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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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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
    Jun 25 at 20:23
  • $\begingroup$ Yes. That is true. $\endgroup$
    – Bayesian
    Jun 26 at 15:47
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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
    Jun 25 at 20:15

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