 The numbers featuring in an ordinal utility function are thus not measuring any quantity of anything. A utility-function in which magnitudes do matter is called ‘cardinal’. Whenever someone refers to a utility function without specifying which kind is meant, you should assume that it’s ordinal. These are the sorts we’ll need for the first set of games we’ll examine. Later, when we come to seeing how to solve games that involve (ex ante) uncertainty—our river-crossing game from Part 1 above, for example—we’ll need to build cardinal utility functions. The technique for doing this was given by  von Neumann &amp; Morgenstern (1944),  and was an essential aspect of their invention of game theory. For the moment, however, we will need only ordinal functions.