Reversing Reserve Logic: Optimal Holdback in Local Allocation under Scalable Entry

Scarce opportunities such as concert tickets and accelerator time may be contested by automated participants that can create accounts and sustain commitments beyond the reach of commitment-limited intended users. When account counts are untrusted, we study anonymous screening rules that ignore them, cap retained burdens, use only an account's commitment and strongest rival, and do not reassign after rejecting the leader. Within this class, we characterize the rule maximizing intended users' expected utility when they commit fully and a scalable entrant stays out. The optimum refunds and allocates at low congestion, retains and allocates at intermediate congestion, and retains while withholding allocation from an otherwise eligible leader when the strongest rival lies in the upper tail. Unlike a conventional reserve, which rejects a low leading bid, this rule treats an unusually strong rival as evidence of entrant imitation. A direct dual certificate proves class optimality; a benchmark shows that upper-tail holdback can raise intended-user surplus before it is necessary to support non-entry. The rule supports an equilibrium with full commitment and entrant non-entry.