Would someone be so kind as to explain me the Revelation Principle with a simple example with two agents bidding for one good where one agent would lie about his perceived value of the good?

  • $\begingroup$ Can you elaborate, please? Revelation Principle says that there exists a mechanism where it's not optimal to lie, so you wonder why one would lie at all? $\endgroup$ – Ilya Nov 20 '14 at 16:20
  • $\begingroup$ Assume that one is lying (being irrational) and show me why it is irrational. $\endgroup$ – David Seres Nov 20 '14 at 16:24
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    $\begingroup$ I think that example may not even require a game. You have a single player who gets whatever his reveals, whereas his utility function is given by $U_\theta(x) = -(x-\theta)^2$ where $\theta$ is his type, and $x$ is what he reveals. Of course, in this case lying about his type $\theta$ will make his utility negative. In mechanism design you try to steer agent's utilities to such shape, that when they solve the game for the mechanism you've provided, they understand that by revealing their types they maximize their utilities. $\endgroup$ – Ilya Nov 20 '14 at 16:31

Example: Take a first price sealed bid auction: Agents {1,2} with values $v_1 = 10$ and $v_2 = 20$. Assuming that bidder 1 bids truthful, bidder 2 would maximize his value by bidding $10+\epsilon$, which results in a utility of 20-10 = 10 for bidder 2 (as $\epsilon$ is arbitrary small). If he reported truthful, his utility would be 20-20=0. This shows, that in first price auctions, bidders might have an incentive to lie.

The revelation principle states that a mechanism which has a BSNE (but truthful reporting is not a dominant strategy), there has to be a payoff-equivalent (revelation) mechanism in which truthful reporting is a dominant strategy. In our example, the second price sealed bid auction is such a mechanism.

Note that this is a simplified example as I did not explain revelation nor show that the first price sealed bid aution has a BSNE, yet it should answer your question.

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