Questions tagged [mechanism-design]
Mechanism design is a field in economics and game theory that takes an engineering approach to designing economic mechanisms or incentives, toward desired objectives, in strategic settings, where players act rationally.
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How much information is required to manipulate a mechanism?
It is well-known that the first-price auction is manipulable, in that a player can improve his utility by bidding less than his true value. But successful manipulation requires information: the player ...
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Truthful assignment for facility allocation problems
We have the following congestion game. $n$ agents and $m$ facilities are positioned on the real line $\mathbb{R}$. The position of agent $i$ is denoted by $x_i\in \mathbb{R}$ and the location of ...
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Definition of information structure in an incomplete information game
I try to understand the model in this paper, pages 48-49. (Bergemann, D., & Morris, S. (2019). Information design: A unified perspective. Journal of Economic Literature, 57(1), 44–95. https://doi....
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"Mechanism design" vs "Implementation theory"
The terms mechanism design and implementation theory seem to me closely related: in both fields, we are given some objective function, and we want to "implement" it, that is, construct a &...
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Does the Gale-Shapley algorithm provide just one allocation?
I know that in a marriage problem for example, you may have more than one stable allocations but I think that the Gale-Shapley algorithm just provide only one.
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Deferred Acceptance Algorithm
Can you help with this statement?
Let N be a set of agents in a two-sided matching market. Apply a
version of the deferred acceptance alghoritm and suppose it
produces the allocation µ in which agent ...
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Mechanism Design with Quantal Best Response
I was wondering if there is a sensible definition of mechanism design (incentive compatibility and individual rationality) when the agent (bidder) is only boundedly rational. In the classical ...
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Screening models with multiple goods and interacting costs
I'm looking for a reference in the literature on monopolistic screening/mechanism design, where there are multiple allocative variables and these interact in the agent's utility function.
For example, ...
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Book: Introduction to Mechanism Design, Problem Outlined on Page 28
Suppose a seller has two distinct indivisible goods, good $A$ and good $B$, for sale. For simplicity, we assume that the seller values the goods at zero and is risk-neutral, so that she seeks to ...
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Every Submodular Valuation Can Be Represented as a Maximum of Additive Valuations
According to this paper, "every submodular function can be represented as a maximum of additive valuations." It gives an algebraic description as well, but I am having trouble internalizing ...
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Mechanism Design and Self-Trade Cancellation
In the case of mechanism design, i am looking to estimate the welfare gains due to difference in rules of market clearing function. If in the price-time priority order book, the incoming aggressive ...
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VCG mechanism exercise
Consider a setting with n potential buyers and a single object to sell. Each buyer has a type equal to K_i
(i = 1; 2) representing the utility from buying the good. Types are independently drawn from ...
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Geometric interpretation of transfer function in incentive-compatible direct mechanism
Consider a set of players $i = 1,...,N$ who need to allocate some good. Each player $i$ valuates the good $v_i \in [0,1]$, with $v_i \sim f_i$. An individually rational direct mechanism $(p,c)$, with $...
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How widely can the objective of mechanism design be generalized?
The mechanism design lectures I've been watching have focused on the objective of maintaining performance guarantees in terms of either total surplus or total revenue/virtual surplus (while also ...
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Geometric Interpretation of the Potential Function of a Game
One geometric interpretation of (at least one term of) the potential function I've come across is as the Riemann-approximated area under an individual player's cost as a function of the number of ...
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Why are Mixed Strategy Nash Equilibria special cases of Correlated Equilibria and Coarse Correlated Equilibria?
In a Mixed Strategy Nash Equilibrium, each player constructs their own probability distribution over the set of their respective possible strategies.
In a Correlated Equilibrium or a Coarse Correlated ...
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Asymmetries in Equilibrium Utility
In this lecture, the professor says that all Nash Equilibria have the same utility in non-atomic selfish routing, whereas this is not guaranteed in atomic selfish routing. It is unclear how general ...
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Interpretation of the Myerson (1981) Bidder Utility (Optimal Auctions, Mechanism Design)
In Myerson 1981, the bidders' utility function does not make sense. $p_{i}$ is a probability of winning the auction, $t_i$ is the bidder's type (or valuation of the item), and $x_i$ is the payment. $r$...
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Why is Dominant-Strategy Incentive Compatibility treated as a virtue, and are there mechanism design models which treat it as undesirable?
Why is Dominant-Strategy Incentive Compatibility treated as such a ubiquitous virtue? In this lecture, the answer given from the perspective of a non-principal player is, "it's easy to play; you ...
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How do economists explain "If You Want to Win, Tell Your Team It’s Losing (a Little)." along with self-efficacy
How do economists explain: "If You Want to Win, Tell Your Team It’s Losing (a Little)." ?
I read this article. And I learnt that—
"The relationship between the score and the likelihood ...
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The concept of 'truthfulness' and 'indirect' in mechanism design
I'm a beginner in mechanism design. I learned that 'a (direct) mechanism is truthful if an agent truthfully reveals his/her type.' Then, how can we define a truthful indirect mechanism? I'm not sure ...
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Single-item single-bidder: why posted price is the only possible DSIC mechanism?
I'm reading Tim Roughgarden's Twenty Lectures on Algorithmic Game Theory. Lecture 5 is on revenue-maximizing auctions. It claims that in the single-parameter qusilinear environment, for the extremely ...
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A question about revelation principle from the game theory online course
I am finding the revelation principle very confusing. So I was watching the Game Theory online course by Stanford and UBC. In their video about revelation principle, here are the original words from ...
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Revenue-maximizing auction with no free disposal
Myerson has a famous theory that can be used to design truthful auctions maximizing the revenue of the seller. The simplest case is when a seller sells a single item to buyers whose values are ...
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Auction Theory and Elections
Can we (is it reasonable to) apply auction theory and the various incentive compatible mechanisms to elections and guarantee cardinal voting?
I am thinking specifically of VCG auctions and ...
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Equivalence from correlated/communication equilibrium to Nash Equilibrium?
Taking into account the seminal papers of Forges and Imre Bárány, they proove a very strong result that gives an exact connection among the communication and the correlation equilibrium solution ...
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Intuition behind Myerson's characterization of DSIC Single Object Allocation Mechanism
Myerson (1981) states that in a single object allocation problem with quasilinear preferences, where $q_i(.)$ is an allocation function, $p_i(.)$ a payment function and $u_i(.)$ a utility function for ...
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Design of efficient cheap talk communication
Are there any papers about efficient cheap talk communication, where the players achieve the equilibrium payoffs of a correlated strategy as in Aumann's seminal paper? Or in case no such paper exists, ...
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What does social choice theory say about how to assign different positions to every member in a committee?
Consider the following setting:
A committee has $N$ members.
There are $m$ types of positions in the committee.
For each type of positions $1 \leq i \leq m$, there are $n_i$ identitical positions for ...
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Definition of direct revelation mechanism
In Algorithmic Game Theory by Noam Nisan, a (general) mechanism for $n$ player is defined as
$$
M=(\{T_i\},\{X_i\},A,\{v_i\},a,\{p_i\}),\tag1
$$
where $T_1,\dots,T_n$ are the players' type spaces (...
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Mechanism design making the Government reveil its indiferrence price towards goods
In order to Tax non-monetary property and wealth the government sets an arbitrary price (they are not even personalized assesments) and often people transact below that price. I have bought and sold ...
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What is the difference between a communication mechanism and a protocol of communication?
What is the difference between a communication mechanism and a protocol of communication in mechanism and information design. Although most papers in the literature make this distinction, it is not ...
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Auction mechanism with quoters and price takers
Consider a market with one buyer with a fixed demand and multiple sellers for a divisible good. The goal of the market is to determine a uniform unit-price for the good as well as which seller ...
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VCG mechanism and budget balance
I have a general question on how we state that in VCG (which doesn't balance the budget) we can't distribute the money as it will destroy incentives. I don't understand how for ex. this would affect ...
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locating specific model from organizational economics
I am trying to find one specific model from organizational economics that I encountered in one of my past classes, but I cant remember the name of the model and google scholar search based on some of ...
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What's the difference between Ex-post Incentive Compatibility and Dominant-Strategy Incentive Compatibility
According to the Wikipedia definition of Dominant-Strategy Incentive Compatibility (DSIC):
DSIC means truth-telling is a weakly-dominant strategy, i.e. you fare best or at least not worse by being ...
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Revelation principle when the type space is infinite [closed]
Consider a mechanism design problem in which the agents have type spaces that are uncountably infinite. I have a couple of questions which are numbered throughout this post.
The revelation principle ...
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Payoff from an option contract
In period 1 the consumer of type $\theta$ selects an option contract consisting of an up-front fee, $B>0$, and exercise price, $\bar{R}$. The consumer pays $B$ at the end of the first period. In ...
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The influence of restricted type space on incentive compatible mechanism design?
When we are to design an IC mechanism for an auction, we usually assume that each agent $i$'s type $\theta_i$ is draw from its type space $\Theta_i$, which contains all the possible types of $i$. For ...
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Is VCG mechanism applicable in reverse auction? If so, how?
The VCG mechanism I've learnt is from Roughgarden's Twenty Lectures on Algorithmic Game Theory. Given an auction, we first identify the allocation that maximize the social welfare and then compute the ...
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Can you please help me find this topic in Mechanism design/Rational choice theory?
When I was in university, I remember studying some kind of topic in adv microeconomics where someone gives you three options, where one is obviously worse and is put there just to deceive you so that ...
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Multi-item multi-unit matching markets
This is a reference request.
I'm interested in auction design problems of the following form:
- Consider one seller and many buyers.
- The seller seeks to sell multiple items where each item has ...
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Multi-item Auctions in Mechanism Design
I'm new to auction theory and only started reading it a few days ago.
My question is this: Is it possible to design efficient auctions of multiple non-identical items? By efficient I mean maximize the ...
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Search terms to find a menu of currency exchange mechanisms?
I'm look to find a good source for comparing mechanism designs for simple currency exchanges.
Is there a name for a category of game (e.g. Stackelberg game) that encapsulates the operation of an ...
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Decentralized Mechanism Design
From what I've read in mechanism design theory, it seems to me that the mechanism designer always plays an essential role in a mechanism. Information is sent to the designer who designs incentives ...
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Efficiency in Auctions
Consider a finite number of bidders, each bidding for a single indivisible object, with private independent values from some probability distribution.
There are 2 intuitive notions of (ex-post) ...
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Approximately Optimal Mechanism Design vs. Revelation Principle
The abstract of the article "Impossibility Results for Truthful Combinatorial Auctions with Submodular Valuations" (Dobzinski, Vondrak, 2016) states
A long-standing open question in algorithmic ...
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Mechanism Design and Multidimensional Type Spaces
Is it possible to design a mechanism of agents with multidimensional types?
In particular, what if the type space has the following form:
$$\Theta_i=\{\theta_i\in\{{1,2,\dots, n}\}\times[0,1]:n\in\...
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Auction theory reference request
I am interested in finding the literature or at least some references (books, journal papers etc.) for the following problem:
Suppose there is an auction with one seller and one buyer. The seller ...
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Allocating chores using auctions
I live in a student dorm with 16 people and we share a kitchen. Every week someone has to clean the kitchen. Right now we just take turns in a way determined by the numbers of our respective rooms. ...
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