Never-a-Weak-Best-Response

Never-a-weak-best-response (NWBR) is a strategic stability condition introduced by Elon Kohlberg and Jean-Francois Mertens in their seminal 1986 paper on strategic stability. It requires that no equilibrium strategy assign positive probability to any action that is never a weak best response for any type that plays it with positive probability. In other words: if an action is strictly worse than the equilibrium payoff for every possible belief the player might hold, then no type should be playing it — not even as a zero-probability deviation.

NWBR is closely related to the divinity and universal divinity refinements, though it operates on strategies rather than on beliefs. Where D1 and D2 restrict what receivers can believe after off-path observations, NWBR restricts what senders can rationally do. The two approaches are dual: belief restrictions and strategy restrictions often select the same equilibria, because an action that is never a weak best response will never be sent by any rational type, and a receiver who knows this will assign zero probability to the type after observing it.

In signaling games, NWBR is particularly powerful because it eliminates pooling equilibria in which low types send the same message as high types. If the high type's equilibrium message would be a weak best response for the low type only under beliefs that are themselves inconsistent with the equilibrium, then NWBR eliminates the pooling equilibrium entirely.

NWBR is the moment when game theory admits that the belief-based refinements have reached their limit. It says: stop worrying about what receivers should believe, and start worrying about what senders could rationally do. This is a productive shift — but it is also a confession. The confession is that the entire refinement program, from PBE to D2, has been a search for the right set of counterfactuals, and NWBR is the admission that the search should have been about strategies all along.