# Why is the policy not a part of the MDP definition?

I'm reading an article on reinforcement learning, and I don't understand why the agent's policy $$\pi$$ is not part of definition of Markov Decision process(MDP):

Bu, Lucian, Robert Babu, and Bart De Schutter. "A comprehensive survey of multiagent reinforcement learning." IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews) 38.2 (2008): 156-172.

My question is:

Why the policy is not a part of the MDP definition?

On the other hand, it can also be interesting sometimes to study multiple different policies all for the same MDP. A very common example would be any off-policy learning algorithm (like $$Q$$-learning): they all involve at least one "target policy" (for which they're learning the $$Q(s, a)$$ values -- usually the greedy policy with respect to the values learned so far), and at least one "behaviour policy" (which they're using to generate experience -- often something like an $$\epsilon$$-greedy policy). A more complex example would be population-based training setups, like the one DeepMind used for their StarCraft 2 training; here they have a large population of different policies that they're all using in a complex training setup (and technically I suppose we should say they also have many different MDPs, where every combination of StarCraft 2 level + training opponent would formally be a different MDP).