Harmful Signaling in Matching Markets

Some labor markets have recently developed formal signalling mechanisms, e.g. the signalling for interviews in the job market for new Ph.D. economists. We evaluate the effect of such mechanisms on two-sided matching markets by considering a game of incomplete information between firms and workers. Workers have almost aligned preferences over firms: each worker has “typical” commonly known preferences with probability close to one and “atypical” idiosyncratic preferences with the complementary probability close to zero. Firms have some commonly known preferences over workers. We show that the introduction of a signalling mechanism is harmful for this environment. Though signals transmit previously unavailable information, they also facilitate information asymmetry that leads to coordination failures. As a result, the introduction of a signalling mechanism lessens the expected number of matches when signals are informative.Signaling, Cheaptalk, Matching

Matching Markets with Signals

A costless signaling mechanism has been proposed as a device to improve welfare in decentralized two-sided matching markets. An example of such an environment is a job market for new Ph.D. economists. We study a market game of incomplete information between firms and workers and show that costless signaling is actually harmful in some matching markets. Specifically, if agents have very similar preferences, signaling lessens the total number of matches and the welfare of firms, as well as it affects ambiguously the welfare of workers. These results run contrary to previous findings that costless signaling facilitates match formation.Matching Markets, Signaling

On the equivalence of Bayesian and dominant strategy implementation in a general class of social choice problems

We consider a standard social choice environment with linear utilities and independent, one-dimensional, private values. We provide a short and constructive proof that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents. We demonstrate the usefulness and applicability of our approach with several examples. Finally, we show that the equivalence between Bayesian and dominant strategy implementation breaks down when utilities are non-linear or when values are interdependent, multi-dimensional, or correlated.

A geometric approach to mechanism design

We develop a novel geometric approach to mechanism design using an important result in convex analysis: the duality between a closed convex set and its support function. By deriving the support function for the set of feasible interim values we extend the wellknown Maskin-Riley-Matthews-Border conditions for reduced-form auctions to social choice environments. We next refine the support function to include incentive constraints using a geometric characterization of incentive compatibility. Borrowing results from majorization theory that date back to the work of Hardy, Littlewood, and Polya (1929) we elucidate the "ironing" procedure introduced by Myerson (1981) and Mussa and Rosen (1978). The inclusion of Bayesian and dominant strategy incentive constraints result in the same support function, which establishes equivalence between these implementation concepts. Using Hotelling's lemma we next derive the optimal mechanism for any social choice problem and any linear objective, including revenue and surplus maximization. We extend the approach to include general concave objectives by providing a fixed-point condition characterizing the optimal mechanism. We generalize reduced-form implementation to environments with multi-dimensional, correlated types, non-linear utilities, and interdependent values. When value interdependencies are linear we are able to include incentive constraints into the support function and provide a condition when the second-best allocation is ex post incentive compatible.Mechanism design, convex set, support function, duality, majorization, ironing, Hotelling's lemma, reduced-from implementation, BIC-DIC equivalence, concave objectives, interdependent values, second-best mechanisms

On the Equivalence of Bayesian and Dominant Strategy Implementation

We consider a standard social choice environment with linear utilities and independent, one-dimensional, private types. We prove that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents and the same ex ante expected social surplus. The short proof is based on an extension of an elegant result due to Gutmann et al. (Annals of Probability, 1991). We also show that the equivalence between Bayesian and dominant strategy implementation generally breaks down when the main assumptions underlying the social choice model are relaxed, or when the equivalence concept is strengthened to apply to interim expected allocations.Bayesian Implementation, Dominant Strategy Implementation, Equivalence

Preference Signaling in Matching Markets

Many labor markets share three stylized facts: employers cannot give full attention to all candidates, candidates are ready to provide information about their preferences for particular employers, and employers value and are prepared to act on this information. In this paper we study how a signaling mechanism, where each worker can send a signal of interest to one employer, facilitates matches in such markets. We find that introducing a signaling mechanism increases the welfare of workers and the number of matches, while the change in firm welfare is ambiguous. A signaling mechanism adds the most value for balanced markets.