Higher-Order Game Theory

TL;DR

This paper introduces a novel game theory framework using higher-order functions to model players' goals, accommodating cases where traditional utility functions are inadequate, and connects it to computational methods from computer science.

Contribution

It presents a new mathematical representation of games with higher-order functions, extending beyond utility-based models and enabling analysis of more complex player motivations.

Findings

Higher-order functions can model player goals without utility functions.

Equilibrium concepts like Nash can be adapted to this framework.

The approach links game theory with computational tools from computer science.

Abstract

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.