Spohn CI varieties for non-binary games

Investigate Spohn conditional independence varieties for undirected graphical models that model n-player games with non-binary strategy sets (i.e., some players have d_i > 2 choices), since their analysis beyond the binary case has not yet been undertaken.

Background

Throughout the paper, the authors focus on binary choices (d_i = 2) to establish dimension results and universality theorems for Spohn CI varieties. This restriction enables concrete algebro-geometric analysis and proofs, including the resolution of a conjecture on codimension.

They note that extending these results to games with non-binary choices remains unaddressed and generates multiple open directions. The paper of Spohn CI varieties in the non-binary setting is therefore identified as an open area for future research.