Description
Sum it, subtract the sum from coalitionValue for excess, and flag blocked for strictly positive excess.
Cooperative-game calculations compare coalition values, allocated payoffs or voting weights. A single coalition term or party share can be useful in a larger calculation without establishing a complete power index, core allocation or bargaining solution.
Sum it, subtract the sum from coalitionValue for excess, and flag blocked for strictly positive excess.
When to use this tool
Use Core Coalition Excess One Subset when you need one explicit coalition, voting or bargaining term.
How to use the tool and how it works
- Enter coalitionValue, allocatedPayoffs. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read allocated, excess, blocked. Inspect blocked before interpreting the associated values.
Require a nonempty allocatedPayoffs list. Sum it, subtract the sum from coalitionValue for excess, and flag blocked for strictly positive excess.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coalitionValue | Coalition Value | Required. Finite number. |
| allocatedPayoffs | Allocated Payoffs | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| allocated | Allocated | Required. Finite number. |
| excess | Excess | Required. Finite number. |
| blocked | Blocked | Required. Boolean. |
{
"input": {
"coalitionValue": 10,
"allocatedPayoffs": [
3,
4
]
},
"output": {
"allocated": 7,
"excess": 3,
"blocked": true
}
}Limitations and assumptions
- The list must represent the chosen subset. This checks one coalition, without allocation efficiency, individual feasibility, or all core constraints.
- 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
Evaluate all required coalitions and allocation constraints for the chosen solution concept. Keep payoff units, quota conventions, feasibility and normalization explicit.
References
Similar or alternative tools
- Shapley One Coalition Marginal Term
Return withValue minus withoutValue and weight 1/[players × binomial(players-1, coalitionSize)], then their product.
- Banzhaf One Swing Indicator Term
Compare coalition weight before and after adding the player, and flag swing only for a losing-to-winning change.