2016-05-25 Departmental seminar: Neil Ghani (MSP)

Tue, 14 Oct 2025 16:51:42 +0000

Neil Ghani (MSP)

A Compositional Approach to Game Theory

Abstract

I will sketch an alternative approach to economic game theory based upon the computer science idea of compositionality: concretely we i) give a number of operators for building up complex and irregular games from smaller and simpler games; and ii) show how the Nash equilibrium of these complex games can be defined recursively from their simpler components. We apply compositional reasoning to sophisticated games where agents must reason about how their actions affect future games and how those future games effect the utility they receive. This forces us into a second innovation — we augment the usual lexicon of games with a dual notion to utility because, in order for games to accept utility, this utility must be generated by other games. Our third innovation is to represent our games as string diagrams so as to give a clear visual interface to manipulate them. Our fourth, and final, innovation is a categorical formalisation of these intuitive diagrams which ensures our reasoning about them is fully rigorous.

The talk will be general so as appeal to as wide an audience as possible. In particular, no knowledge of category theory will be assumed!

2016-05-25 15:30:00 UTC
LT908