Researchers have developed algorithms to find approximate equilibria in bimatrix games. They found that deterministic algorithms need at least k^2 queries to find an approximate Nash equilibrium. However, randomized algorithms can break this barrier by using fewer queries. For well-supported Nash equilibria, a randomized algorithm can find an approximate equilibrium using k.log k /ϵ^4 queries. The study also shows that randomized algorithms require at least k^2 queries to find an approximate Nash equilibrium with ϵ < 1/4k.