|
on Economic Design |
|
Issue of 2022‒05‒23
nine papers chosen by Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford |
| By: | Wanchang Zhang |
| Abstract: | I consider a mechanism design problem of selling multiple goods to multiple bidders when the designer has minimal amount of information. I assume that the designer only knows the upper bounds of bidders' values for each good and has no additional distributional information. The designer takes a minimax regret approach. The expected regret from a mechanism given a joint distribution over value profiles and an equilibrium is defined as the difference between the full surplus and the expected revenue. The designer seeks a mechanism, referred to as a minimax regret mechanism, that minimizes her worst-case expected regret across all possible joint distributions over value profiles and all equilibria. I find that a separate second-price auction with random reserves is a minimax regret mechanism for general upper bounds. Under this mechanism, the designer holds a separate auction for each good; the formats of these auctions are second-price auctions with random reserves. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.13726&r= |
| By: | Jerry Anunrojwong; Santiago Balseiro; Omar Besbes |
| Abstract: | Classical Bayesian mechanism design relies on the common prior assumption, but the common prior is often not available in practice. We study the design of prior-independent mechanisms that relax this assumption: the seller is selling an indivisible item to $n$ buyers such that the buyers' valuations are drawn from a joint distribution that is unknown to both the buyers and the seller; buyers do not need to form beliefs about competitors, and the seller assumes the distribution is adversarially chosen from a specified class. We measure performance through the worst-case regret, or the difference between the expected revenue achievable with perfect knowledge of buyers' valuations and the actual mechanism revenue. We study a broad set of classes of valuation distributions that capture a wide spectrum of possible dependencies: independent and identically distributed (i.i.d.) distributions, mixtures of i.i.d. distributions, affiliated and exchangeable distributions, exchangeable distributions, and all joint distributions. We derive in quasi closed form the minimax values and the associated optimal mechanism. In particular, we show that the first three classes admit the same minimax regret value, which is decreasing with the number of competitors, while the last two have the same minimax regret equal to that of the case $n = 1$. Furthermore, we show that the minimax optimal mechanisms have a simple form across all settings: a second-price auction with random reserve prices, which shows its robustness in prior-independent mechanism design. En route to our results, we also develop a principled methodology to determine the form of the optimal mechanism and worst-case distribution via first-order conditions that should be of independent interest in other minimax problems. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.10478&r= |
| By: | Diego Carrasco-Novoa (School of Economics, University of Queensland, Brisbane, Australia); Allan Hernández-Chanto (School of Economics, University of Queensland, Brisbane, Australia) |
| Abstract: | We analyze security-bid auctions in which two risk-neutral sellers compete for riskaverse bidders. Sellers face a tradeoff in steepness because steeper securities extract more surplus but feature lower participation ex-ante. Nonetheless, steeper securities also provide higher insurance, making bidders more aggressive. We show that when bidders are homogeneously risk-averse, all equilibria are symmetric. Meanwhile, when they are heterogeneously risk-averse, there is always an equilibrium in which one seller chooses a steeper family to serve the more-risk-averse bidders, while the other chooses a flatter family to serve the less-risk-averse bidders. This result resembles a “Hotelling location” model in the steepness spectrum. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:qld:uq2004:655&r= |
| By: | Felix Brandt; Patrick Lederer; Warut Suksompong |
| Abstract: | Social decision schemes (SDSs) map the preferences of individual voters over multiple alternatives to a probability distribution over the alternatives. In order to study properties such as efficiency, strategyproofness, and participation for SDSs, preferences over alternatives are typically lifted to preferences over lotteries using the notion of stochastic dominance (SD). However, requiring strategyproofness or participation with respect to this preference extension only leaves room for rather undesirable SDSs such as random dictatorships. Hence, we focus on the natural but little understood pairwise comparison (PC) preference extension, which postulates that one lottery is preferred to another if the former is more likely to return a preferred outcome. In particular, we settle three open questions raised by Brandt (2017): (i) there is no Condorcet-consistent SDS that satisfies PC-strategyproofness; (ii) there is no anonymous and neutral SDS that satisfies PC-efficiency and PC-strategyproofness; and (iii) there is no anonymous and neutral SDS that satisfies PC-efficiency and strict PC-participation. All three impossibilities require m >= 4 alternatives and turn into possibilities when m |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.12436&r= |
| By: | Jacob Coreno; Ivan Balbuzanov |
| Abstract: | This paper considers the problem of allocating bundles of heterogeneous and indivisible objects to agents, when monetary transfers are not allowed and agents reveal only ordinal preferences over objects, e.g., allocating players' contract rights to teams in professional sporting leagues. Preferences over objects are extended to incomplete preferences over bundles using pairwise dominance. We provide a simple characterization of the class of draft rules: they are the only allocation rules satisfying $\textit{efficiency}$, $\textit{respectfulness of the priority}$, $\textit{envy-freeness up to one object}$ and $\textit{resource-monotonicity}$. We also prove two impossibility theorems: (i) $\textit{non-wastefulness}$, $\textit{respectfulness of the priority}$ and $\textit{envy-freeness up to one object}$ are incompatible with $\textit{weak strategy-proofness}$; (ii) $\textit{efficiency}$ and $\textit{envy-freeness up to one object}$ are incompatible with $\textit{weak strategy-proofness}$. If agents may declare some objects unacceptable, then draft rules are characterized by $\textit{efficiency}$, $\textit{respectfulness of the priority}$, $\textit{envy-freeness up to one object}$, $\textit{resource-monotonicity}$ together with a mild invariance property called $\textit{truncation-invariance}$. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.08300&r= |
| By: | Marco Sahm |
| Abstract: | I characterize the optimal accuracy level r of an unbiased Tullock contest between two players with heterogeneous prize valuations. The designer maximizes the winning probability of the strong player or the winner’s expected valuation by choosing a contest with an all-pay auction equilibrium (r ≥ 2). By contrast, if she aims at maximizing the expected aggregate effort or the winner’s expected effort, she will choose a contest with a pure-strategy equilibrium, and the optimal accuracy level r |
| Keywords: | Tullock contest, heterogeneous valuations, accuracy, discrimination, optimal design, all-pay auction |
| JEL: | C72 D72 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9601&r= |
| By: | Onur A. Koska; Frank Stähler |
| Abstract: | This paper discusses the role of secret versus public reserve prices when bidders’ valuations depend positively on the seller’s private signal. A public reserve price is announced before the auction starts, and a secret reserve price is disclosed after the highest bid has been reached. The public reserve price regime may warrant a distortion as a good seller type may have to increase the reserve price beyond payo˙-maximization in order to be able to credibly signal her type. We introduce and determine a rational signaling equilibrium which adds two domination-based conditions to the belief structure of a weak perfect Bayesian equilibrium. We show that a secret (public) reserve price design qualifies as an equilibrium if the distortion is large (small). |
| Keywords: | auctions, interdependent values, optimal reserve prices, rational signaling |
| JEL: | D44 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9581&r= |
| By: | Jian Low; Chen Hajaj; Yevgeniy Vorobeychik |
| Abstract: | We present a rotating proposer mechanism for team formation, which implements a Pareto efficient subgame perfect Nash equilibrium of an extensive-form team formation game. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.04251&r= |
| By: | David Turchick; Siyang Xiong, Charles Z. Zheng |
| Abstract: | One of the proofs in Xiong and Zheng (2007) has a subtle mistake. This note provides a simple correction without changing the structure of the proof or altering any assumption in the said paper. |
| Keywords: | core equivalence; production; core; coalition; blocking |
| JEL: | C71 D51 |
| Date: | 2022–05–03 |
| URL: | http://d.repec.org/n?u=RePEc:spa:wpaper:2022wpecon13&r= |