We consider a general sum partially observableMarkovgamewhere agents ofdifferent types share asingle policy network, conditioned on agent-specific information. This paper aims at i) formally understanding equilibria reached by such agents, and ii) matching emergent phenomena ofsuch equilibria toreal-worldtargets. Parameter sharing with decentralized execution has been introduced as an efficient way to train multiple agents using a single policy network.

In this work, we investigate the geometry of the k-th homology embedding and focus on cases reminiscent of spectral clustering. Namely, we analyze the connected sum of manifolds as a perturbation of the direct sum of their homology embeddings.