Kuhn’s theorem

Theorem

In every game in extensive form, if player $i$ has perfect recall, then for every mixed strategy of player $i$ there exists an equivalent behavior strategy.

Kuhn's theorem for infinite games

Let $G$ be an extensive form game with an infinite game tree such that each vertex in the game tree has a finite number of children. If player $i$ has perfect recall then for each mixed strategy of player $i$ there is an equivalent behavior strategy and for each behavior strategy of player $i$ there is an equivalent mixed strategy.

See also

• equivalent mixed and behavior strategies#Conditions for existence of equivalent mixed strategy to any behavior strategy

References

1. M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, p. 232.
2. https://gki.informatik.uni-freiburg.de/teaching/ss13/gametheory/gametheory15.pdf
3. https://faculty.econ.ucdavis.edu/faculty/schipper/unawkuhn.pdf