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.