Weighted reward criteria in Competitive Markov Decision Processes

We consider Competitive Markov Decision Processes in which the controllers/players are antagonistic and aggregate their sequences of expected rewards according to “weighted” or “horizonsensitive” criteria. These are either a convex combination of two discounted objectives, or of one discounted and one limiting average reward objective. In both cases we establish the existence of the game-theoretic value vector, and supply a description of 6-optimal non-stationary strategies.