Ascending exit auction
Track irreversible auction exits and a carried budget using paper points.
Logic & rule checking
- Players
- 3
- Time
- 15–25 minutes
- Materials
- Three value cards, two lots X/Y,10-point budgets
Prepare
Three players each have budget 10. Privately assign value pairs X/Y: A8/2, B6/6, C2/8. Values are scoring numbers, not money. Auction X then Y; remaining budgets carry to Y. Each lot has one copy and no resale.
Play
Start a lot at price 0 with all three active. At each integer price, players simultaneously reveal Stay or Exit. Exit is permanent for that lot. A player whose remaining budget is below the current price must exit. Do not reveal an exit before everyone has selected.
Worked example
If exactly one stays, that player pays the current price and receives the lot; add their value minus price to their final score. If zero stay, the lot is unsold. If at least two stay and price is below 10, increase price by 1 and repeat. At 10 with at least two staying the lot is unsold, with no tie bid.
Finish and check
Example: at price 3, A and B stay and C exits. At 4 only A stays, so A pays 4, has budget 6 left and scores 8−4=4 from X. An earlier exit cannot re-enter just because the price remains affordable.
Adaptation and limits
After Y, sum value minus price for lots won; highest total wins, equal ties. Unspent budget is not extra score. Reveal value cards and audit affordability. Use paper counters only; an adult can read private cards aloud separately without changing anyone’s choices.
Purpose, observation and provenance
Within this activity: Track irreversible auction exits and a carried budget using paper points.
A partner can replay each legal action and explain the stopping condition; this is an observable task, not evidence of lasting improvement.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Rules to keep beside the materials
- Three players each have budget 10. Privately assign value pairs X/Y: A8/2, B6/6, C2/8. Values are scoring numbers, not money. Auction X then Y; remaining budgets carry to Y. Each lot has one copy and no resale.
- Start a lot at price 0 with all three active. At each integer price, players simultaneously reveal Stay or Exit. Exit is permanent for that lot. A player whose remaining budget is below the current price must exit. Do not reveal an exit before everyone has selected.
- If exactly one stays, that player pays the current price and receives the lot; add their value minus price to their final score. If zero stay, the lot is unsold. If at least two stay and price is below 10, increase price by 1 and repeat. At 10 with at least two staying the lot is unsold, with no tie bid.
- Example: at price 3, A and B stay and C exits. At 4 only A stays, so A pays 4, has budget 6 left and scores 8−4=4 from X. An earlier exit cannot re-enter just because the price remains affordable.
- After Y, sum value minus price for lots won; highest total wins, equal ties. Unspent budget is not extra score. Reveal value cards and audit affordability. Use paper counters only; an adult can read private cards aloud separately without changing anyone’s choices.
Ascending exit auction — player materials
| Lot | Price | A | B | C |
|---|---|---|---|---|
| X | 0 | |||
| X | 1 | |||
| X | 2 | |||
| X | 3 | |||
| X | 4 | |||
| X | 5 | |||
| X | 6 | |||
| X | 7 | |||
| X | 8 | |||
| X | 9 | |||
| X | 10 | |||
| Y | 0 | |||
| Y | 1 | |||
| Y | 2 | |||
| Y | 3 | |||
| Y | 4 | |||
| Y | 5 | |||
| Y | 6 | |||
| Y | 7 | |||
| Y | 8 | |||
| Y | 9 | |||
| Y | 10 |
| Player | Paid X/Y | Budget left | Value−price score |
|---|---|---|---|
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
Host check — keep separate
At 4 sole A pays 4, budget 6 and X score 4; unsold lots score nothing.
Examples are stipulated model cases, not measured experimental or learning outcomes.