Stochastic Games generalize MDPs to multiple interacting decision-makers.
Mentioned in F1TENTH Research Proposal.
A Markov Game is a tuple
- where is a finite set of states for player
- where is a finite set of actions for player
- is a state transition probability matrix
- is a reward function, where
- is a discount factor,
Nash Equilibrium A Nash Equilibrium of the Markov game is a joint policy , such that for any and
- where represents the indices of all agents in N except agent .
- Turn-based markov game formalization: https://arxiv.org/pdf/2002.10620.pdf