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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 truthful, regardless of what the others do

I didn't find the formal definition of ex-post IC there, but I found this paper On the Foundations of Ex Post Incentive Compatible Mechanisms by Yamashita and Zhu. The ex-post IC is also defined as truth-telling is the best strategy no matter what the others do.

I am really confused about these two notations. I think there must be some difference between them, otherwise, it doesn't make sense to me why we develop two terminologies for one thing?

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3 Answers 3

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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) means that for every realization of all other agents’ types, each agent finds it optimal to report his type truthfully given the others are truthful. This is different than Bayesian incentive compatibility (BIC) which requires truth telling to be optimal against the given distribution of types. EPIC is weaker than DSIC because the latter requires to truth telling to be better agaist whatever the others do independent of their actual type. With private values, truth telling is an ex post equilibrium if and only if truth telling is a dominant strategy. This is not true for interdependent valuations.

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  • $\begingroup$ Thanks for the explanation, but I think I don't quite understand "With private values, truth telling is an ex post equilibrium if and only if truth telling is a dominant strategy". With this conclusion, is it true that "with private values, ex-post IC is the same as DSIC"? $\endgroup$
    – Francis
    Commented Jun 25, 2021 at 20:23
  • $\begingroup$ Yes. That is true. $\endgroup$
    – Bayesian
    Commented Jun 26, 2021 at 15:47
  • $\begingroup$ why "with private values, truth telling is an ex post quilibrium if and only if truth telling is a dominant strategy"? The "if" direction is obvious but I didn't figure out why the "only if" direction holds. $\endgroup$
    – Mengfan Ma
    Commented Oct 2, 2022 at 6:12
  • $\begingroup$ Because with private types you don't care about which types the other agents actually have. Suppose truth telling is not a dominant strategy. Then reporting the true type is not a best response against some report vector of the others. Suppose these are their actual types. Then there is no ex post equilibrium. $\endgroup$
    – Bayesian
    Commented Oct 3, 2022 at 19:23
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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. it is assumed that the others report truthfully.

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  • $\begingroup$ Thanks for pointing it out, I thought $\theta_{-i}$ can be any specific realization of other agents' types, didn't notice that $\theta_{-i}$ must be the other bidder's true type. $\endgroup$
    – Francis
    Commented Jun 25, 2021 at 20:15
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There are two agents 1, 2. They compete for a good with externality (sport facility, amusement park or something causes revitalization of a town) and gain v1, v2 of values with win respectively. If lose, however, because of the externality, they gain v2/2, v1/2. The competition is held by a modified second price auction: The price is a half of the loser's bid. This is not a DEIC but EPIC mechanism (and vulnerable to collusion and budget).

bids for the auction

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