It is our intention, in this chapter, to propose and discuss the Best Payoff Method, a new method to resolve games. This is made exemplifying the application of the method to a pay raise voting game, that is a perfect information sequential game, without having yet formulated it, and then deploying the algorithm for its implementation. In the next examples we consider an imperfect information game and a game with random characteristics. We finish confronting the equilibrium concepts mentioned in this work: Subgame Perfect Nash Equilibrium, Nash Equilibrium, and Best Payoff Equilibrium through the formulation of some conjectures, and with a short conclusions section.