The Marriage Problem with Interdependent Preferences

2020 ◽  
Vol 22 (02) ◽  
pp. 2040005
Author(s):  
Mohsen Pourpouneh ◽  
Rasoul Ramezanian ◽  
Arunava Sen
Keyword(s):  
Private Information ◽  
Common Knowledge ◽  
Priority Rules ◽  
Marriage Problem ◽  
Interdependent Preferences ◽  
Incentive Compatible ◽  
Ex Post ◽  
Women’S Preferences ◽  
Matching Rules

This paper considers the Gale–Shapley model with interdependent preferences. Women’s preferences over men are common knowledge but whether or not a man is acceptable depends on the preferences of men which are private information. It is shown that no ex-post incentive-compatible and ex-post stable matching rules exist. A characterization of ex-post incentive-compatible, ex-post individually rational and ex-post nonbossy matching rules in terms of modified priority rules is provided.

scholarly journals Ex-post IR Dynamic Auctions with Cost-per-Action Payments

2018 ◽  
Author(s):  
Weiran Shen ◽  
Zihe Wang ◽  
Song Zuo
Keyword(s):  
Common Knowledge ◽  
Incentive Compatibility ◽  
Individual Rationality ◽  
Incentive Compatible ◽  
Dynamic Auctions ◽  
Ex Post ◽  
Ex Ante ◽  
Ad Auctions ◽  
The Cost ◽  
General Reduction

Motivated by online ad auctions, we consider a repeated auction between one seller and many buyers, where each buyer only has an estimation of her value in each period until she actually receives the item in that period. The seller is allowed to conduct a dynamic auction but must guarantee ex-post individual rationality. In this paper, we use a structure that we call credit accounts to enable a general reduction from any incentive compatible and ex-ante individual rational dynamic auction to an approximate incentive compatible and ex-post individually rational dynamic auction with credit accounts. Our reduction obtains stronger individual rationality guarantees at the cost of weaker incentive compatibility. Surprisingly, our reduction works without any common knowledge assumption. Finally, as a complement to our reduction, we prove that there is no non-trivial auction that is exactly incentive compatible and ex-post individually rational under this setting.

Robust Mechanism Design of Exchange

2020 ◽  
Author(s):  
Pasha Andreyanov ◽  
Tomasz Sadzik
Keyword(s):  
Mechanism Design ◽  
Private Information ◽  
Information Structure ◽  
Utility Functions ◽  
Double Auction ◽  
Exchange Economies ◽  
Incentive Compatible ◽  
Ex Post ◽  
Interdependent Values ◽  
Robust Mechanism Design

Abstract In this article, we provide mechanisms for exchange economies with private information and interdependent values, which are ex post individually rational, incentive compatible, generate budget surplus, and are ex post nearly efficient, with many agents. Our framework is entirely prior-free, and we make no symmetry restrictions. The mechanisms can be implemented using a novel discriminatory conditional double auction, without knowledge of information structure or utility functions. We also show that no other mechanism satisfying the constraints can generate inefficiency of smaller order.

Monopoly Regulation Under Relaxed Pareto Efficiency

2017 ◽  
Vol 5 (2) ◽  
pp. 162-176
Author(s):  
Ismail Saglam
Keyword(s):  
Marginal Cost ◽  
Regulatory Environment ◽  
Pareto Dominance ◽  
Incentive Compatible ◽  
Monopoly Regulation ◽  
Dominance Relationships ◽  
Ex Post ◽  
Ex Ante ◽  
Pareto Axiom ◽  
Set Of Points

Baron and Myerson (BM; 1982, Econometrica, 50(4), 911–930) propose an incentive-compatible, individually rational and ex ante socially optimal direct-revelation mechanism to regulate a monopolistic firm with unknown costs. Their mechanism is not ex post Pareto dominated by any other feasible direct-revelation mechanism. However, there also exist an uncountable number of feasible direct-revelation mechanisms that are not ex post Pareto dominated by the BM mechanism. To investigate whether the BM mechanism remains in the set of ex post undominated mechanisms when the Pareto axiom is slightly weakened, we introduce the ∈-Pareto dominance. This concept requires the relevant dominance relationships to hold in the support of the regulator’s beliefs everywhere except for a set of points of measure ∈, which can be arbitrarily small. We show that a modification of the BM mechanism which always equates the price to the marginal cost can ∈-Pareto dominate the BM mechanism at uncountably many regulatory environments, while it is never ∈-Pareto dominated by the BM mechanism at any regulatory environment.

The randomized communication complexity of revenue maximization

2021 ◽  
Vol 19 (2) ◽  
pp. 75-83
Author(s):  
Aviad Rubinstein ◽  
Junyao Zhao
Keyword(s):  
Lower Bounds ◽  
Communication Complexity ◽  
Social Choice Rule ◽  
Valuation Function ◽  
Optimal Auctions ◽  
Incentive Compatible ◽  
First Approximation ◽  
Exponential Separation ◽  
Open Question

We study the communication complexity of incentive compatible auction-protocols between a monopolist seller and a single buyer with a combinatorial valuation function over n items [Rubinstein and Zhao 2021]. Motivated by the fact that revenue-optimal auctions are randomized [Thanassoulis 2004; Manelli and Vincent 2010; Briest et al. 2010; Pavlov 2011; Hart and Reny 2015] (as well as by an open problem of Babaioff, Gonczarowski, and Nisan [Babaioff et al. 2017]), we focus on the randomized communication complexity of this problem (in contrast to most prior work on deterministic communication). We design simple, incentive compatible, and revenue-optimal auction-protocols whose expected communication complexity is much (in fact infinitely) more efficient than their deterministic counterparts. We also give nearly matching lower bounds on the expected communication complexity of approximately-revenue-optimal auctions. These results follow from a simple characterization of incentive compatible auction-protocols that allows us to prove lower bounds against randomized auction-protocols. In particular, our lower bounds give the first approximation-resistant, exponential separation between communication complexity of incentivizing vs implementing a Bayesian incentive compatible social choice rule, settling an open question of Fadel and Segal [Fadel and Segal 2009].

scholarly journals Multitasking: incentivizing agents differing either in their work ethic or intrinsic motivation

2020 ◽  
Author(s):  
Carsten Helm ◽  
Franz Wirl
Keyword(s):  
Intrinsic Motivation ◽  
Private Information ◽  
Work Ethic ◽  
Monetary Incentives ◽  
The Difference

Abstract Saint Thomas Aquinus ’agen autem non movet nisi ex intentione finis (an agent does not move except out of intention for an end, quoted from Nassim Nicholas Taleb, Antifragile, p. 169.)’. This paper uses the familiar multitasking framework in order to compare contracting with agents holding private information either about their work ethic or intrinsic motivation. Those characterizations are observation equivalent in the absence of incentives but matter once monetary incentives are offered. Indeed the difference is stark: First, incentives change the characterization of which types are efficient or inefficient. Second, contracts in terms of an agent’s work ethic are robust if constraints (ensuring sufficient effort for the unobservable task) are introduced while such constraints can render only fixed wages feasible for intrinsically motivated agents.

scholarly journals Budget Feasible Mechanisms on Matroids

Algorithmica ◽  
2020 ◽  
Author(s):  
Stefano Leonardi ◽  
Gianpiero Monaco ◽  
Piotr Sankowski ◽  
Qiang Zhang
Keyword(s):  
Polynomial Time ◽  
Private Information ◽  
Independent Set ◽  
Deterministic Algorithm ◽  
Matroid Intersection ◽  
Practical Applications ◽  
Incentive Compatible ◽  
The Cost ◽  
Special Case ◽  
Budget Feasible

AbstractMotivated by many practical applications, in this paper we study budget feasible mechanisms with the goal of procuring an independent set of a matroid. More specifically, we are given a matroid $${\mathcal {M}}=(E,{\mathcal {I}})$$ M = ( E , I ) . Each element of the ground set E is controlled by a selfish agent and the cost of the element is private information of the agent itself. A budget limited buyer has additive valuations over the elements of E. The goal is to design an incentive compatible budget feasible mechanism which procures an independent set of the matroid of largest possible value. We also consider the more general case of the pair $${\mathcal {M}}=(E,{\mathcal {I}})$$ M = ( E , I ) satisfying only the hereditary property. This includes matroids as well as matroid intersection. We show that, given a polynomial time deterministic algorithm that returns an $$\alpha $$ α -approximation to the problem of finding a maximum-value independent set in $${\mathcal {M}}$$ M , there exists an individually rational, truthful and budget feasible mechanism which is $$(3\alpha +1)$$ ( 3 α + 1 ) -approximated and runs in polynomial time, thus yielding also a 4-approximation for the special case of matroids.

scholarly journals DIAGNOSIS AND REPAIR OF GYPSUM PLASTER COATINGS: STATISTICAL CHARACTERIZATION AND LESSONS LEARNED FROM A FIELD SURVEY

2014 ◽  
Vol 20 (4) ◽  
pp. 485-496 ◽  
Author(s):  
Ana Pereira ◽  
Filipe Palha ◽  
Jorge de Brito ◽  
José Dinis Silvestre
Keyword(s):  
Field Survey ◽  
Common Knowledge ◽  
Lessons Learned ◽  
Statistical Characterization ◽  
Partition Walls ◽  
Gypsum Plaster ◽  
Detailed Statistical Analysis ◽  
Quantitative Indicators ◽  
Pathological Situation

This paper provides the statistical characterization of the pathological situation of 119 gypsum plaster coatings applied to partition walls and ceilings (inner gypsum plasters – IGP), the diagnosis methods that can be used to characterize the defects and confirm their causes, and the most suitable repair solutions. The results presented in this paper were achieved via the use of an expert system developed by the authors in an extensive inspection programme covering 23 buildings. A comprehensive set of charts and their detailed statistical analysis describe the results achieved, including the characteristics (temporal, spatial and severity) and frequency of the defects in the sample and the main causes of their occurrence in walls and ceilings. The most appropriate diagnosis methods, preventive measures and repair solutions prescribed for these defects in the sample are also analyzed and the most significant correlations presented. Even though in some instances the pathological situation of IGP is common knowledge, this time it has been characterized via quantitative indicators and using a statistically significant sample, which means that important lessons can be learned.

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