A multicriteria competitive Markov decision process

In this paper, we deal with a multicriteria competitive Markov decision process. In the decision process there are two decision makers with a competitive behaviour, so they are usually called players. Their rewards are coupled because they depend on the actions chosen by both players in each state of the process. We propose as solution of this game the set of Pareto-optimal security strategies for any of the players in the original problem. We show that this solution set can be obtained as the efficient solution set of a multicriteria linear programming problem.