In Monopoly, what is the name of the rule that limits houses when the bank runs out?

The Monopoly rule limiting construction when the bank runs out of houses is called a building shortage.

Under the standard rules, the bank has a finite supply of houses. If no houses remain, players must wait until houses are returned to the bank before building. This creates a strategic constraint because properties cannot be developed simply by paying money when the physical pieces are unavailable.

The shortage can become especially important when players hold several properties in the same color group. Because houses must generally be distributed evenly within a group, one player may deliberately keep houses in use and reduce the supply available to opponents. This tactic is often called “house hoarding” by players, although that is descriptive rather than the formal name of a separate rule.

Hotels also depend on the supply of pieces, and exchanging houses for hotels can affect availability across the board.