The Revelation Principle for Mechanism Design with Signaling Costs

2021 ◽  
Vol 9 (1) ◽  
pp. 1-35
Author(s):  
Andrew Kephart ◽  
Vincent Conitzer
Keyword(s):  
Mechanism Design ◽  
Polynomial Time ◽  
Arbitrary Mapping ◽  
Revelation Principle ◽  
Np Hardness ◽  
Primary Contribution

The revelation principle is a key tool in mechanism design. It allows the designer to restrict attention to truthful mechanisms, greatly facilitating analysis. This is also borne out algorithmically, allowing certain computational problems in mechanism design to be solved in polynomial time. Unfortunately, when not every type can misreport every other type (the partial verification model) or—more generally—misreporting can be costly, the revelation principle can fail to hold. This also leads to NP-hardness results. The primary contribution of this article consists of characterizations of conditions under which the revelation principle still holds when reporting can be costly. (These are generalizations of conditions given earlier for the partial verification case [11, 21].) Furthermore, our results extend to cases where, instead of reporting types directly, agents send signals that do not directly correspond to types. In this case, we obtain conditions for when the mechanism designer can restrict attention to a given (but arbitrary) mapping from types to signals without loss of generality.

The revelation principle and mechanism design

2021 ◽  
pp. 473-490
Author(s):  
Harald Wiese
Keyword(s):  
Mechanism Design ◽  
Revelation Principle

scholarly journals Internet shopping optimization problem

2010 ◽  
Vol 20 (2) ◽  
pp. 385-390 ◽  
Author(s):  
JACEK B£A ZÿEWICZ ◽  
Mikhail Kovalyov ◽  
Jędrzej Musiał ◽  
Andrzej Urbanski ◽  
Adam Wojciechowski
Keyword(s):  
Polynomial Time ◽  
Optimization Problem ◽  
Partial Solution ◽  
The Internet ◽  
Internet Shopping ◽  
Single Product ◽  
Polynomial Time Algorithms ◽  
Special Cases ◽  
Multiple Item ◽  
Np Hardness

Internet shopping optimization problemA high number of Internet shops makes it difficult for a customer to review manually all the available offers and select optimal outlets for shopping. A partial solution to the problem is brought by price comparators which produce price rankings from collected offers. However, their possibilities are limited to a comparison of offers for a single product requested by the customer. The issue we investigate in this paper is a multiple-item multiple-shop optimization problem, in which total expenses of a customer to buy a given set of items should be minimized over all available offers. In this paper, the Internet Shopping Optimization Problem (ISOP) is defined in a formal way and a proof of its strong NP-hardness is provided. We also describe polynomial time algorithms for special cases of the problem.

Mechanism Design and the Law

2017 ◽  
Author(s):  
Werner Güth
Keyword(s):  
Mechanism Design ◽  
Institutional Design ◽  
Common Knowledge ◽  
Legal Rules ◽  
Revelation Principle ◽  
Game Theoretic ◽  
The Law ◽  
Legal Mechanism ◽  
Dominance Solvability

Mechanism design is the game theoretic jargon for institutional design and the even older tradition (in German) of ‘Ordnungspolitik’ (institutional design policy). When implementing institutions or mechanisms (or simply rules of conduct) such regulation should usually be codified by complementing the law appropriately. This article first derives and discusses legal rules as traditionally justified and implemented legally. This is then confronted with game theoretic mechanism design, relying on Dominance Solvability or the Revelation Principle. It is argued that the Revelation Principle is very useful for welfaristic or, more generally, consequentialistic explorations of what is attainable but offers no practical basis for legal mechanism design due to its unrealistic common knowledge restrictions.

scholarly journals Transportation and Batching Scheduling for Minimizing Total Weighted Completion Time

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 819 ◽  
Author(s):  
Hongjun Wei ◽  
Jinjiang Yuan ◽  
Yuan Gao
Keyword(s):  
Computational Complexity ◽  
Approximation Algorithm ◽  
Polynomial Time ◽  
Completion Time ◽  
Total Weighted Completion Time ◽  
Single Vehicle ◽  
Weighted Completion Time ◽  
Np Hardness

We consider the coordination of transportation and batching scheduling with one single vehicle for minimizing total weighted completion time. The computational complexity of the problem with batch capacity of at least 2 was posed as open in the literature. For this problem, we show the unary NP-hardness for every batch capacity at least 3 and present a polynomial-time 3-approximation algorithm when the batch capacity is at least 2.

scholarly journals A Polynomial-time, Truthful, Individually Rational and Budget Balanced Ridesharing Mechanism

2021 ◽  
Author(s):  
Tatsuya Iwase ◽  
Sebastian Stein ◽  
Enrico H. Gerding
Keyword(s):  
Mechanism Design ◽  
Polynomial Time ◽  
Social Cost ◽  
Common Origin ◽  
The Right

Ridesharing has great potential to improve transportation efficiency while reducing congestion and pollution. To realize this potential, mechanisms are needed that allocate vehicles optimally and provide the right incentives to riders. However, many existing approaches consider restricted settings (e.g., only one rider per vehicle or a common origin for all riders). Moreover, naive applications of standard approaches, such as the Vickrey-Clarke-Groves or greedy mechanisms, cannot achieve a polynomial-time, truthful, individually rational and budget balanced mechanism. To address this, we formulate a general ridesharing problem and apply mechanism design to develop a novel mechanism which satisfies all four properties and whose social cost is within 8.6% of the optimal on average.

The revelation principle and mechanism design

2020 ◽  
pp. 661-719
Author(s):  
David M. Kreps
Keyword(s):  
Mechanism Design ◽  
Adverse Selection ◽  
Optimal Contract ◽  
Gains From Trade ◽  
Revelation Principle ◽  
Ex Post ◽  
The Government ◽  
Role Of The Government

This chapter evaluates a more general attack on optimal contract and mechanism design stressing cases of adverse selection, which makes use of the revelation principle. One should be clear about the uses to which the revelation principle is put. It can be thought of as a statement about how actually to implement contracts. But it may be better to use it with greater circumspection as a tool of analysis for finding the limits of what outcomes can be implemented, without reference to how best to implement a particular outcome. In some contexts of direct revelation, there will be situations ex post where the party in the role of the government knows that it can obtain further gains from trade from one or more of the parties who participated. Meanwhile, in many applications of the revelation principle, the party in the role of mechanism designer must be able to commit credibly to no subsequent (re)negotiation once it learns the types of the parties with which it is dealing.

Mechanism design with partial verification and revelation principle

2010 ◽  
Vol 22 (1) ◽  
pp. 217-223 ◽  
Author(s):  
Lan Yu
Keyword(s):  
Mechanism Design ◽  
Revelation Principle

scholarly journals A constructive existence theorem related to local transformations of graphs for the independent set problem

2019 ◽  
Vol 21 (2) ◽  
pp. 215-221
Author(s):  
Dmitry V. Sirotkin ◽  
Dmitry S. Malyshev
Keyword(s):  
Existence Theorem ◽  
Polynomial Time ◽  
Independence Number ◽  
Independent Set ◽  
Independent Set Problem ◽  
Power Set ◽  
Np Hardness

For a given graph, the independent set problem is to find the size of a maximum set of pairwise non-adjacent its vertices. There are numerous cases of NP-hardness and polynomial-time solvability of this problem. To determine a computational status of the independent set problem, local transformations of graphs are often used. The paper considers some class of replacements of subgraphs in graphs that change the independence number in a controllable way. Every such local transform of a graph is determined by some pattern which is a subset of the power set. It is obvious that this pattern must be gradable. The paper shows that replacing subgraph exists for any gradable pattern.

scholarly journals Generating All Maximal Independent Sets: NP-Hardness and Polynomial-Time Algorithms

1980 ◽  
Vol 9 (3) ◽  
pp. 558-565 ◽  
Author(s):  
E. L. Lawler ◽  
J. K. Lenstra ◽  
A. H. G. Rinnooy Kan
Keyword(s):  
Polynomial Time ◽  
Independent Sets ◽  
Polynomial Time Algorithms ◽  
Maximal Independent Sets ◽  
Np Hardness
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