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In mechanism design, we do just the opposite by starting with the outcomes. We identify the outcomes we would like to have. And then we work backwards to see whether we can engineer institutions (mechanisms) that will lead to those outcomes. This is the normative or prescriptive part of economics.
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Mechanism design, sometimes called implementation theory or institution design, [1] is a branch of economics, social choice, and game theory that deals with designing game forms (or mechanisms) to implement a given social choice function. Because it starts with the end of the game (an optimal result) and then works backwards to find a game that ...
- 1 Basics of Auction Mechanism
- 2 Design Goals and Properties
- Inition 2.1 (Dominant Strategy).
- Inition 2.2 (Equilibrium).
- Inition 2.3 (Direct mechanism).
- Orem 2.1 (Revelation Principle).
- Proof.
- Inition 2.4 (Incentive Compatibility Or Truthfulness).
- Inition 2.5 (Individual Rationality).
- 3 Second-Price Sealed-Bid Mechanism
An auction mechanism can be viewed as a process of buying and selling commodities or services. Generally, an auction consists of the following basic elements: 1. Buyer: The one who wants to buy commodities in auctions is regarded as a buyer. For wireless communications, buyers are users who are eager to obtain radio resources for their own transmis...
In order to understand the core of auction mechanisms and the key of applying auctions in market-driven applications, we formally introduce the essential objectives and properties of auction mechanism design. For illustration purpose and the convenience of explanation, let us consider a forward auction system with a single seller who wants to sell ...
A dominant strategy of a buyer is one that maximizes its utility regardless of other buyers’ strategies. Specifically, bi is the dominant bidding strategy for buyer i if its utility Ui cannot be improved for any bi ′ ≠ bi , and any strategy profile of the other buyers \(\boldsymbol{b}_{-i} =\{ b_{1},\ldots,b_{i-1},b_{i+1},\ldots,b_{N}\}\), i.e.,
An N-tuple of bidding strategies \(\boldsymbol{b}:=\boldsymbol{\beta }=\{\beta _{1}(v_{1}),\ldots,\beta _{N}(v_{N})\}\) is an equilibrium of the auction mechanism if for every buyer i, given the strategies \(\boldsymbol{\beta }_{-i}\) of all other buyers, βi (vi ) is the dominant strategy of buyer ithat maximizes its utility. Since there is no rest...
All buyers are asked to directly report their values \(\boldsymbol{v}\) in the direct mechanism \((\boldsymbol{Q},\boldsymbol{P})\), where \(\boldsymbol{Q} =\{ Q_{1}(\boldsymbol{v}),\ldots,Q_{N}(\boldsymbol{v})\}\) and \(\boldsymbol{P} =\{ P_{1}(\boldsymbol{v}),\ldots,P_{N}(\boldsymbol{v})\}\). As the outcome, \(Q_{i}(\boldsymbol{v}) \in \{ 0,1\}\)...
Given an auction mechanism with a corresponding equilibrium, there exists a direct mechanism in which (i) it is an equilibrium for each buyer to report its value truthfully, and (ii) the outcome is the same as the one produced by the equilibrium of the given mechanism.
From definitions, we have \(\boldsymbol{Q} = Q(\beta (\boldsymbol{v}))\) and \(\boldsymbol{P} = P(\beta (\boldsymbol{v}))\), which demonstrates that the direct mechanism \((\boldsymbol{Q},\boldsymbol{P})\) is a composition of functions (Q, P) and β, as shown in Fig. 2.2. Thus, conclusions (i) and (ii) can be verified routinely. □ The underlying ide...
An auction mechanism \((\boldsymbol{Q},\boldsymbol{P})\) is incentive-compatible or truthful if no buyer i can improve its own utility Ui by bidding bi = vi ′ ≠ vi , i.e.,
An auction mechanism \((\boldsymbol{Q},\boldsymbol{P})\) is individual-rational if every buyer i can receive a non-negative utility after the auction, i.e., Ui ≥ 0. Incentive compatibility is essential to resist market manipulation and ensure auction fairness and efficiency . In untruthful auctions, selfish buyers may misreport their values to mani...
Second-price sealed-bid (SPSB) mechanism is also well-known as Vickrey auction mechanism which was first proposed by the Nobel prize winner Dr. William Vickrey in 1961. In this mechanism, buyers are asked to submit sealed bids for a single commodity. The buyer who reports the highest bid wins (i.e., it is awarded the commodity), while pays the pri...
- Changyan Yi, Jun Cai
- 2016
Mechanism design helps us understand how the answers to these questions depend on the details of the underlying environment. In turn, this helps us understand which details matter and which do not. To get a sense of what mechanism design is, we begin with a fable, first told by the Nobelist, Ronald Coase. It involves, as all good fables do, a ...
18 Oct 2007. Mechanism design theory is a major breakthrough in the modern economic analysis of institutions and markets. It revolutionalised the way economists think about optimal institutions and regulation when governments don't “know it all.”. It has had a major impact on current policy-making and will continue to do so in the future.
Mechanism design sits at the intersection of economics, game theory and artificial intelligence. It takes an engineering approach to solving a wide range of problems where there are interactions among individuals, markets and institutions. Its theoretical foundations were formed in the 1960s by University of Minnesota professor Leonid Hurwicz ...
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Jan 8, 2024 · This article provides an introduction to the theory of mechanism design and its application to engineering problems. Our aim is to provide the fundamental principles of mechanism design for control engineers and theorists, along with state-of-the-art methods in engineering applications. We start our exposition with a brief overview of game theory, highlighting the fundamental notions necessary ...
