Games are abstract models of decision-making in which decision-makers(players)interact in a shared environment to accomplish their goals. Several models have been proposed to analyze a wide variety of applications in many disciplines such as mathematics, computer science and even political and social sciences among others. In this work, we focus on Game Theory and Game Logics. We present a first-order modal logic based on CTL, namely Game Analysis Logic (GAL), to model and reason about out games. The standard models of Game Theory (strategic games, extensiv games and coalition games) as well as their solution concepts (Nash equilibrium, subgame perfect equilibrium and co re),respectively, are express as models dels of GAL and formulas of GAL. Moreover, we study the alternatives of De Re and De Dicto quantification in the context of extensive games. We also show that two of the most representative game logics, namely Alternating-time lternating-Temp empor oral Logic (A ATL) TL) and Coalitional Game Logic (CGL), are fragments of GAL. We also characterize haracterize a class of multi-agent systems, which is based on the architecture Belief-Desire- Intention (BDI), for which there is a somehow equivalent class of games and vice-versa. As a consequence, criteria of rationality for agents can be directly applied to players and vice-versa. Game analysis formal tools can be applied to MAS as well. From a practical poin of view, we provide and develop a model-checker for GAL. In addition, we perform case studies using our prototype.