The article shows how to turn a non-zero sum game into a zero-sum game by adding a passive player. This transformation ensures that there is always an optimal strategy that leads to equilibrium. In the new game, each player competes against all others, including the passive player. This approach guarantees a solution for equilibrium, even though the strategies and outcomes may differ from the original game. The researchers illustrate this concept using the Prisoner's Dilemma as an example.