In this programmatic talk, I will talk about three major examples of paraconsistency and paradoxes in games. Paraconsistent logic is a family of non-classical logics in which contradictions do not entail everything. In this talk, first, I will discuss game theoretical semantics for paraconsistent logic and observe how semantic games change in different, especially in paraconsistent logics. Then, I will consider a self-referential paradox of epistemic game theory, called Brandenburger-Keisler Paradox, and present a model for it. Following, I will shift my attention non-self-referential paradoxes and suggest a non-self-referential paradox in games. These three major cases, I will argue, will be a call for the necessity of the use of non-classical logics in game theoretical reasoning.