For simple stuff, or just to get started, put the logic in the Players. Players can hold on to data and play for the role of a model to some extent. However, for any significant production, all the business logic should exist outside of the Limelight code, in which case the Players just act like connective tissue between the model and the UI.
For an example, checkout the hangman production: http://github.com/slagyr/hangman/tree/master/hangman/
You'll see that all the business logic source code lives in 'lib' directory. The production loads up all the business logic needed by the production as can be seen here: http://github.com/slagyr/hangman/blob/master/hangman/production.rb. In the DefaultScene Player (http://github.com/slagyr/hangman/blob/master/hangman/default_scene/players/default_scene.rb), all the code if UI related and the real work is delegated to the business layer.
Does that help?
Micah