To establish that the LMSS is a symmetric sequential equilibrium strategy, we again appeal to the Optimality Principle of Dynamic Programming. If we show that there is no point at which a single change in the trader's current action only (followed by later adherence to the LMSS) can raise the trader's expected payoff at that point, then there is no point at which some more complicated deviation can be profitable, either.

DEFINE: Explains the Optimality Principle of Dynamic Programming — checking only single-action changes validates the whole strategy.

PAUL R. MILGRO, PAUL R. MILGRO - THE ROLE O…, loc. 102