scholarly journals Limitations of Incentive Compatibility on Discrete Type Spaces

2020 ◽  
Vol 34 (02) ◽  
pp. 2136-2143
Author(s):  
Taylor Lundy ◽  
Hu Fu
Keyword(s):  
Convex Hull ◽  
Incentive Compatibility ◽  
Dominant Strategy ◽  
Negative Answer ◽  
Incentive Compatible ◽  
Type Spaces ◽  
Strategy Incentive ◽  
Discrete Type

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.

scholarly journals Mechanism design without quasilinearity

2020 ◽  
Vol 15 (2) ◽  
pp. 511-544 ◽  
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.

scholarly journals Multi-Unit Bilateral Trade

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.

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

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.

Dictatorial Mechanisms in Constrained Combinatorial Auctions

2013 ◽  
Vol 13 (1) ◽  
pp. 363-380 ◽  
Author(s):  
Anat Lerner ◽  
Rica Gonen
Keyword(s):  
Dominant Strategy ◽  
Combinatorial Auctions ◽  
Budget Constraints ◽  
Basic Properties ◽  
Incentive Compatible ◽  
Private Values ◽  
Multidimensional Types ◽  
Possibility Space ◽  
Pareto Efficient ◽  
Strategy Incentive

AbstractWe study the possibility space of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto efficient combinatorial auctions in a model with two players and two nonidentical items (four outcomes). Our model has multidimensional types, private values, nonnegative prices, and quasilinear preferences for the players with one relaxation – the players are subject to publicly known budget constraints. We show that the space we study essentially includes one type of mechanisms: 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 efficient. The mechanisms in the autocratic families are identical except for two to three price parameters that differentiate them.

scholarly journals Incentive-Compatible Diffusion Auctions

2020 ◽  
Author(s):  
Bin Li ◽  
Dong Hao ◽  
Dengji Zhao
Keyword(s):  
Social Relations ◽  
Incentive Compatibility ◽  
Dominant Strategy ◽  
Necessary Condition ◽  
Design Problems ◽  
Allocation Policy ◽  
Incentive Compatible ◽  
Multidimensional Problems ◽  
The Social ◽  
Sufficient And Necessary Condition

Diffusion auction is a new model in auction design. It can incentivize the buyers who have already joined in the auction to further diffuse the sale information to others via social relations, whereby both the seller's revenue and the social welfare can be improved. Diffusion auctions are essentially non-typical multidimensional mechanism design problems and agents' social relations are complicatedly involved with their bids. In such auctions, incentive-compatibility (IC) means it is best for every agent to honestly report her valuation and fully diffuse the sale information to all her neighbors. Existing work identified some specific mechanisms for diffusion auctions, while a general theory characterizing all incentive-compatible diffusion auctions is still missing. In this work, we identify a sufficient and necessary condition for all dominant-strategy incentive-compatible (DSIC) diffusion auctions. We formulate the monotonic allocation policies in such multidimensional problems and show that any monotonic allocation policy can be implemented in a DSIC diffusion auction mechanism. Moreover, given any monotonic allocation policy, we obtain the optimal payment policy to maximize the seller's revenue.

Autocratic Mechanisms: A Form of Dictatorship in Constrained Combinatorial Auctions

2015 ◽  
Vol 17 (04) ◽  
pp. 1550010 ◽  
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.

Book Reviews

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.”

scholarly journals Rationality in games and institutions

Synthese ◽  
2021 ◽  
Author(s):  
Philippe van Basshuysen
Keyword(s):  
Institutional Design ◽  
Incentive Compatibility ◽  
Social Goals ◽  
General Constraint ◽  
Rational Agents ◽  
Economic Agents ◽  
Incentive Compatible ◽  
Inclusive Concept ◽  
The One ◽  
Orthodox View

AbstractAgainst the orthodox view of the Nash equilibrium as “the embodiment of the idea that economic agents are rational” (Aumann, 1985, p 43), some theorists have proposed ‘non-classical’ concepts of rationality in games, arguing that rational agents should be capable of improving upon inefficient equilibrium outcomes. This paper considers some implications of these proposals for economic theory, by focusing on institutional design. I argue that revisionist concepts of rationality conflict with the constraint that institutions should be designed to be incentive-compatible, that is, that they should implement social goals in equilibrium. To resolve this conflict, proponents of revisionist concepts face a choice between three options: (1) reject incentive compatibility as a general constraint, (2) deny that individuals interacting through the designed institutions are rational, or (3) accept that their concepts do not cover institutional design. I critically discuss these options and I argue that a more inclusive concept of rationality, e.g. the one provided by Robert Sugden’s version of team reasoning, holds the most promise for the non-classical project, yielding a novel argument for incentive compatibility as a general constraint.

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