In this masters thesis we focus on the use of Bayesian networks for solving finite two-person zero-sum games with one decision. We look into the details of an iterative solution procedure suggested by George W. Brown in 1949 and verifies it formally as well as in practice. We show that the solutions found by Brown''s procedure are \textit{Nash equilibria} of the games we use as test-bed. We show that we can use the principles from Brown''s solution procedure to create adaptive Bayesian networks capable of solving a game by letting intelligent agents based on the adaptive networks face each other. Their distributions will during the series of games converge against the \textit{Nash equilibrium} for the game. Finally we show that Bayesian networks are capable of solving more complex games with more than one decision, by using training methods of the same principle as Brown''s solution procedure.