<p>Is there a literature out there for games where you don't know your own type, but know it's from a distribution, and can e.g., invest resources to learn your own type prior to moving on with the game?</p>
<p>An example:</p>
<p>At the beginning of the game, the contestent observes their type with some error (i.e., Type = x + e).</p>
<p>They can pay a fee to remove that error w/ probability p (w/ prob. 1-p, it stays the same), or proceed with the competition without knowing their type for certain.</p>
<p>The judge of the contest either a.) observes their type with a different error (i.e., Type = x + e* =/= x + e), or b.) observes the true type x w/ probability p, and observes x + e* w/ probability 1 - p if the fixed fee is paid.</p>
<p>E.g., if you're a swimmer looking to enter a tournament but don't know how well you stack up relative to the other contestants but can pay to have someone scout the other contestants for you.</p>

CC BY-SA 4.0
2024-04-02T21:56:48.280Z
Something to consider that in this formulation "your own type" is not really your own from a modelling perspective, it is just a parameter that has an effect on your expected payoff, not unlike other parameters, such as other swimmers' qualities in your example.
Giskard
CC BY-SA 4.0
2024-04-03T10:26:10.963Z
Thanks for this. If I include a mechanism through which one can pay to learn their own type, then would we have strategic behavior in the post-learning period, and the swimmers would just act by taking expectations in the pre-learning period?
dazednconfused
CC BY-SA 4.0
2024-04-03T10:50:48.463Z
Depends on the details of your exact model.
Giskard
CC BY-SA 4.0
2024-04-03T11:05:11.130Z
Perhaps the idea is more akin to a beauty contest. At the beginning of the game, the contestent observes their type with some error (i.e., Type = x + e). They can pay a fee to remove that error w/ probability p (w/ prob. 1-p, it stays the same), or proceed with the competition without knowing their type for certain. the judge of the contest either a.) observes their type with a different error (i.e., Type = x + e* =/= x + e), or b.) observes the true type x w/ probability p, x + e*   w/ probability 1 - p if the fixed fee is paid. Is there literature out there following a similar struture?
dazednconfused
CC BY-SA 4.0
2024-04-03T11:13:04.037Z
I don't know of any; if you want, you can include this example in your question. (It is not something I would call beauty contest though; for some reason that seems to be used for average guessing game attributed to Keynes.)
Giskard
<game-theory><bayesian-game>
Game where you don't know (but can learn) your own type?
dazednconfused
# Game where you don't know (but can learn) your own type?

(Asked by: username_0 on 2024-04-02)

Is there a literature out there for games where you don't know your own type, but know it's from a distribution, and can e.g., invest resources to learn your own type prior to moving on with the game?

An example:

At the beginning of the game, the contestent observes their type with some error (i.e., Type = x + e).

They can pay a fee to remove that error w/ probability p (w/ prob. 1-p, it stays the same), or proceed with the competition without knowing their type for certain.

The judge of the contest either a.) observes their type with a different error (i.e., Type = x + e\* =/= x + e), or b.) observes the true type x w/ probability p, and observes x + e\* w/ probability 1 - p if the fixed fee is paid.

E.g., if you're a swimmer looking to enter a tournament but don't know how well you stack up relative to the other contestants but can pay to have someone scout the other contestants for you.

**Tags:** game-theory, bayesian-game
> **Comments:**
> **username_1**: Something to consider that in this formulation "your own type" is not really your own from a modelling perspective, it is just a parameter that has an effect on your expected payoff, not unlike other parameters, such as other swimmers' qualities in your example.  
> **username_0**: Thanks for this. If I include a mechanism through which one can pay to learn their own type, then would we have strategic behavior in the post-learning period, and the swimmers would just act by taking expectations in the pre-learning period?  
> **username_1**: Depends on the details of your exact model.  
> **username_0**: Perhaps the idea is more akin to a beauty contest. At the beginning of the game, the contestent observes their type with some error (i.e., Type = x + e). They can pay a fee to remove that error w/ probability p (w/ prob. 1-p, it stays the same), or proceed with the competition without knowing their type for certain. the judge of the contest either a.) observes their type with a different error (i.e., Type = x + e* =/= x + e), or b.) observes the true type x w/ probability p, x + e*   w/ probability 1 - p if the fixed fee is paid. Is there literature out there following a similar struture?  
> **username_1**: I don't know of any; if you want, you can include this example in your question. (It is not something I would call beauty contest though; for some reason that seems to be used for average guessing game attributed to Keynes.)  

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