Description
Check one transferable-utility coalition's payoff-allocation inequality.
Game-theoretic calculations depend on specified players, actions, payoff direction, probabilities and continuation assumptions. A single incentive term, coalition inequality or candidate best response is only part of a complete equilibrium argument. Supplied preferences and payoffs are model inputs rather than observed behavior or a moral allocation rule.
Check one transferable-utility coalition's payoff-allocation inequality.
When to use this tool
Use Transferable Utility Core Coalition Slack when checking the stated local payoff, strategy, matching or repeated-game condition.
How to use the tool and how it works
- Enter coalitionAllocatedPayoffs, coalitionValue. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read allocatedTotal, coalitionSlack, satisfiesCoalitionInequality. Inspect satisfiesCoalitionInequality before interpreting the associated values.
Sum signed coalitionAllocatedPayoffs. Return allocatedTotal-coalitionValue and whether the total>=value, including equality.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coalitionAllocatedPayoffs | Coalition Allocated Payoffs | Required. Array of finite number; maximum items 256. |
| coalitionValue | Coalition Value | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| allocatedTotal | Allocated Total | Required. Finite number. |
| coalitionSlack | Coalition Slack | Required. Finite number. |
| satisfiesCoalitionInequality | This coalition’s allocated sum>=coalition value, not a full core-membership check. | Required. Boolean. |
{
"input": {
"coalitionAllocatedPayoffs": [
3,
4
],
"coalitionValue": 6
},
"output": {
"allocatedTotal": 7,
"coalitionSlack": 1,
"satisfiesCoalitionInequality": true
}
}Limitations and assumptions
- One coalition inequality does not prove that an allocation is efficient, feasible or in the full transferable-utility core.
- 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
Use the complete game, feasible strategy space and justified information/continuation assumptions for equilibrium, welfare or actual decision analysis.
References
Similar or alternative tools
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