Description
Compare immediate deviation gain with cooperation-minus-punishment payoff times the sum of discount powers from period one through that count, using the count directly at discount one.
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.
Compare immediate deviation gain with cooperation-minus-punishment payoff times the sum of discount powers from period one through that count, using the count directly at discount one.
When to use this tool
Use Repeated Game Finite Punishment Payoff Term when you need one transparent payoff or incentive comparison.
How to use the tool and how it works
- Enter cooperatePayoff, deviationPayoff, punishmentPayoff, discount, punishmentPeriods. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read deviationGain, discountedPunishmentLoss, deters. Inspect deters before interpreting the associated values.
Require discount in [0, 1] and nonnegative integer punishment periods. Compare immediate deviation gain with cooperation-minus-punishment payoff times the sum of discount powers from period one through that count, using the count directly at discount one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| cooperatePayoff | Cooperate Payoff | Required. Finite number. |
| deviationPayoff | Deviation Payoff | Required. Finite number. |
| punishmentPayoff | Punishment Payoff | Required. Finite number. |
| discount | Per-period discount multiplier in [0, 1], not a discount-rate percentage. | Required. Finite number; minimum 0; maximum 1. |
| punishmentPeriods | Punishment Periods | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| deviationGain | Deviation Gain | Required. Finite number. |
| discountedPunishmentLoss | Discounted Punishment Loss | Required. Finite number. |
| deters | Deters | Required. Boolean. |
{
"input": {
"cooperatePayoff": 3,
"deviationPayoff": 5,
"punishmentPayoff": 1,
"discount": 0.5,
"punishmentPeriods": 2
},
"output": {
"deviationGain": 2,
"discountedPunishmentLoss": 1.5,
"deters": false
}
}Limitations and assumptions
- This is a supplied finite-punishment incentive comparison, not a complete repeated-game equilibrium proof; punishment credibility and later continuation 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
- Repeated Payoff Truncation Bound
Return bound × discountFactor^omittedFrom/(1-discountFactor).
- Nash Deviation One Player Slack
Return its product with deviation minus equilibrium payoff, the opposite obedience slack, and profitable only for positive probability and strictly higher deviation payoff.