1
$\begingroup$

Say I have n random variables, {X0...Xn}, n>9. I also have another set of random variables constructed from the first set, where each of these are the sum of 9 random variables in the original set, i.e. {X0+X1...+X9, X0+X1...+X10, ...}.

I can find a linear combination of random variables from the second set which satisfies some constraints; you can think of this as a game where you pick 9-variable combinations, and the solutions to the linear combination is the proportion of picks that would result in a Nash equilibrium.

Once I have that linear combination of sets, I can back out a distribution of usage of each variable from the first set; I.e. X0 is used in 80% of Nash equilibrium picks, X1 is used in 60%, etc.

My question: given the parameters of the distributions of each random variable in set 1, is it possible to find the post-Nash variable usage without first building all the permutations and computing the equilibrium distribution?

Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ "where each of these are the sum of 9 random variables in the original set, i.e. ${X_0+X_1...+X_9, X_0+X_1...+X_{10}, ...}$." --- those two sums have 10 and 11 terms respectively, not 9. $\endgroup$
    – Glen_b
    Feb 5 at 22:29

0

Reset to default

Your Answer

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