Weighted reward criteria in Competitive Markov Decision Processes

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