Description
Return their maximum, nonnegative alternative-minus-candidate regret, and bestResponse when candidate plus tolerance reaches the maximum.
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 their maximum, nonnegative alternative-minus-candidate regret, and bestResponse when candidate plus tolerance reaches the maximum.
When to use this tool
Use Best Response One Action Payoff Gap when you need one transparent payoff or incentive comparison.
How to use the tool and how it works
- Enter candidatePayoff, alternativePayoffs, tolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read bestAlternative, regret, bestResponse. Inspect bestResponse before interpreting the associated values.
Require nonempty alternativePayoffs and nonnegative tolerance. Return their maximum, nonnegative alternative-minus-candidate regret, and bestResponse when candidate plus tolerance reaches the maximum.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| candidatePayoff | Candidate Payoff | Required. Finite number. |
| alternativePayoffs | Alternative Payoffs | Required. Array of finite number; maximum items 256. |
| tolerance | Tolerance | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| bestAlternative | Best Alternative | Required. Finite number. |
| regret | Regret | Required. Finite number. |
| bestResponse | Best Response | Required. Boolean. |
{
"input": {
"candidatePayoff": 5,
"alternativePayoffs": [
3,
7,
4
],
"tolerance": 0
},
"output": {
"bestAlternative": 7,
"regret": 2,
"bestResponse": false
}
}Limitations and assumptions
- Regret remains the unadjusted positive gap even if tolerance makes bestResponse true. Only supplied alternatives are evaluated, not an entire strategy space.
- 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
- Tie Payoff Action Indifference Gap
Return first payoff minus second and whether its absolute value is no greater than tolerance.
- Nash Deviation One Player Slack
Return its product with deviation minus equilibrium payoff, the opposite obedience slack, and profitable only for positive probability and strictly higher deviation payoff.