Graphon Design for Human-Machine Coordination under Bounded Rationality: Optimality of Stochastic Block Models

What the math gives to ML

The paper provides a constructive graphon-design mechanism: for agents with a bimodal rationality profile following logit learning in a stag-hunt coordination game, an optimal interaction graphon can be searched for within the much smaller family of stochastic block models (SBMs). The fixed edge-density constraint converts topology design into a continuous allocation problem over block-to-block connection probabilities, solved locally by a water-filling procedure that saturates the most valuable block pairs first. This can transfer to modular neural systems by designing block-sparse attention, recurrent communication, or MoE expert-interaction graphs according to module reliability and noise classes rather than learning an unconstrained dense topology.