We describe a class of semantic extensive entailment game (eeg) with algorithmic players, related to game-theoretic semantics (gts), and generalized to classical first-order semantic entailment. Players have preferences for parsimonious spending of computational resources, and compute partial strategies, under qualitative uncertainty about future histories. We prove the existence of local preferences for moves, and strategic fixpoints, that allow to map eeg game-tree to the building rules and closure rules of Smullyan's semantic tableaux (st). We also exhibit a strategy profile that solves the fixpoint selection problem, and can be mapped to systematic constructions of semantic trees, yielding a completeness result by translation. We conclude on possible generalizations of our games
