We study models of the untyped lambda calculus in the setting of the game semantics introduced by Abramsky and Hyland. In particular we show that two natural, and apparently general, model constructions give extensional lambda-models which, somewhat unexpectedly, all induce the same theory. This is H*, the maximal theory induced by the classical $D_{\infty}$ model, introduced by D. Scott in 1968. New techniques for overcoming this apparent rigidity of game lambda-models are called for.