added multiplayer functions

[zsunberg]

@jonathan-laurent here is my best suggestion for how we should support multiplayer environments (in response to #43 ). What do you think?

This includes the following optional functions:

• player_indices
• player
• all_act!
• all_observe
• UtilityStyle

[jonathan-laurent]

This looks reasonable to me! Also, the documentation is good.

[zsunberg]

Ok, I am going to implement a quick example of tictactoe just to make sure that is pretty easy.

One thing I did think of is that it will get really hard for algorithm writers if player_indices can return something other than a range of integers because then how does an algorithm writer know what kind of container to submit to all_act!? I think it is better for all_act! to always use a vector of actions. Hence player_indices should always return a list of integers.

But in that case should we just switch from player_indices to num_players?

[zsunberg]

Unfortunately I probably won't be able to touch this again until Tuesday. I or someone else also needs to update the Documenter docs for this.

[findmyway]

One thing I did think of is that it will get really hard for algorithm writers if player_indices can return something other than a range of integers because then how does an algorithm writer know what kind of container to submit to all_act!? I think it is better for all_act! to always use a vector of actions. Hence player_indices should always return a list of integers.

I think if we force all_act! to always use a vector of actions, then player_indices can return anything else only if it is ordered. And maybe we can simply rename it to players?

[zsunberg]

After thinking about it a bit more, I see no compelling reason to support anything other than integer indices for players right now. That being said, players feels better than num_players and feels like it could be expanded in the future, and player/players seems more consistent than player/player_indices (player_index/player_indices would be more consistent).

Going with player/players and players returns an ordered list of integers starting at one for now. Will make the change and merge soon and then tag a version later tonight, so stop me soon if there are any objections :)