Rengoku: The Tower of Purgatory

Set in a dark and distant future, Rengoku: The Tower of Purgatory lets you play as a well-armed android that must fight its way to the pinnacle of a great tower to confront a mysterious foe. As you progress to higher levels, you’ll improve your skills and acquire new weapons and technologies. You must strategically manage your resources to tackle the missions at hand. With the PSP’s wireless capabilities, you can trade equipment and materials or battle with up to three other players in the multiplayer mode.
— Summary provided by Gamefaqs.com