What's the name of this pairwise price-setting scheme?
This is known as the "split-the-difference" mechanism, originally due to Samuelson (1985). See Section 6 of Gibbons et al. (1987) for a discussion of this rule. In particular,


this kind of rule only efficiently dissolves the partnership between the two siblings if they have equal (or sufficiently close to equal) shares in the house. Precisely, each sibling should own no more than 57.7\% of the house.
such a mechanism does not typically induce an equilibrium with sincere bidding (i.e., the siblings will report less than their true value for the house).