TITLE: Are there any interesting connections between Game Theory and Algebraic Topology?
QUESTION [14 upvotes]: I've been learning game theory on my own and was just curious how it connected with previous things I've learned.  So are there any interesting connections between Game Theory and Algebraic Topology? or possibly other branches of topology?

REPLY [4 votes]: I'm coming from the other side: familiar with game theory and learning about algebraic topology.

I know Kakutani's fixed point theorem was used to simplify Nash's seminal paper.
If you think about a simple normal-form game like Prisoner's Dilemma or Coordination Game,  (source: Wayback Machine)

the arrows between the payoff matrix are governed by $>_A$ and $>_B$ meaning the ordering of payoffs by players A and B. I know topological spaces aren't necessarily orderable, but this seems topological in flavour since distance doesn't matter. (Whether you lose £3 or get your head chopped off, I don't care as long as it doesn't affect me.) I think of this as like a "topological gravity" creating the Nash equilibria.