Associative Criteria in Mutually Dependent Markov Decision Processes

In this paper, we consider associative criteria in mutually dependent Markov decision processes (MDMDP). The MDMDP model is structured upon two types of finite-stage Markov decision process: main-process and sub-process. At each stage, the reward in one process is given by the optimal value of the alternative process problem, whose initial state is determined by the current state and decision in the original process. We introduce an associative criterion to each MDMDP and derive mutually dependent recursive equations by dynamic programming with an invariant imbedding technique.