This chapter introduces the concept of \(\delta \) -dissipative dynamical systems, which generalizes classical dissipativity by focusing on the time derivatives of system inputs and outputs. The framework aligns with traditional energy-based analysis while adopting a derivative-based perspective and relates closely to generalized passivity notions such as Krasovskii, differential, and incremental passivity. The \(\delta \) -dissipativity property provides a versatile tool for analyzing interconnected systems and plays a key role in studying evolutionary and payoff dynamics in population games. By enabling a unified treatment of various decision-making processes in large-scale multi-agent systems, it establishes the theoretical foundations for subsequent analyses. The chapter formalizes the definition of \(\delta \) -dissipativity, presents stability conditions for equilibria, examines preservation properties under interconnections, and illustrates the concepts through an optimization-based example.