Description
Check a normalized repeated-game deviation inequality under a constant punishment continuation.
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 a normalized repeated-game deviation inequality under a constant punishment continuation.
When to use this tool
Use Repeated Game Deviation Deterrence Gap when checking the stated local payoff, strategy, matching or repeated-game condition.
How to use the tool and how it works
- Enter cooperationPayoff, deviationPayoff, punishmentPayoff, discountFactor. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read normalizedDeterrenceGap, cooperationDetersDeviation. Inspect cooperationDetersDeviation before interpreting the associated values.
Require discountFactor in [0,1). Gap=cooperationPayoff-(1-factor)*deviationPayoff-factor*punishmentPayoff; cooperationDetersDeviation means gap>=0.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| cooperationPayoff | Cooperation Payoff | Required. Finite number. |
| deviationPayoff | Deviation Payoff | Required. Finite number. |
| punishmentPayoff | Punishment Payoff | Required. Finite number. |
| discountFactor | Discount Factor | Required. Finite number; minimum 0; strictly below 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| normalizedDeterrenceGap | Cooperation-(1-discount)*one-period deviation-discount*constant punishment payoff. | Required. Finite number. |
| cooperationDetersDeviation | Cooperation Deters Deviation | Required. Boolean. |
{
"input": {
"cooperationPayoff": 3,
"deviationPayoff": 5,
"punishmentPayoff": 1,
"discountFactor": 0.75
},
"output": {
"normalizedDeterrenceGap": 1,
"cooperationDetersDeviation": true
}
}Limitations and assumptions
- This assumes a one-period deviation followed by the supplied constant punishment continuation; monitoring, credibility and all deviations 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
Similar or alternative tools
- Strategy Deviation Regret
Calculate a strategy-deviation gain and its nonnegative regret component.
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Calculate one probability-weighted incentive contribution for a correlated recommendation.