12 votes
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What is the definition of "First Best", "Second Best", etc. in contract theory?

In contract theory The first-best refers to the best you could do if you knew agents' preferences over labor and income (i.e., if you did not have to impose the incentive compatibility constraint), ...
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12 votes

What is the difference between contract theory and mechanism design?

Contracts are a subset of all mechanisms where agreements are enforcable. An example of a mechanism that is not a contract: A second price auction (or Vickrey auction) is a truth-telling mechanism ...
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11 votes
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Available code for computing solutions to matching algorithms?

While answering a comment, I realized I had a post-worth response. R has become the "default language" for a lot of computational research statistics (for a number of reasons; nice NYT ...
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  • 1,048
9 votes
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What is virtual valuation?

Suppose you face a single buyer whose willingness to pay, $v$, is distributed according to $F(v)$. If you charge a price $p$, he will buy if and only if $v>p$, leaving you with expected revenue of $...
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6 votes

What is the difference between contract theory and mechanism design?

As the previous answer mentions Contract Theory is a subset of Mechanism Design. Contract Theory is the study of Mechanism Design restricted to a single agent, i.e how to incentivize a single agent ...
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  • 161
6 votes
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Screening theory: Bundling problem

Consider the incentive and participation constraints. That is, look at which buyer types would choose which option. A buyer does not buy anything if $$v_a < p_a \quad v_b < p_b \quad v_a +v_b &...
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  • 5,090
6 votes

What's the difference between Ex-post Incentive Compatibility and Dominant-Strategy Incentive Compatibility

In Def. 3 of the paper you link to, EPIC is not "defined as truth-telling is the best strategy no matter what the others do". What the $-i$-agents report is held fixed at $\theta_{-i}$, i.e. ...
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  • 4,564
6 votes
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What's the difference between Ex-post Incentive Compatibility and Dominant-Strategy Incentive Compatibility

I think the right paper here is Jehiel, Meyer-ter-Vehn, Moldovanu and Zame (Econometrica 2006): The Limits of ex post Implementation. Take a direct mechanism. Ex post incentive compatibility (EPIC) ...
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  • 5,090
5 votes

What is the definition of "First Best", "Second Best", etc. in contract theory?

The solution to an optimal contract problem is called "first best" if it maximizes the principal's objective function subject to all constraints except the incentive constraints. The solution to an ...
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  • 551
5 votes

Bidder Count Impact on Uniform Price Economics

It is a known result in Mechanism Design that both first-price as well as second-price auctions yield the same expected revenue, under certain conditions (like independence of valuations, private ...
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5 votes
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Ex-post vs Ex-ante Budget Balance in Auctions

These are widely used technical terms with a precise mathematical meaning: Ex-ante budget balance means that the expected sum of all transfers is zero. Ex-post budget balance means that the sum of ...
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5 votes

What is virtual valuation?

The idea is simple: the seller wants to target that individuals who's ready to pay him the highest amount, thus targets the person with the highest virtual valuation. To target the individual who's ...
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  • 515
5 votes
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Mechanism Design: Proving that the expected utility is differentiable

By definition we have $$ \begin{align*} u(\theta) & = \theta q(\theta)-t(\theta) \\ \\ u(\theta + \delta) & = (\theta + \delta) q(\theta + \delta)-t(\theta + \delta) \end{align*} $$ By ...
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5 votes
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Can you please help me find this topic in Mechanism design/Rational choice theory?

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).
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5 votes

Payoff from an option contract

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 \...
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  • 5,090
5 votes
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Intuition behind Myerson's characterization of DSIC Single Object Allocation Mechanism

Maybe using simple calculus makes things clearer. Assume that everything is sufficiently smooth. The payoff of $i$ stating their type to be $x$ when the real type is $t_i$ is $$q_i(x,t_{-i})t_i-p_i(x,...
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4 votes

Incentive compatibility

First of all, the general form of the problem you got there is extremely demanding. In multidimensional screening problems, analytically often all hell breaks loose in a sense that it is just not ...
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  • 5,090
4 votes

Incentive compatibility: Weakly dominant strategy versus Nash equilibrium?

A Nash equilibrium that consists of weakly dominant strategies is a stronger solution concept than a NE itself. Consider the following simple matrix game where best replies have been marked with * \...
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  • 2,330
4 votes

What is the definition of "First Best", "Second Best", etc. in contract theory?

First Best is the ideal optimal solution of a given problem, i.e. the mathematical solution of the model with "no imperfections". If that solution is not attainable then the solution must be binding ...
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4 votes
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Non-Bayesian Mechanism Design

Most prominently, it was Bob Wilson who criticized the role of common priors in game theory. Starting from the "Wilson doctrine", some work in mechanism was done in that direction. Note that ...
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  • 5,090
4 votes
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Difference between social choice function and mechanism outcome function

A social choice function presumes the individuals' preference parameters $\theta_i$'s are observable, whereas in a mechanism, such knowledge is not presupposed. Therefore, in a mechanism, the ...
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4 votes
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Direct revelation mechanism's sets of strategies and types

In mechanism design you are free to choose the rules of the game. The designer can determine $(S, g)$, i.e., what players can do and what happens when players played some strategy profile $s \in S := \...
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  • 5,090
4 votes

Multi-item Auctions in Mechanism Design

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 ...
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4 votes
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Is VCG mechanism applicable in reverse auction? If so, how?

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 ...
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  • 5,090
4 votes
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The influence of restricted type space on incentive compatible mechanism design?

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 ...
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  • 5,090
4 votes

VCG mechanism and budget balance

In your example, the playstation is a public good to be used by both roommates. Note that $\theta_1,\theta_2 < \theta_3$, but $\theta_1+\theta_2>\theta_3$, that is, one roommate alone would not ...
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  • 5,090
4 votes
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Single-item single-bidder: why posted price is the only possible DSIC mechanism?

Yes, this follows from Myerson's lemma. A monotone function from an interval to $\{0,1\}$ must be constant or a threshold function that is zero up to a certain point and then one (actually, there are ...
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3 votes
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Derivation on p.99 of Salanie, The Economics of Taxation (2nd edition)

I think it is the chain rule. Let $w'(w) = w$, since we are looking for revealing mechanisms. The condition $$ \frac{\partial V}{\partial w'} (w'(w),w) = 0 $$ holds for all $w$ because the mechanism ...
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