Description
Apply a positive affine transformation to one payoff.
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.
Apply a positive affine transformation to one payoff.
When to use this tool
Use Payoff Affine Transform when checking the stated local payoff, strategy, matching or repeated-game condition.
How to use the tool and how it works
- Enter payoff, positiveScale, offset. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read transformedPayoff. Use the output convention below.
Require positiveScale>0. Return positiveScale*payoff+offset.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| payoff | Payoff | Required. Finite number. |
| positiveScale | Positive Scale | Required. Finite number; strictly above 0. |
| offset | Offset | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| transformedPayoff | Transformed Payoff | Required. Finite number. |
{
"input": {
"payoff": 3,
"positiveScale": 2,
"offset": 5
},
"output": {
"transformedPayoff": 11
}
}Limitations and assumptions
- A positive affine transform preserves a player's payoff ordering under the same expected-utility convention; no whole game or interpersonal payoff comparability is established.
- 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
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