Participatory Rostering:
A Two-Stage Game-Theoretic Framework

1. The Friction of Top-Down Scheduling

In healthcare, logistics, and retail, shift scheduling is traditionally a zero-sum game. Managers mandate schedules based on coverage needs, leading to high employee dissatisfaction. When shifts inevitably become understaffed due to call-outs or unpopular hours, managers deploy expensive, flat-rate surge incentives to desperately plug holes. This approach is financially inefficient and psychologically corrosive.

2. The Two-Step Market Mechanism

Presolve Labs replaces this rigid system with a dynamic, participatory marketplace. The process is broken into two distinct stages designed to foster collaboration and find mathematical equilibrium:

• Stage 1: Blind Preference Bidding Employees submit their ideal shift preferences. Rather than immediately assigning shifts, the algorithm generates a "Market Reveal" showing the supply/demand curve to the whole team. Employees see exactly which shifts are oversubscribed and which are desperately understaffed.
• Stage 2: Reverse-Auction Incentives Instead of the manager offering a flat €150 bonus for an empty Friday night shift, a gamified reverse auction begins. The algorithm sets an incentive budget ceiling, and employees bid on the minimum bonus they would accept to reallocate their schedule.

3. Collaborative Psychology & Cost Efficiency

The mathematical elegance of this model lies in market efficiency. Employees who value flexibility will bid lower incentives to take the Friday shift, while the system automatically protects hard constraints (like maximum consecutive hours).

Crucially, because the team participates in resolving the imbalance, adherence and satisfaction rates skyrocket. Employees are no longer victims of the schedule; they are active market participants. For the enterprise, this prevents standard overpayment for understaffed shifts, turning scheduling from a sunk cost into an optimized variable asset.