# Tag Info

5

I think you're referring to the decoy effect. A popular example of this is the Economist subscription puzzle, popularized in Dan Ariely's TED Talk (starting at 12:22).

4

The type space is the support of the belief about the types. It seems a bit weird to allow a mechanism designer to arbitrarily restrict their belief support. However, you are right: if the designer can find out more about the private types by acquiring information, this would intuitively allow them to reduce information rent, because it makes the type "...

4

In general, VCG is also applicable to reverse auction settings. VCG is not even restricted to auction settings and can be used quite generally, see wikipedia for an introduction. If you want a deeper treatment, I recommend Tilman Börger's book (it used to be fully online, maybe there are still copies flying around). In reality, there are often problems ...

4

In addition to @Tomcat's suggestions, you may also want to check out the literature on matching markets. Easley and Kleinberg have an introductory textbook* on the subject. Chapter 10 covers the basic model of matching markets. Chapter 15 goes over the auction of ad slots as an application. *Easley, David, and Jon Kleinberg (2010) Networks, Crowds, and ...

3

When integrals look different than what pops into your head, often the reason is integration by parts. For your example note that $$\int_R^1 (\theta -R) g(\theta) d \theta + \int_R^1 G(\theta) d \theta = (1-R) - 0,$$ where the right-hand side is equivalent to $\int^1_R 1 d\theta$. Hence, the two expressions you consider are equivalent. It's of the form \...

3

I agree with Sander's reply, but want to add that you have to find such a way to circumvent your issue. Standard mechanism design applies to Bayesian games. In a Bayesian game, the action space is type-independent, and since the designer does not know the types and can only decide on outcomes contingent on the agents' actions, we need to specify when the ...

3

Mechanism design with multi-dimensional types (here: the willingness-to-pay for each object) is a notoriously difficult problem. Even when you abstract from bundling as you do by assuming that the seller only wants to buy one of the goods. Your problem is studied by John Thanassoulis in "Haggling over substitutes", JET 2004. Unfortunately, there is ...

2

A key part of the paper is that they are interested in computationally efficient truthful mechanisms The VCG mechanism is a truthful and efficient direct mechanism, but it is not computationally efficient. In many combinatorial auctions, it is impossible to compute the VCG transfers in a reasonable amount of time using current technology. In the past, ...

2

The area of research you are looking for is market microstructure, the study of how markets work and the process of price formation. Naturally, this means studying liquidity, information diffusion, uncertainty, and dynamic games. There is not a lot of mechanism design in market microstructure -- though work along those lines would certainly be welcomed. For ...

2

I gave you an extremely vague lead in my other comment. Thinking about it a bit harder, I beieve you are right with having a look into the matching literature which I know a bit less. Here is a setting that might be of interest: Kelso & Crawford, Econometrica 1982. They study $m$ workers (=buyers in your setting) and $n$ firms (=items), where a worker ...

1

I can't suggest any research papers, but I can suggest one way of studying this problem: using an agent-based model. For example, this is a simple model of an auction on NetLogo: https://ccl.northwestern.edu/netlogo/models/BiddingMarket. Maybe you can tweak the code to make the model run a simulation of your problem. If this wasn't what you were looking for, ...

1

I suggest to have a look at Krishna's "Auction Theory", Chapter 16 "Non-identical items". Regarding your particular multiproduct problem, I would go from Armstrong's "Multiproduct nonlinear pricing", Econometrica 1996, and see what happens. While I don't want to discourage you, let me mention that mechanism design with ...

1

I am not sure if this is the answer you were aiming at, but... what about the revelation principle? There is no requirement to communicate with the designer. However, researchers are ofter first interested in what the optimal allocation rule is. In that search, it is wlog to consider direct mechanisms by the revelation principle: Suppose an indirect ...

1

If bidders have quasilinear preferences and monetary transfers are possible, then the two notions are equivalent: If $x$ is an allocation of the object and $t$ is a vector of monetary transfers with a balanced budget (so the sum of all transfers is 0), then the pair $(x,t)$ is Pareto efficient if and only if $x$ is the utilitarian allocation (object goes to ...

1

If I understand you correctly, there are two questions here. First, why do computationally efficient IC direct mechanisms perform poorly relative to the optimal IC direct mechanism? The naive answer is simply that the optimal mechanism is really complicated; the paper seems to address this point carefully. Second, why are there computationally efficient ...

1

Yes, it is essentially the same idea as with just one unit. For example, see the text leading to Proposition 14.1 in the book "Auction Theory" by Vijay Krishna. Let $x$ be the vector of willingness-to-pay. Define $U(x) = \max_z \{ q(z)x - m(z)\}$ as the equilibrium utility of type $x$. The incentive compatibility (I am quoting Krishna now) "...

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