Description
Check whether a chosen action lies within supplied tolerance of the best payoff.
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 whether a chosen action lies within supplied tolerance of the best payoff.
When to use this tool
Use Pure Strategy Best Response Flag when checking the stated local payoff, strategy, matching or repeated-game condition.
How to use the tool and how it works
- Enter chosenIndex, payoffs, suppliedTolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read bestPayoff, chosenPayoff, bestResponse. Inspect bestResponse before interpreting the associated values.
Require an in-range whole chosenIndex and suppliedTolerance>=0. Return maximum and chosen payoff; bestResponse means maximum-chosen<=tolerance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| chosenIndex | Chosen Index | Required. Safe integer; minimum 0. |
| payoffs | Payoffs | Required. Array of finite number; maximum items 256. |
| suppliedTolerance | Nonnegative payoff shortfall allowance, not a fitted error bound. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| bestPayoff | Best Payoff | Required. Finite number. |
| chosenPayoff | Chosen Payoff | Required. Finite number. |
| bestResponse | Best Response | Required. Boolean. |
{
"input": {
"chosenIndex": 1,
"payoffs": [
2,
5,
5
],
"suppliedTolerance": 0
},
"output": {
"bestPayoff": 5,
"chosenPayoff": 5,
"bestResponse": true
}
}Limitations and assumptions
- The index is zero-based and ties pass; the tolerance is caller-chosen and no opponent strategy, probability distribution or complete equilibrium is evaluated.
- 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
- Maximin Single Strategy Guaranteed Payoff
Find one strategy's worst payoff and the first opponent action attaining it.
- Best Response One Action Payoff Gap Tool
Calculate best response one action payoff gap from explicit caller-supplied inputs.