This is the second post in catching up on aspects of open-games-hs that are ahead of my papers, following open games with stateful payoffs. Subgame perfection has been an embarrassing thorn in my side since 2016 when I had to do major surgery on my PhD thesis because the category of “open games with subgame perfect equilibria” turned out to not be monoidal. Currently there are two approaches: One in iterated open games which is quite pragmatic and requires the “user” specifying an open game to manually mark where the subgames are by applying a functor; and one in morphisms of open games which I find very elegant but requires both an extra categorical dimension and an equivalent amount of effort by the “user”.
I always wanted an “automatic” approach to subgame perfection in open games, like I failed to do in my thesis – just draw the usual string diagram, and get subgame perfect equilibria out. I now have a way to do it, implemented in OpenGames.Engine.SubgamePerfect, which I’ll document here.Continue reading “Subgame perfection made difficult”