Description
Calculate a repeated-game discount weight for a zero-based period.
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.
Calculate a repeated-game discount weight for a zero-based period.
When to use this tool
Use Repeated Game Discount Weight when checking the stated local payoff, strategy, matching or repeated-game condition.
How to use the tool and how it works
- Enter discountFactor, zeroBasedPeriod. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read weight. Use the output convention below.
Require discountFactor in [0,1] and whole zeroBasedPeriod>=0. Return factor^period; period zero has weight one, including the implementation's 0^0 convention.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| discountFactor | Discount Factor | Required. Finite number; minimum 0; maximum 1. |
| zeroBasedPeriod | Whole period index starting at zero; factor^0=1 including factor zero. | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| weight | Weight | Required. Finite number. |
{
"input": {
"discountFactor": 0.5,
"zeroBasedPeriod": 3
},
"output": {
"weight": 0.125
}
}Limitations and assumptions
- No normalization by 1-factor or payoff sum is added; one period weight is not a repeated-game equilibrium or chosen patience parameter.
- 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
- Repeated Game Deviation Deterrence Gap
Check a normalized repeated-game deviation inequality under a constant punishment continuation.
- Cashflow Discount Reference Shift
Rebase a discounted cash-flow value using a signed reference-period shift.