You have seen how players interact in a one-shot game or repeat the same game over many rounds. But many real interactions change over time — an economy grows or shrinks, a company’s market position improves, a couple’s relationship deepens. Stochastic games give us the language and tools to study exactly that: strategic play in an environment where the “rules” can depend on a state that evolves, sometimes randomly, as a result of everyone’s actions. By the end of this chapter you will be able to recognize when a situation is a stochastic game, find simple equilibria where players just react to the current state, and understand why even a small discount factor can completely change what is rational.