We consider a simple simultaneous first price auction for two identical items in a complete information setting. Our goal is to analyze this setting for a simple, yet highly interesting, AND-OR game, where one agent is single minded and the other is unit demand. We find a mixed equilibrium of this game and show that every other equilibrium admits the same expected allocation and payments. In addition, we study the equilibrium, highlighting the change in revenue and social welfare as a function of the players’ valuations.