Description
Return lowerBound+(value-lowerBound)(bidders-1)/bidders and the complementary shading.
Auction arithmetic depends on the bidding rule, reserve and treatment of ties. A payment formula for one supplied bid profile differs from determining optimal bidding behavior or operating an actual market.
Return lowerBound+(value-lowerBound)(bidders-1)/bidders and the complementary shading.
When to use this tool
Use Auction First Price Symmetric Value Factor when you need an explicit auction-profile or benchmark bidding calculation.
How to use the tool and how it works
- Enter value, bidders, lowerValueBound. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read bid, shading. Use the output convention below.
Require at least two integer bidders and value no below lowerValueBound. Return lowerBound+(value-lowerBound)(bidders-1)/bidders and the complementary shading.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| value | Value under the stated unit, type, and placeholder convention. | Required. Finite number. |
| bidders | Bidders | Required. Safe integer; minimum 2. |
| lowerValueBound | Supplied lower endpoint of the uniform-private-value benchmark, not an auction reserve automatically enforced. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| bid | Bid | Required. Finite number. |
| shading | Shading | Required. Finite number. |
{
"input": {
"value": 100,
"bidders": 4,
"lowerValueBound": 0
},
"output": {
"bid": 75,
"shading": 25
}
}Limitations and assumptions
- This is the symmetric risk-neutral independent-uniform private-value benchmark with a supplied lower bound, not a general bidding recommendation. Upper support, reserve, risk preferences and real market assumptions are not checked.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Apply the complete auction specification and verify tie, reserve, allocation and payment rules. Use a model matching actual value and information assumptions before interpreting a theoretical bidding benchmark.
References
Similar or alternative tools
- Second Price Auction One Bid Payment
Win only at or above reserve and above the highest rival, allowing equality when tieWins; a winner pays max(reserve, highest rival), otherwise zero.
- Auction Reserve Equality Token
Compare bid with reserve inclusively or strictly according to equalityAccepts and return bid minus reserve.