Description
Return its product with deviation minus equilibrium payoff, the opposite obedience slack, and profitable only for positive probability and strictly higher deviation payoff.
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 its product with deviation minus equilibrium payoff, the opposite obedience slack, and profitable only for positive probability and strictly higher deviation payoff.
When to use this tool
Use Nash Deviation One Player Slack when you need one transparent payoff or incentive comparison.
How to use the tool and how it works
- Enter equilibriumPayoff, deviationPayoff, probabilityOthers. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read weightedGain, obedienceSlack, profitable. Inspect profitable before interpreting the associated values.
Require probabilityOthers in [0, 1]. Return its product with deviation minus equilibrium payoff, the opposite obedience slack, and profitable only for positive probability and strictly higher deviation payoff.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| equilibriumPayoff | Equilibrium Payoff | Required. Finite number. |
| deviationPayoff | Deviation Payoff | Required. Finite number. |
| probabilityOthers | Probability Others | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| weightedGain | Weighted Gain | Required. Finite number. |
| obedienceSlack | Obedience Slack | Required. Finite number. |
| profitable | Profitable | Required. Boolean. |
{
"input": {
"equilibriumPayoff": 3,
"deviationPayoff": 5,
"probabilityOthers": 0.25
},
"output": {
"weightedGain": 0.5,
"obedienceSlack": -0.5,
"profitable": true
}
}Limitations and assumptions
- This is one weighted deviation term; a zero-probability event gives no profitable flag. Other players, actions, and equilibrium conditions 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
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
- Correlated Device One Obedience Term
Multiply it by obeyPayoff minus deviatePayoff.
- Best Response One Action Payoff Gap
Return their maximum, nonnegative alternative-minus-candidate regret, and bestResponse when candidate plus tolerance reaches the maximum.