The Game of Marginal Utilities

What the math gives to ML

The paper provides a constructive congestion-aware resource-allocation structure that can be transplanted into sparse mixture-of-experts routing. Its key transferable asset is the equimarginal rule: an agent should move routing mass toward experts with the largest marginal payoff, while that payoff decreases as other agents load the same expert. The nested-support result suggests a cheap sorted-prefix router rather than a dense softmax over all experts, and the projected marginal-utility iteration gives a directly implementable routing solver. This is most promising for group-wise routing where expert capacity is shared and ordinary load-balancing penalties are too indirect.