Description
Return first payoff minus second and whether its absolute value is no greater than tolerance.
Game-theoretic payoffs describe a chosen model of actions and incentives. A deviation, discounted term or local payoff contribution is only one part of the relevant equilibrium or welfare conditions.
Return first payoff minus second and whether its absolute value is no greater than tolerance.
When to use this tool
Use Tie Payoff Action Indifference Gap when you need one transparent payoff or incentive comparison.
How to use the tool and how it works
- Enter firstPayoff, secondPayoff, tolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read gap, indifferentWithinTolerance. Inspect indifferentWithinTolerance before interpreting the associated values.
Require nonnegative tolerance. Return first payoff minus second and whether its absolute value is no greater than tolerance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstPayoff | First Payoff | Required. Finite number. |
| secondPayoff | Second Payoff | Required. Finite number. |
| tolerance | Tolerance | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| gap | Difference on the stated unit and subtraction basis. | Required. Finite number. |
| indifferentWithinTolerance | Indifferent Within Tolerance | Required. Boolean. |
{
"input": {
"firstPayoff": 5,
"secondPayoff": 5,
"tolerance": 0
},
"output": {
"gap": 0,
"indifferentWithinTolerance": true
}
}Limitations and assumptions
- Payoffs and tolerance share units. Within-tolerance indifference is a supplied numerical policy, not proof of equal preferences or 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
Evaluate the complete strategy space, timing and payoff model for an equilibrium claim. Test robustness to assumptions rather than treating a local incentive inequality as a prediction of actual behavior.
References
Similar or alternative tools
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