Description
Return columnPreferred/(columnPreferred+columnOther) for row's first-action probability and rowOther/(rowPreferred+rowOther) for column's.
A two-action game can be represented by a small payoff matrix, but the interpretation depends on which player chooses each axis and whether their interests are opposed or coordinated. Indifference and a pure saddle are different conditions.
Return columnPreferred/(columnPreferred+columnOther) for row's first-action probability and rowOther/(rowPreferred+rowOther) for column's.
When to use this tool
Use Battle Of Sexes Mixed Probability Term when you need a stated two-action payoff identity or classification.
How to use the tool and how it works
- Enter rowPreferred, rowOther, columnPreferred, columnOther. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read rowFirstProbability, columnFirstProbability. Use the output convention below.
Require four positive preferred/other coordination payoffs. Return columnPreferred/(columnPreferred+columnOther) for row's first-action probability and rowOther/(rowPreferred+rowOther) for column's.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| rowPreferred | Row Preferred | Required. Finite number; strictly above 0. |
| rowOther | Row Other | Required. Finite number; strictly above 0. |
| columnPreferred | Column Preferred | Required. Finite number; strictly above 0. |
| columnOther | Column Other | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| rowFirstProbability | Row First Probability | Required. Finite number. |
| columnFirstProbability | Column First Probability | Required. Finite number. |
{
"input": {
"rowPreferred": 2,
"rowOther": 1,
"columnPreferred": 2,
"columnOther": 1
},
"output": {
"rowFirstProbability": 0.6666666666666666,
"columnFirstProbability": 0.3333333333333333
}
}Limitations and assumptions
- The prescribed two-action coordination model assumes zero mismatched payoffs and stated preference ordering. No arbitrary matrix or complete equilibrium set is solved.
- 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
Solve the full game with its intended payoff conventions when equilibrium is the question. Check all best responses and feasibility conditions rather than inferring equilibrium from a single local equality.
References
Similar or alternative tools
- Coordination Game Mixed Equilibrium Payoff Gap
Return B/(A+B), AB/(A+B), and that modeled mixed payoff minus outsidePayoff.
- Mixed Strategy Two Action Indifference
Return (d-b)/(a-b-c+d) as opponentFirstProbability and whether it lies in [0, 1].