Description
Use ownEffort^exponent divided by the sum of powered efforts as win probability; multiply by prize and subtract cost.
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.
Use ownEffort^exponent divided by the sum of powered efforts as win probability; multiply by prize and subtract cost.
When to use this tool
Use Contest Success Two Effort Share when you need one transparent payoff or incentive comparison.
How to use the tool and how it works
- Enter ownEffort, rivalEffort, exponent, prize, cost. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read winProbability, expectedPayoff. Use the output convention below.
Require nonnegative efforts with positive total, positive exponent, and nonnegative cost. Use ownEffort^exponent divided by the sum of powered efforts as win probability; multiply by prize and subtract cost.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| ownEffort | Own Effort | Required. Finite number; minimum 0. |
| rivalEffort | Rival Effort | Required. Finite number; minimum 0. |
| exponent | Exponent | Required. Finite number; strictly above 0. |
| prize | Prize | Required. Finite number. |
| cost | Cost | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| winProbability | Win Probability | Required. Finite number. |
| expectedPayoff | Expected Payoff | Required. Finite number. |
{
"input": {
"ownEffort": 2,
"rivalEffort": 2,
"exponent": 1,
"prize": 100,
"cost": 20
},
"output": {
"winProbability": 0.5,
"expectedPayoff": 30
}
}Limitations and assumptions
- This is the supplied two-player contest-success model, not an equilibrium effort solution or a prediction of real contest outcomes. Extreme powers can leave the finite-output domain.
- 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
- Public Good Voluntary Contribution Payoff Term
Return total contributions, retained private endowment, and private remainder plus coefficient times total.
- Mixed Strategy Two Action Indifference Tool
Solve q*a+(1-q)*b=q*c+(1-q)*d; a degenerate indifference equation is rejected.