 We were able to solve this game straightforwardly because we set the utility functions in such a way as to make it zero-sum, or strictly competitive. That is, every gain in expected utility by one player represents a precisely symmetrical loss by the other. However, this condition may often not hold. Suppose now that the utility functions are more complicated. The pursuer most prefers an outcome in which she shoots the fugitive and so claims credit for his apprehension to one in which he dies of rockfall or snakebite; and she prefers this second outcome to his escape. The fugitive prefers a quick death by gunshot to the pain of being crushed or the terror of an encounter with a cobra. Most of all, of course, he prefers to escape. Suppose, plausibly, that the fugitive cares more strongly about surviving than he does about getting killed one way rather than another. We cannot solve this game, as before, simply on the basis of knowing the players’ ordinal utility functions, since the intensities of their respective preferences will now be relevant to their strategies.