Description
Find one strategy's worst payoff and the first opponent action attaining it.
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.
Find one strategy's worst payoff and the first opponent action attaining it.
When to use this tool
Use Maximin Single Strategy Guaranteed Payoff when checking the stated local payoff, strategy, matching or repeated-game condition.
How to use the tool and how it works
- Enter payoffsAgainstOpponentActions. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read guaranteedPayoff, firstWorstActionIndex. Use the output convention below.
Require a nonempty payoff list. Return its minimum as guaranteedPayoff and the zero-based first index attaining that minimum.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| payoffsAgainstOpponentActions | Payoffs Against Opponent Actions | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| guaranteedPayoff | Guaranteed Payoff | Required. Finite number. |
| firstWorstActionIndex | Zero-based first action attaining the minimum payoff. | Required. Safe integer. |
{
"input": {
"payoffsAgainstOpponentActions": [
4,
-2,
6
]
},
"output": {
"guaranteedPayoff": -2,
"firstWorstActionIndex": 1
}
}Limitations and assumptions
- This evaluates one fixed strategy against listed actions; it does not maximize across strategies or solve a zero-sum game.
- 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
- Pure Strategy Best Response Flag
Check whether a chosen action lies within supplied tolerance of the best payoff.
- Tremble Probability Single Action Term Tool
Mix one explicit action probability with a uniform tremble across a supplied positive action count without validating a full strategy vector.