Closed-form selection of a canonical core point from dual prices

Determine whether a canonical core selection, such as the bidder-optimal core point, can be obtained in closed form directly from the dual variables of the winner-determination problem rather than by solving a secondary optimization problem.

Background

The paper establishes that dual (nodal) pricing produces a core-stable outcome for the origin–destination auction, but optimal dual solutions may be non-unique when the underlying linear program is degenerate. Consequently, the resulting payment vector is not necessarily unique. The authors note that selecting the bidder-optimal core point could reduce bidders’ incentives to manipulate prices, but currently describe such a selection as requiring a secondary optimization problem.

The unresolved issue is whether the dual information generated by the winner-determination problem itself admits a closed-form rule for selecting a canonical core allocation, avoiding an additional optimization stage.