An item sharing machine is configured to receive share requests in the example form of allocation requests submitted by requesters for an allocable region of a graphical user interface. The allocation requests specify numerical values accorded to the allocable region by the requesters. The item sharing machine determines a distribution of the numerical values and, based on the distribution, generates an allocation plan defined by configuration parameters for the allocable region. The item sharing machine is configured to repeatedly update the allocable region based on the allocation plan by cyclically and selectively linking the allocable region to different computers of different requesters based on the allocation plan. The allocable region accordingly becomes linked to computers of different requesters at different times, and the item sharing machine is configured to cause one or more user devices to present the allocable region linked to such computers at different times.