Paper
Publication
Real World Games Look Like Spinning Tops
Abstract

In this paper we investigate the geometrical properties of real world games (e.g. Tic-Tac-Toe, Go, StarCraft II). We hypothesise that they resemble a spinning top, with the upright axis representing transitive strength, and the radial axis, which corresponds to the number of cycles that exist at a particular transitive strength, representing the non-transitive dimension. We prove the existence of this geometry for a wide class of real world games by exposing their temporal nature. Additionally, we show that this unique structure also has consequences for learning - it clarifies why populations of policies are necessary for training of agents, and how population size relates to the structure of the game. Finally, we empirically validate these claims by using a selection of 9 real world two-player zero-sum symmetric games, showing 1) the spinning top structure is revealed and can be easily re-constructed by using a new method of Nash clustering to measure the interaction between transitive and cyclical policy behaviour, and 2) the effect that population size has on the convergence in these games.

Authors' notes