<p>In Def. 3 of the paper you link to, EPIC is not &quot;<em>defined as truth-telling is the best strategy no matter what the others do</em>&quot;. What the <span class="math-container">$-i$</span>-agents report is held fixed at <span class="math-container">$\theta_{-i}$</span>, i.e. it is assumed that the others report <em>truthfully</em>.</p>

CC BY-SA 4.0
2021-06-25T20:15:40.997Z
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.
Francis
CC BY-SA 4.0
2021-06-25T11:28:26.257Z
2021-06-25T11:28:26.257Z
VARulle
<p>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).</p>
<p><img src="https://drive.google.com/file/d/1LGpTup4pCv0fAfMV3a1AZkw5di_W9Ouh/view?usp=sharing" alt="bids for the auction" /></p>

CC BY-SA 4.0
2024-06-11T04:16:28.373Z
2024-06-11T04:16:28.373Z
Wataru abe
<p>I think the right paper here is <a href="https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1468-0262.2006.00675.x?casa_token=OH0zlC84_5sAAAAA:i4FIh1v4z0TS-pNl3VlJsl3npErEeE_Tg9_yIgPSDPcplPS2tscF7j2BtR6ofFWu-ZkEjZi0ZZsZsGw" rel="noreferrer">Jehiel, Meyer-ter-Vehn, Moldovanu and Zame (Econometrica 2006): The Limits of ex post Implementation</a>.</p>
<p>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.</p>

CC BY-SA 4.0
2021-06-25T20:23:24.450Z
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"?
Francis
CC BY-SA 4.0
2021-06-26T15:47:15.010Z
Yes. That is true.
Bayesian
CC BY-SA 4.0
2022-10-02T06:12:10.510Z
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.
Mengfan Ma
CC BY-SA 4.0
2022-10-03T19:23:47.600Z
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.
Bayesian
CC BY-SA 4.0
2021-06-25T11:33:17.577Z
2021-06-25T11:33:17.577Z
Bayesian
<p>According to the <a href="https://en.wikipedia.org/wiki/Incentive_compatibility" rel="nofollow noreferrer">Wikipedia definition</a> of Dominant-Strategy Incentive Compatibility (DSIC):</p>
<blockquote>
<p>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</p>
</blockquote>
<p>I didn't find the formal definition of ex-post IC there, but I found this paper <a href="https://www.tse-fr.eu/sites/default/files/TSE/documents/doc/wp/2018/wp_tse_938.pdf" rel="nofollow noreferrer">On the Foundations of Ex Post Incentive Compatible Mechanisms</a> by Yamashita and Zhu. The ex-post IC is also defined as truth-telling is the best strategy no matter what the others do.</p>
<p>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?</p>

<game-theory><definition><mechanism-design><incentives>
What's the difference between Ex-post Incentive Compatibility and Dominant-Strategy Incentive Compatibility
Francis
# What's the difference between Ex-post Incentive Compatibility and Dominant-Strategy Incentive Compatibility

(Asked by: username_0 on 2021-06-24)

According to the [Wikipedia definition](https://en.wikipedia.org/wiki/Incentive_compatibility) 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](https://www.tse-fr.eu/sites/default/files/TSE/documents/doc/wp/2018/wp_tse_938.pdf) 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?

**Tags:** game-theory, definition, mechanism-design, incentives

---

## 3 answers

### Answer by username_3 on 2021-06-25. Score: 6 | Accepted answer

I think the right paper here is [Jehiel, Meyer-ter-Vehn, Moldovanu and Zame (Econometrica 2006): The Limits of ex post Implementation](https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1468-0262.2006.00675.x?casa_token=OH0zlC84_5sAAAAA:i4FIh1v4z0TS-pNl3VlJsl3npErEeE_Tg9_yIgPSDPcplPS2tscF7j2BtR6ofFWu-ZkEjZi0ZZsZsGw).

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.

> **Comments:**
> **username_0**: 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"?  
> **username_3**: Yes. That is true.  
> **username_4**: 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.  
> **username_3**: 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.  

---

### Answer by username_1 on 2021-06-25. Score: 6

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*.

> **Comments:**
> **username_0**: 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.  

---

### Answer by username_2 on 2024-06-11. Score: 0

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](https://drive.google.com/file/d/1LGpTup4pCv0fAfMV3a1AZkw5di_W9Ouh/view?usp=sharing)


---

