The Incompatibility of Pareto Optimality and Dominant-Strategy Incentive Compatibility in Sufficiently-Anonymous Budget-Constrained Quasilinear Settings

In the design of incentive compatible mechanisms, a common approach is to enforce incentive compatibility as constraints in programs that optimize over feasible mechanisms. Such constraints are often imposed on sparsified representations of the type spaces, such as their discretizations or samples, in order for the program to be manageable. In this work, we explore limitations of this approach, by studying whether all dominant strategy incentive compatible mechanisms on a set T of discrete types can be extended to the convex hull of T.Dobzinski, Fu and Kleinberg (2015) answered the question affirmatively for all settings where types are single dimensional. It is not difficult to show that the same holds when the set of feasible outcomes is downward closed. In this work we show that the question has a negative answer for certain non-downward-closed settings with multi-dimensional types. This result should call for caution in the use of the said approach to enforcing incentive compatibility beyond single-dimensional preferences and downward closed feasible outcomes.

Download Full-text

Autocratic Mechanisms: A Form of Dictatorship in Constrained Combinatorial Auctions

International Game Theory Review ◽

10.1142/s0219198915500103 ◽

2015 ◽

Vol 17 (04) ◽

pp. 1550010 ◽

Cited By ~ 1

Author(s):

Anat Lerner ◽

Rica Gonen

Keyword(s):

Pareto Optimality ◽

Dominant Strategy ◽

Combinatorial Auctions ◽

Pareto Optimal ◽

Basic Properties ◽

Incentive Compatible ◽

Welfare Maximization ◽

Private Values ◽

Multidimensional Types ◽

Strategy Incentive

We characterize the space of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal combinatorial auctions where efficiency is not required. We examine a model with two players and k nonidentical items (2k outcomes), multidimensional types, private values, non-negative prices, and quasilinear preferences for the players with one relaxation — the players are subject to publicly-known budget constraints. We show that if it is publicly known that the players value the bundles more than the smaller of their budgets then the studied space includes one type of mechanism: autocratic mechanisms (a form of dictatorship). Furthermore, we prove that there are families of autocratic mechanisms that uniquely fulfill the basic properties of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal. Interestingly the above basic properties are a weaker requirement than it may initially appear, as the property of Pareto optimality in our model of budget-constrained players and non-negative prices do not coincide with welfare maximization, i.e., efficiency as such is a much weaker requirement.

Download Full-text

Book Reviews

Journal of Economic Literature ◽

10.1257/jel.54.2.589.r1 ◽

2016 ◽

Vol 54 (2) ◽

pp. 589-591

Keyword(s):

Graduate Students ◽

Mechanism Design ◽

Incentive Compatibility ◽

Dominant Strategy ◽

University Of Michigan ◽

Dynamic Mechanism Design ◽

Temple University ◽

The University ◽

Robust Mechanism Design

Dimitrios Diamantaras of Temple University reviews “An Introduction to the Theory of Mechanism Design,” by Tilman Börgers. The Econlit abstract of this book begins: “Presents explanations of classic results in the theory of mechanism design and examines the frontiers of research in mechanism design in a text written for advanced undergraduate and graduate students of economics who have a good understanding of game theory. Discusses screening; examples of Bayesian mechanism design; examples of dominant strategy mechanisms; incentive compatibility; Bayesian mechanism design; dominant strategy mechanisms; nontransferable utility; informational interdependence; robust mechanism design; and dynamic mechanism design. Börgers is Samuel Zell Professor of the Economics of Risk at the University of Michigan.”

Download Full-text

Polyhedral Clinching Auctions for Two-Sided Markets

Mathematics of Operations Research ◽

10.1287/moor.2021.1124 ◽

2021 ◽

Author(s):

Hiroshi Hirai ◽

Ryosuke Sato

Keyword(s):

Pareto Optimality ◽

Network Flow ◽

Flow Model ◽

Incentive Compatibility ◽

The Internet ◽

Matching Markets ◽

Budget Balance ◽

Multiunit Auctions ◽

Exchange Markets ◽

Two Sided Markets

In this paper, we present a new model and mechanisms for auctions in two-sided markets of buyers and sellers, where budget constraints are imposed on buyers. Our model incorporates polymatroidal environments and is applicable to a variety of models that include multiunit auctions, matching markets, and reservation exchange markets. Our mechanisms are built on the polymatroidal network flow model by Lawler and Martel. Additionally, they feature nice properties such as the incentive compatibility of buyers, individual rationality, Pareto optimality, and strong budget balance. The first mechanism is a two-sided generalization of the polyhedral clinching auction by Goel et al. for one-sided markets. The second mechanism is a reduce-to-recover algorithm that reduces the market to be one-sided, applies the polyhedral clinching auction by Goel et al., and lifts the resulting allocation to the original two-sided market via the polymatroidal network flow. Both mechanisms are implemented by polymatroid algorithms. We demonstrate how our framework is applied to the Internet display advertisement auctions.

Download Full-text

Efficient multiunit auctions for normal goods

Theoretical Economics ◽

10.3982/te3430 ◽

2020 ◽

Vol 15 (1) ◽

pp. 361-413 ◽

Cited By ~ 1

Author(s):

Brian Baisa

Keyword(s):

Incentive Compatibility ◽

Dominant Strategy ◽

Impossibility Theorem ◽

Budget Balance ◽

Auction Design ◽

Vickrey Auction ◽

Multiunit Auctions ◽

Private Values ◽

Multidimensional Types ◽

Normal Goods

I study multiunit auction design when bidders have private values, multiunit 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 multidimensional types.

Download Full-text

A dominant strategy double clock auction with estimation‐based tâtonnement

Theoretical Economics ◽

10.3982/te3311 ◽

2021 ◽

Vol 16 (3) ◽

pp. 943-978

Author(s):

Simon Loertscher ◽

Claudio Mezzetti

Keyword(s):

Private Information ◽

Asymptotic Efficiency ◽

Incentive Compatibility ◽

Dominant Strategy ◽

Demand And Supply ◽

Strategy Equilibrium ◽

Ex Post ◽

Good Market ◽

Asymptotically Efficient ◽

Homogeneous Good

The price mechanism is fundamental to economics but difficult to reconcile with incentive compatibility and individual rationality. We introduce a double clock auction for a homogeneous good market with multidimensional private information and multiunit traders that is deficit‐free, ex post individually rational, constrained efficient, and makes sincere bidding a dominant strategy equilibrium. Under a weak dependence and an identifiability condition, our double clock auction is also asymptotically efficient. Asymptotic efficiency is achieved by estimating demand and supply using information from the bids of traders that have dropped out and following a tâtonnement process that adjusts the clock prices based on the estimates.

Download Full-text

Multi-Unit Bilateral Trade

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v33i01.33011973 ◽

2019 ◽

Vol 33 ◽

pp. 1973-1980

Author(s):

Matthias Gerstgrasser ◽

Paul W. Goldberg ◽

Bart De Keijzer ◽

Philip Lazos ◽

Alexander Skopalik

Keyword(s):

Social Welfare ◽

Finite Number ◽

Bilateral Trade ◽

Dominant Strategy ◽

Specific Class ◽

Single Item ◽

Incentive Compatible ◽

Ex Post ◽

Strategy Incentive

We characterise the set of dominant strategy incentive compatible (DSIC), strongly budget balanced (SBB), and ex-post individually rational (IR) mechanisms for the multi-unit bilateral trade setting. In such a setting there is a single buyer and a single seller who holds a finite number k of identical items. The mechanism has to decide how many units of the item are transferred from the seller to the buyer and how much money is transferred from the buyer to the seller. We consider two classes of valuation functions for the buyer and seller: Valuations that are increasing in the number of units in possession, and the more specific class of valuations that are increasing and submodular.Furthermore, we present some approximation results about the performance of certain such mechanisms, in terms of social welfare: For increasing submodular valuation functions, we show the existence of a deterministic 2-approximation mechanism and a randomised e/(1 − e) approximation mechanism, matching the best known bounds for the single-item setting.

Download Full-text

Mechanism design without quasilinearity

Theoretical Economics ◽

10.3982/te2910 ◽

2020 ◽

Vol 15 (2) ◽

pp. 511-544 ◽

Cited By ~ 5

Author(s):

Tomoya Kazumura ◽

Debasis Mishra ◽

Shigehiro Serizawa

Keyword(s):

Mechanism Design ◽

Dominant Strategy ◽

Monotonicity Property ◽

Allocation Rule ◽

Type Space ◽

Outside Option ◽

Incentive Compatible ◽

Type Spaces ◽

Good Provision ◽

Strategy Incentive

This paper studies a model of mechanism design with transfers where agents' preferences need not be quasilinear. In such a model, (i) we characterize dominant strategy incentive compatible mechanisms using a monotonicity property, (ii) we establish a revenue uniqueness result (for every dominant strategy implementable allocation rule, there is a unique payment rule that can implement it), and (iii) we show that every dominant strategy incentive compatible, individually rational, and revenue‐maximizing mechanism must charge zero payment for the worst alternative (outside option). These results are applicable in a wide variety of problems (single object auction, multiple object auction, public good provision, etc.) under suitable richness of type space. In particular, our results are applicable to two important type spaces: (a) type space containing an arbitrarily small perturbation of quasilinear type space and (b) type space containing all positive income effect preferences.

Download Full-text

Approximately Maximizing the Broker's Profit in a Two-sided Market

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2019/22 ◽

2019 ◽

Author(s):

Jing Chen ◽

Bo Li ◽

Yingkai Li

Keyword(s):

Production Cost ◽

Dominant Strategy ◽

Valuation Function ◽

Optimal Production ◽

Single Item ◽

Incentive Compatible ◽

Private Value ◽

Cost Monotonicity ◽

Strategy Incentive ◽

Two Sided Markets

We study how to maximize the broker's (expected) profit in a two-sided market, where she buys items from a set of sellers and resells them to a set of buyers. Each seller has a single item to sell and holds a private value on her item, and each buyer has a valuation function over the bundles of the sellers' items. We consider the Bayesian setting where the agents' values/valuations are independently drawn from prior distributions, and aim at designing dominant-strategy incentive-compatible (DSIC) mechanisms that are approximately optimal. Production-cost markets, where each item has a publicly-known cost to be produced, provide a platform for us to study two-sided markets. Briefly, we show how to covert a mechanism for production-cost markets into a mechanism for the broker, whenever the former satisfies cost-monotonicity. This reduction holds even when buyers have general combinatorial valuation functions. When the buyers' valuations are additive, we generalize an existing mechanism to production-cost markets in an approximation-preserving way. We then show that the resulting mechanism is cost-monotone and thus can be converted into an 8-approximation mechanism for two-sided markets.

Download Full-text

Randomized Wagering Mechanisms

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v33i01.33011845 ◽

2019 ◽

Vol 33 ◽

pp. 1845-1852

Author(s):

Yiling Chen ◽

Yang Liu ◽

Juntao Wang

Keyword(s):

Pareto Optimality ◽

Design Space ◽

Incentive Compatibility ◽

Ground Truth ◽

Impossibility Result ◽

Individual Rationality ◽

Budget Balance ◽

Information Elicitation ◽

Recent Extension ◽

Noisy Labels

Wagering mechanisms are one-shot betting mechanisms that elicit agents’ predictions of an event. For deterministic wagering mechanisms, an existing impossibility result has shown incompatibility of some desirable theoretical properties. In particular, Pareto optimality (no profitable side bet before allocation) can not be achieved together with weak incentive compatibility, weak budget balance and individual rationality. In this paper, we expand the design space of wagering mechanisms to allow randomization and ask whether there are randomized wagering mechanisms that can achieve all previously considered desirable properties, including Pareto optimality. We answer this question positively with two classes of randomized wagering mechanisms: i) one simple randomized lottery-type implementation of existing deterministic wagering mechanisms, and ii) another family of randomized wagering mechanisms, named surrogate wagering mechanisms, which are robust to noisy ground truth. Surrogate wagering mechanisms are inspired by an idea of learning with noisy labels (Natarajan et al. 2013) as well as a recent extension of this idea to the information elicitation without verification setting (Liu and Chen 2018). We show that a broad set of randomized wagering mechanisms satisfy all desirable theoretical properties.

Download Full-text