Who is the first person/paper to introduce "mixed strategy"? The PNAS by Nash used this notion without citing anyone.

Does the earlier book: Von Neumann, J., and Morgenstern, O., The Theory of Games and Economic Behavior

include the introduction of mix strategy?


Although I don't have the book here, I am quite certain that mixed strategies are already present in the book from 1944. I believe that I have read somewhere the claim that "mixed strategies" where actually introduced in an earlier version of the book (published in German in 1928, says Wikipedia). However, what I have read mostly is the claim that Emile Borel (yes, THE Borel) first wrote down this idea in a note in 1921. I guess here is a man with enough authority to state that:

E. Borel was the first author to evolve the concept of a strategy, pure as well as mixed, although he did not go beyond the case of the symmetric two-person game.

says von Neumann here: "Communication on the Borel Notes", J. von Neumann and M. Fréchet, Econometrica 1953.

  • 1
    $\begingroup$ The Econometrica issue actually has translations of the original Borel notes: jstor.org/stable/i332594 $\endgroup$
    – Bayesian
    Sep 18 '20 at 19:51
  • $\begingroup$ Just read Borel 1921. It is indeed the first one discussing mix strategy in games! $\endgroup$
    – High GPA
    Sep 18 '20 at 21:19

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.