  In applied game theory the motivation of players is a key element. It is
encoded in the payoffs of the game form and often based on utility functions.
But there are cases were formal descriptions in the form of a utility function
do not exist. In this paper we introduce a representation of games where
players' goals are modeled based on so-called higher-order functions. Our
representation provides a general and powerful way to mathematically summarize
players' intentions. In our framework utility functions as well as preference
relations are special cases to describe players' goals. We show that in
higher-order functions formal descriptions of players may still exist where
utility functions do not using a classical example, a variant of Keynes' beauty
contest. We also show that equilibrium conditions based on Nash can be easily
adapted to our framework. Lastly, this framework serves as a stepping stone to
powerful tools from computer science that can be usefully applied to economic
game theory in the future such as computational and computability aspects.

Computer Science and Game Theory