Diegetic Representation of Feedback in Open Games

TL;DR

This paper introduces a diegetic framework for representing feedback in open games, aligning game dynamics with gradient-based learning and providing a new perspective on Nash equilibria through a functorial construction.

Contribution

It develops a diegetic approach to feedback in open games, connecting game dynamics with gradient-based learning and Nash equilibria without relying on traditional equilibrium predicates.

Findings

Feedback propagation in games can be viewed as backpropagation.

Players' fixpoint behaviors correspond to Nash equilibria.

The framework overlaps with gradient-based learning methods.

Abstract

We improve the framework of open games with agency by showing how the players' counterfactual analysis giving rise to Nash equilibria can be described in the dynamics of the game itself (hence diegetically), getting rid of devices such as equilibrium predicates. This new approach overlaps almost completely with the way gradient-based learners are specified and trained. Indeed, we show feedback propagation in games can be seen as a form of backpropagation, with a crucial difference explaining the distinctive character of the phenomenology of non-cooperative games. We outline a functorial construction of arena of games, show players form a subsystem over it, and prove that their 'fixpoint behaviours' are Nash equilibria.