<p>In <a href="http://users.cms.caltech.edu/~adamw/courses/241/lectures/search2.pdf" rel="noreferrer">Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz(2007)</a>, there's a hand-waving argument to justify their setting as a game of complete information:</p>

<blockquote>
  <p>we assume that all values are common
  knowledge: over time, advertisers are likely to
  learn all relevant information about each other's
  values.</p>
</blockquote>

<p>My question is, to what degree, this reasoning can be justified?</p>

<p>My feeling is that, for an auction with an infinite type space and at least one bidder having a partition of infinite cells, it is wrong(see <a href="http://www.polemarchakis.org/a14-cdf.pdf" rel="noreferrer">Geanakoplos and Polemarchakis (1982)</a>). To proceed, it seems to me, one needs to represent a bidder's bidding strategy as a function measurable with respect to her own type, and history records of bidding, which seems to be quite complicated.</p>

CC BY-SA 3.0
2015-06-07T11:27:27.223Z
As you state, that sounds quite complicated. This is probably why they make this assumption.
Giskard
CC BY-SA 3.0
2015-06-07T11:38:51.987Z
@denesp I don't know.  Because I think they should have  difficulty in  formulating stable assignment under incomplete information, which they tried to link their proposed envy-free equilibrium with. It  is conceptually difficult(see Luciano Pomatto's job market paper).  I think whether learning can lead to common knowledge, which I'm interested to know something about in this post, is quite a different issue,  Maybe they have trouble in both, but I don't know.
Metta World Peace
CC BY-SA 3.0
2015-06-08T08:32:41.283Z
Don't EOS show that all the bidders (except the highest value guy) learn each others' values in equilibrium if they treat the GSP auction like an English auction? Demange, Gale and Sotomayor (http://www.eecs.harvard.edu/~parkes/cs286r/spring02/papers/dgs86.pdf) have shown such a process to have nice convergence properties and (if I understand correctly) Gul and Stacchetti (http://www.princeton.edu/~fgul/english.pdf) have shown that the bidders can do no better than comply with this English auction-like process until it converges.
Ubiquitous
CC BY-SA 3.0
2015-06-08T22:15:12.797Z
@Ubiquitous Please correct me if I got it wrong. I don't think they have shown that at the stationary state each others' value is common knowledge. Actually, each bidder can take on a continuum of types, and when the type is chosen, the bidder knows her own type, so each bidder's partition has at least a continuum of cells. I don't think they generalize Geanakoplos and Polemarchakis (1982)'s result from finite cells to a continuum of cells.
Metta World Peace
CC BY-SA 3.0
2015-06-08T22:15:20.037Z
But they need the assumption of common knowledge of types, because they don't have an appropriate definition of stable assignment under incomplete information at that time.
Metta World Peace
CC BY-SA 3.0
2015-06-09T11:47:18.550Z
Yes, I see. The English auction in EOS assumes that we (i) run the English auction, (ii) use the results to determing the GSP allocation, and only then (iii) realise payoffs. In practice, though, the English auction phase would have to take place within the framework of the GSP mechanism so that there will be a stream of payoffs accruing to the bidders during the period in which prices converge the the envy-free equilibrium. Those small payoffs would break the usual English auction convergence results.
Ubiquitous
<reference-request><academic-graduate><auctions><bayesian-game><dynamic-games>
Can repeated bidding in an auction make each player's type common knowledge?
Metta World Peace
# Can repeated bidding in an auction make each player's type common knowledge?

(Asked by: username_0 on 2015-06-07)

In [Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz(2007)](http://users.cms.caltech.edu/~adamw/courses/241/lectures/search2.pdf), there's a hand-waving argument to justify their setting as a game of complete information:

> we assume that all values are common
> knowledge: over time, advertisers are likely to
> learn all relevant information about each other's
> values.

My question is, to what degree, this reasoning can be justified?

My feeling is that, for an auction with an infinite type space and at least one bidder having a partition of infinite cells, it is wrong(see [Geanakoplos and Polemarchakis (1982)](http://www.polemarchakis.org/a14-cdf.pdf)). To proceed, it seems to me, one needs to represent a bidder's bidding strategy as a function measurable with respect to her own type, and history records of bidding, which seems to be quite complicated.

**Tags:** reference-request, academic-graduate, auctions, bayesian-game, dynamic-games

> **Comments:**
> **username_1**: As you state, that sounds quite complicated. This is probably why they make this assumption.  
> **username_0**: @denesp I don't know.  Because I think they should have  difficulty in  formulating stable assignment under incomplete information, which they tried to link their proposed envy-free equilibrium with. It  is conceptually difficult(see Luciano Pomatto's job market paper).  I think whether learning can lead to common knowledge, which I'm interested to know something about in this post, is quite a different issue,  Maybe they have trouble in both, but I don't know.  
> **username_2**: Don't EOS show that all the bidders (except the highest value guy) learn each others' values in equilibrium if they treat the GSP auction like an English auction? Demange, Gale and Sotomayor (http://www.eecs.harvard.edu/~parkes/cs286r/spring02/papers/dgs86.pdf) have shown such a process to have nice convergence properties and (if I understand correctly) Gul and Stacchetti (http://www.princeton.edu/~fgul/english.pdf) have shown that the bidders can do no better than comply with this English auction-like process until it converges.  
> **username_0**: @username_2 Please correct me if I got it wrong. I don't think they have shown that at the stationary state each others' value is common knowledge. Actually, each bidder can take on a continuum of types, and when the type is chosen, the bidder knows her own type, so each bidder's partition has at least a continuum of cells. I don't think they generalize Geanakoplos and Polemarchakis (1982)'s result from finite cells to a continuum of cells.  
> **username_0**: But they need the assumption of common knowledge of types, because they don't have an appropriate definition of stable assignment under incomplete information at that time.  
> **username_2**: Yes, I see. The English auction in EOS assumes that we (i) run the English auction, (ii) use the results to determing the GSP allocation, and only then (iii) realise payoffs. In practice, though, the English auction phase would have to take place within the framework of the GSP mechanism so that there will be a stream of payoffs accruing to the bidders during the period in which prices converge the the envy-free equilibrium. Those small payoffs would break the usual English auction convergence results.  

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## 0 answers

