3
$\begingroup$

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.

$\endgroup$
6
  • 3
    $\begingroup$ 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
    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? $\endgroup$ Apr 3 at 10:26
  • $\begingroup$ Depends on the details of your exact model. $\endgroup$
    – Giskard
    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? $\endgroup$ 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
    Apr 3 at 11:13

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.