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A stochastic game is a dynamic game with probabilistic transitions between states, played by one or more players, where the transition probabilities are often affected by the players' actions.

The state space in a stochastic game is the set of all possible configurations or situations the game can be in at any step.

The action space is the set of all actions that players can take. In a stochastic game, these actions can influence the transition probabilities between states.

Transition probabilities in a stochastic game are the likelihoods of moving from one state to another, given a particular set of actions by the players.

The payoff function in a stochastic game assigns a numerical reward (or cost) to each player based on the current state of the game and the actions taken by the players.

The discount factor is a value between 0 and 1 that determines the present value of future payoffs, reflecting the concept of time preference in a stochastic game.