Description
Return bound × discountFactor^omittedFrom/(1-discountFactor).
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 bound × discountFactor^omittedFrom/(1-discountFactor).
When to use this tool
Use Repeated Payoff Truncation Bound when you need one transparent payoff or incentive comparison.
How to use the tool and how it works
- Enter discountFactor, maxAbsoluteStagePayoff, omittedFrom. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read absoluteTailBound. Use the output convention below.
Require discountFactor in [0, 1), nonnegative stage-payoff bound and nonnegative integer omittedFrom. Return bound × discountFactor^omittedFrom/(1-discountFactor).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| discountFactor | Discount Factor | Required. Finite number; minimum 0; strictly below 1. |
| maxAbsoluteStagePayoff | Max Absolute Stage Payoff | Required. Finite number; minimum 0. |
| omittedFrom | Zero-based first omitted period; power zero is undiscounted. | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| absoluteTailBound | Absolute Tail Bound | Required. Finite number. |
{
"input": {
"discountFactor": 0.5,
"maxAbsoluteStagePayoff": 10,
"omittedFrom": 3
},
"output": {
"absoluteTailBound": 2.5
}
}Limitations and assumptions
- Period zero is undiscounted. This bounds an infinite discounted tail under the supplied uniform absolute bound, not realized omitted payoffs or equilibrium error generally.
- 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 Game Finite Punishment Payoff Term
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.
- Repeated Game Discount Weight
Return the period weight for a supplied geometric discount convention, including weight one in period zero.