Which type of property interest is contingent on the action of another party for its continuation?

The correct choice pertains to an estate at will, which is a tenancy that allows for a duration that is not fixed and can be terminated by either party at any time, contingent upon the actions of another party, often the property owner. This type of arrangement typically exists when there is an informal agreement to occupy the property without a formal lease; thus, the tenant's right to reside in the property continues only as long as the landlord allows.

Other types of interests mentioned, such as an estate for years, are established for a fixed term and do not depend on the actions of the owner for their continuation. Similarly, a tenancy at sufferance arises when a tenant remains in the property after their lease has expired, showing that it does not rely on the owner's actions for validity. An estate from period to period, or periodic tenancy, is established for successive periods and automatically renews based on the continued acceptance of payment, again not contingent on the action of another party to remain valid.

Therefore, the essence of an estate at will lies in its flexibility and uncertainty, contingent on the mutual agreement and the landlord's willingness to allow the tenant to stay.