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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.

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    $\begingroup$ 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. $\endgroup$
    – Giskard
    Commented Apr 2 at 21:56
  • $\begingroup$ 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? $\endgroup$
    – dazednconfused
    Commented Apr 3 at 10:26
  • $\begingroup$ Depends on the details of your exact model. $\endgroup$
    – Giskard
    Commented Apr 3 at 10:50
  • $\begingroup$ 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? $\endgroup$
    – dazednconfused
    Commented Apr 3 at 11:05
  • $\begingroup$ 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.) $\endgroup$
    – Giskard
    Commented Apr 3 at 11:13

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