Time management in chess, both for computers and humans, does not seem to have well established principles like minimax and alpha-beta search. Distill time management into an incomplete information game, removing the chess aspect. Each player begins with a certain amount of "effort", and operates on a probability distribution, perhaps bell curve. On each turn, a player can expend effort to modify (or perhaps learn?) the parameters of the probability distribution. At the end of the game, the distribution is sampled to determine the winner.
Many details yet to be worked out.
Spending a lot of effort early is a bet that the game will not be long.