Unlike physical combat which results in either you or a denizen (computer controlled character) dying, you may also engage in ego battles with the denizen instead. Ego battles use the Influence skill to try to change the behaviour of the denizen. You can make a denizen paranoid or convince him or her  to give you gold. Losing ego battles will result in a loss of experience as  though you had died while winning an ego battle will result in a gain in experience

In an ego battle, your ego will be drained upon using an influence skill. 
The denizen will then continually nag at you which will result in more loss of ego. If your ego drops to 0, you will lose and the denizen will win. Upon the completion of an ego battle (whether the denizen won or lost), that denizen will not be able to be influenced for some period of time.

There are 5 categories of influence: Seduction, Empower, Weaken, Charity and Paranoia. Once you begin an ego battle using a skill in one of these categories, you can only use influence skills of the same type of category. As you engage in an ego battle, the more you use one skill of a category, the more resistant the denizen will become to it, so the strategy in ego battles is to vary your influence attacks as much as possible (assuming you have multiple skills in a category).

As a final note, the more prestige you display from the clothes and jewellery you wear, the more effective your ego attacks will be. The one exception to this is charity attacks which are more effective the less prestige you carry (i.e., tattered clothing is more effective when begging). Being naked, however, is not an effective strategy in any ego battle (as it will be hard for the denizen to take you seriously.)