What if we have a stochastic game S and a set of agents A and in each game s we might have a different subset of A playing? What type of game is that? This of course is only relevant when dealing with |A| > 2 agents. Also, the agents that play in each s could be stochastic or fixed. Of course we can always make it harder by making the number actions varied for the agents.
This seems like it could model tournaments if the games are competitive or stochastic coalition games.
This seems sort of like a Bayesian game… Not sure though.
I think that games would have to run in parallel. So all players would be playing somewhere just depending on the state, who they are playing with is different. I guess they would need to run in parallel it just would mean that in that state there are x number of possible games that need to be played before going to the next state and how they are played determines the next state. How does one write a learning algorithm for that? The matrix system is growing and becoming harder to construct meaningful examples. I need to write a game builder which will generate these structures.