Logical evaluation games are an alternative characterization of truth to standard Tarskian semantics. Analyzing truth with the apparatus of formal game theory has led to some interesting generalizations of classical logic, like Independence-friendly logic by Hintikka, based on making evaluation a game of imperfect information. Hintikka-style evaluation games have become standard means of analyzing new logics. Mathematical fuzzy logic provides a formalism for reasoning about vague statements. Its roots can be traced back to works by Lukasiewicz and Gödel. In the second half of the twentieth century Zadeh coined the term fuzzy logic for a formalism used in automation. The approaches were unified in Hajek's framework and have been an active research topic since. A close alignment of evaluation games, for classical and prominent fuzzy logics, with formal game theory reveals a gap between the presentation of logical evaluation games and formal definitions of extensive games of perfect information. This work joins the two notions by providing an explicit game rule of negation as an in-game move and aligning the definitions. The two resulting games, one for classical logic and one for Zadeh's fuzzy logic, along with correspondence proofs to standard semantics are a central result of this thesis. The direction of analyzing game theoretic concepts with formal logic, especially modal logic is a comparatively new field and has yielded highly expressive formalisms, like Game Logic, for reasoning about players' powers for certain game situations. Examining the minor imprecisions in evaluation game definitions in literature led us to the idea of formalizing the games a distinctive step further: we construct modal axiomatizations of the game trees, by viewing them as Kripke structures and carry out extensive formal proofs showing that those axioms describe the games. A thorough analysis of first-order modal logic and modal correspondence theory is carried out in order to capture as many aspects as possible syntactically. The provided axiomatization may serve as a base for concretely analyzing the class of logical evaluation games in richer formal systems.