Two-person Non-constant Sum Games

So far the fundamental question posed by the formal theory of decisions could be phrased as follows: given a decision situation, that is, a choice between a set of alternatives, how should a rational actor determine his choice so as to maximize the utility of the outcome? In the context of decisions under certainty, the answer was obvious. The alternative should be the one that leads (with certainty) to the outcome to which the largest utility has been assigned. What problems still remained had to do with methods of finding that alternative (optimization problems).