Description
Sum inside and outside support and return one minus total mass.
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 inside and outside support and return one minus total mass.
When to use this tool
Use Mixed Strategy Support Residual when you need a probability-mass or thresholded-support diagnostic.
How to use the tool and how it works
- Enter probabilities, inSupport. 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 outsideMass, supportedMass, totalResidual. Use the output convention below.
Require aligned probability and support arrays with each probability in [0, 1]. Sum inside and outside support and return one minus total mass.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| probabilities | Probabilities | Required. Array of finite number; maximum items 256. |
| inSupport | In Support | Required. Array of boolean; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| outsideMass | Outside Mass | Required. Finite number. |
| supportedMass | Supported Mass | Required. Finite number. |
| totalResidual | Total Residual | Required. Finite number. |
{
"input": {
"probabilities": [
0.2,
0.3,
0.5
],
"inSupport": [
true,
false,
true
]
},
"output": {
"outsideMass": 0.3,
"supportedMass": 0.7,
"totalResidual": 0
}
}Limitations and assumptions
- The input need not sum to one; a negative residual exposes over-allocation. The support flags do not establish payoff indifference or optimality.
- 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
- Strategy Support Positive Count
Count entries strictly above tolerance and entries no greater than it.
- Mixed Deviation Support Mass
Sum flagged probability mass and total mass.