A Rational Game on the Square
An example of a two-person zero-sum game on a closed unit square having as payoff a continuous rational function with rational coefficients. It is shown that the only optimal strategy available to either player is the Cantor function.
Gross, Oliver Alfred, A Rational Game on the Square. Santa Monica, CA: RAND Corporation, 1954. https://www.rand.org/pubs/papers/P557.html. Also available in print form.
Gross, Oliver Alfred, A Rational Game on the Square, Santa Monica, Calif.: RAND Corporation, P-557, 1954. As of November 17, 2021: https://www.rand.org/pubs/papers/P557.html