Description
Sum all weight and weight whose payoff differs from reference by at most tolerance; return their ratio or flagged undefined zero.
A strategy's support identifies actions assigned positive mass under a stated threshold. Support flags, normalized probabilities and payoff indifference are separate properties, so one check does not establish a valid mixed-strategy equilibrium.
Sum all weight and weight whose payoff differs from reference by at most tolerance; return their ratio or flagged undefined zero.
When to use this tool
Use Strategy Indifference Support Share when you need a probability-mass or thresholded-support diagnostic.
How to use the tool and how it works
- Enter payoffs, supportWeights, referencePayoff, tolerance. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read supportMass, indifferentMass, share, defined. Inspect defined before interpreting the associated values.
Require aligned payoffs and nonnegative support weights plus nonnegative tolerance. Sum all weight and weight whose payoff differs from reference by at most tolerance; return their ratio or flagged undefined zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| payoffs | Payoffs | Required. Array of finite number; maximum items 256. |
| supportWeights | Support Weights | Required. Array of finite number; minimum 0; maximum items 256. |
| referencePayoff | Reference Payoff | Required. Finite number. |
| tolerance | Tolerance | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| supportMass | Support Mass | Required. Finite number. |
| indifferentMass | Indifferent Mass | Required. Finite number. |
| share | Dimensionless share on the numerator and denominator basis stated above. | Required. Finite number. |
| defined | Whether the stated denominator or normalization exists; inspect before interpreting a zero placeholder. | Required. Boolean. |
{
"input": {
"payoffs": [
2,
3,
2
],
"supportWeights": [
0.2,
0.5,
0.3
],
"referencePayoff": 2,
"tolerance": 0
},
"output": {
"supportMass": 1,
"indifferentMass": 0.5,
"share": 0.5,
"defined": true
}
}Limitations and assumptions
- Weights need not sum to one. Indifference covers the supplied reference and tolerance, without verifying all best responses or an equilibrium.
- 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
Validate the complete distribution and compare payoffs of all relevant deviations. State any numerical tolerance and zero-mass convention before interpreting support as an equilibrium property.
References
Similar or alternative tools
- Tie Payoff Action Indifference Gap
Return first payoff minus second and whether its absolute value is no greater than tolerance.
- Mixed Strategy Support Residual
Sum inside and outside support and return one minus total mass.