In this talk I will discuss a method of building new game models of linear logic from old. The construction works by prepending a `bidding round' to existing games, quite similar to the passage from Whist to Bridge. From a theoretical point of view, we are building hybrids of game models and dialectica categories (which are not usually seen as game models). This transformation behaves like a closure operator on models: it preserves completeness, and it has a monad-like structure. Intuitively we can expect never to get a 'worse' model, and possibly to get a 'better' model, after applying the transformation.