to correlate the outcome of their randomization to reduce the probability with which they fire non-performing workers. Correlated randomization leads to aggregate fluctuations. Aggregate fluctuations are endogenous---they emerge because firms choose to randomize and they choose to randomize in a correlated fashion---and they are stochastic---they are the manifestation of a randomization process. The hallmark of a theory of endogenous and stochastic fluctuations is that the stochastic process for aggregate "shocks" is an equilibrium object.

Keywords: Endogenous and stochastic cycles, coordinated randomization, unemployment fluctuations

JEL classification: D86, E24, E32




Title: Coalition formation and history dependence

Pages: 159-197

Authors: Bhaskar Dutta, Hannu Vartiainen

Abstract: Farsighted formulations of coalitional formation, for instance by Harsanyi (1974) and Ray and Vohra (2015),  have typically been based on the von Neumann-Morgenstern (1944) stable set.  These  farsighted stable sets  use  a  notion of indirect dominance in which an outcome can be dominated by a chain of coalitional `moves' in which each coalition that is involved in the sequence eventually stands to gain. Dutta and Vohra (2017) point out that these solution concepts do not require coalitions to make optimal moves. Hence,  these solution concepts can yield unreasonable predictions.  Dutta and Vohra (2017)  restricted coalitions to hold common, history independent expectations that incorporate optimality regarding the continuation path.  This paper extends the Dutta-Vohra analysis by allowing for history dependent expectations. The paper provides characterization results for two solution concepts corresponding to two versions of optimality. It demonstrates  the power of history dependence by establishing non-emptyness results for all finite games as well as transferable utility partition function games.  The paper also provides partial comparisons of the solution concepts to other solutions.

Keywords: Coalition formation, farsightedness, vnM stable sets, history dependence

JEL classification: C71




Title: First-price auctions with budget constraints

Pages: 199-237

Authors: Maciej H. Kotowski

Abstract: Consider a first-price, sealed-bid auction with interdependent valuations and private budget constraints. Focusing on the two-bidder case, we identify new sufficient conditions for the existence of a symmetric equilibrium in pure strategies. In equilibrium, agents may adopt discontinuous bidding strategies resulting in a stratification of competition along the budget dimension. Private budgets can simultaneously lead to more aggressive bidding (a high-budget agent leverages his wealth to outbid rivals) and more subdued bidding (competition becomes less intense among bidders at distinct budget levels). The presence of budget constraints may lead to multiple symmetric equilibria in the first-price auction.

Keywords: First-price auction, budget constraints, interdependent values

JEL classification: D44




Title: Locally Bayesian learning in networks

Pages: 239-278

Authors: Wei Li, Xu Tan

Abstract: Agents in a network want to learn the true state of the world from their own signals and their neighbors' reports. Agents know only their local networks, consisting of their neighbors and the links among them. Every agent is Bayesian with the (possibly misspecified) prior belief that her local network is the entire network. We present a tractable learning rule to implement such locally Bayesian learning: each agent extracts new information using the full history of observed reports in her local network. Despite their limited network knowledge, agents learn correctly when the network is a social quilt, a tree-like union of cliques. But they fail to learn when a network contains interlinked circles (echo chambers), despite an arbitrarily large number of correct signals.

Keywords: Locally Bayesian learning, rational learning with misspecified priors, efficient learning in finite networks

JEL classification: D03, D83, D85




Title: Willpower and compromise effect

Pages: 279-317

Authors: Yusufcan Masatlioglu, Daisuke Nakajima, Emre Ozdenoren

Abstract: This paper provides a behavioral foundation for the willpower as limited cognitive resource model which bridges the standard utility maximization and the Strotz models. Using the agent's ex ante preferences and ex post choices, we derive a representation that captures key behavioral traits of willpower constrained decision making. We use the model to study the pricing problem of a profit-maximizing monopolist who faces consumers with limited willpower. We show that the optimal contract often consists of three alternatives and the consumer's choices reflect a form of the "compromise effect" which is induced endogenously.

Keywords: Willpower, compromise effect, self control, temptation, contracting

JEL classification: D4, D9




Title: Information design and sequential screening with ex post participation constraint

Pages: 319-359

Authors: Tibor Heumann

Abstract: We study a principal--agent model. The parties are symmetrically informed at first; the principal then designs the process by which the agent learns his type and, concurrently, the screening mechanism. Because the agent can opt out of the mechanism ex post, it must leave him with nonnegative rents ex post.  We characterize the profit-maximizing mechanism.

In that optimal mechanism, learning proceeds in continuous time and, at each moment, the agent learns a lower bound on his type. For each type, there is one of two possible outcomes: the type is allocated the efficient quantity or is left with zero rents ex post.

Keywords: Sequential screening, ex post participation constraint, information design,  sequential information disclosure, dynamic mechanism design

JEL classification: D82, D83




Title: Efficient multi-unit auctions for normal goods

Pages: 361-413

Authors: Brian Baisa

Abstract: I study multi-unit auction design when bidders have private values, multi-unit demands, and non-quasilinear preferences. Without quasilinearity, the Vickrey auction loses its desired incentive and efficiency properties. I give conditions under which we can design a mechanism that retains the Vickrey auction’s desirable incentive and efficiency properties: (1) individual rationality, (2) dominant strategy incentive compatibility, and (3) Pareto efficiency. I show that there is a mechanism that retains the desired properties of the Vickrey auction if there are two bidders who have single-dimensional types. I also present an impossibility theorem that shows that there is no mechanism that satisfies Vickrey’s desired properties and weak budget balance when bidders have multi-dimensional types.

Keywords: Multi-unit auctions, multi-dimensional mechanism design, wealth effects

JEL classification: D44, D47, D61, D82

Publication Date: 
Monday, February 3, 2020