It is well known that you can use the algorithm for finding the equilibrium of a Zero-sum game to solve a linear program. In particular, you can take a LP and reduce it to a zero-sum game, and use the famous algorithm for zero sum games proposed by Grigoriadis and Khachiyan.
Is this equivalence used in practice, or the simplex algorithm (or any interior point methods) is always preferable? Why?
Notably, the approach of zero sum games offers an approximate solution in polynomial time, and converges in $O(1/\epsilon^2)$ iterations, contrary to the simplex algorithm which find the optimal solution in (worst-case) exponential time.