  Sufficient conditions are identified under which the value function and the
optimal strategy of a Markov decision process (MDP) are even and quasi-convex
in the state. The key idea behind these conditions is the following. First,
sufficient conditions for the value function and optimal strategy to be even
are identified. Next, it is shown that if the value function and optimal
strategy are even, then one can construct a "folded MDP" defined only on the
non-negative values of the state space. Then, the standard sufficient
conditions for the value function and optimal strategy to be monotone are
"unfolded" to identify sufficient conditions for the value function and the
optimal strategy to be quasi-convex. The results are illustrated by using an
example of power allocation in remote estimation.
