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

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.

A Nash equilibrium in a stochastic game is a strategy profile where no player has an incentive to unilaterally deviate, considering the probabilistic nature of the game and the strategies of the other players.

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.

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.