Memory Allocation Games Arising in Algorithmic Information Theory

We consider some memory allocation games to solve two problems in Algorithmic Information Theory. One is whether (monotonic) descriptional complexity is equal (to within an additive constant) to the logarithm of a priori probability. The solution uses games which have some independent interest. In them, User sends incremental requests of memory space for certain structured items, Server allocates this space in a write-once memory. For each itam, some of the allocated space is required to be in one piece, to give a short address