Dialectica models of additive-free linear logic

We define a transformation of models of additivefree propositional linear logic, closely related to de Paiva’s dialectica categories, but with a modified exponential based on Oliva’s dialectica interpretation of higher-order linear logic. As a result of this modification we obtain an elegant factorisation of dialectica models as linear-nonlinear adjunctions. From the point of view of game semantics, the transformation can be intuitively seen as prepending games with a round of simultaneous bidding. Two theorems suggest the transformation behaves like a closure operator on models: it has a monad-like structure, and it preserves completeness.