I am very new to mechanism design so I am a bit lost among the concepts, even the most basic ones.

One thing that is not clear to me is the concept of direct mechanism and its relationship with the revelation principle.

From what I got a direct mechanism is a mechanisms, in which, instead of messages, the agents report their preference/type. Are we assuming this is a truthful report?

I am asking that because the revelation principle is stated as "anything that can be accomplished by any mechanism can actually be accomplished by a direct revelation mechanism that is individual rational and incentive compatible" in this notes but as "a social choice function can be implemented by an arbitrary mechanism (i.e. if that mechanism has an equilibrium outcome that corresponds to the outcome of the social choice function), then the same function can be implemented by an incentive-compatible-direct-mechanism (i.e. in which players truthfully report type) with the same equilibrium outcome (payoffs)." on Wikipedia.

So I don't get if truthfulness is implied by the direct mechanism or if it is an additional requirement.

Incentive compatible here means that you have no incentive to lie. A direct mechanism that is not incentive compatible would entice some agents to report a false type.

  • Thanks! Thus, for example, the revelation principle in dominant strategies is saying if a social choice function is implementable, than it is implementable using a direct mechanism, i.e. truth-telling is always a dominant strategy. Is it the right way to think about it? – Alessandro Dec 7 at 1:24
  • Not sure waht you mean by "always a dominant strategy", the always seems redundant to me. If a social choice function is implementable in dominant strategies you can construct a mechanism where truth-telling is a dominant strategy. – denesp Dec 7 at 5:44

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.