Stochastic games

A Stochastic game is defined by the following data:

  • A number of players ,
  • A set of states the game can be in (normally thought of as tuples),
  • A set of actions for each player this may depend on the state we refer to the joint set of actions as ,
  • A model which determines for each set of states and action what the transition probabilities there are from to given action , i.e. ,
  • A reward function for each player for being at a given state. and
  • A discount factor for discounted rewards.

When provided with this we are looking for a strategy for each player that determines what action we take in each state.