Description
Mix one action probability with uniform tremble probability.
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.
Mix one action probability with uniform tremble probability.
When to use this tool
Use Tremble Probability Single Action Term when checking the stated local payoff, strategy, matching or repeated-game condition.
How to use the tool and how it works
- Enter baseActionProbability, trembleFraction, actionCount. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read perturbedActionProbability. Use the output convention below.
Require base probability/tremble fraction in [0,1] and whole actionCount>=1. Return (1-tremble)*baseProbability+tremble/actionCount.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| baseActionProbability | Base Action Probability | Required. Finite number; minimum 0; maximum 1. |
| trembleFraction | Tremble Fraction | Required. Finite number; minimum 0; maximum 1. |
| actionCount | Action Count | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| perturbedActionProbability | Perturbed Action Probability | Required. Finite number. |
{
"input": {
"baseActionProbability": 1,
"trembleFraction": 0.2,
"actionCount": 4
},
"output": {
"perturbedActionProbability": 0.8500000000000001
}
}Limitations and assumptions
- This mixes one action with a uniform tremble term; the full base distribution and compatibility with actionCount are not checked.
- 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
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