Description
Return B/(A+B), AB/(A+B), and that modeled mixed payoff minus outsidePayoff.
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 B/(A+B), AB/(A+B), and that modeled mixed payoff minus outsidePayoff.
When to use this tool
Use Coordination Game Mixed Equilibrium Payoff Gap when you need a stated two-action payoff identity or classification.
How to use the tool and how it works
- Enter coordinationA, coordinationB, outsidePayoff. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read mixProbability, mixedPayoff, outsideGap. Use the output convention below.
Require positive coordinationA and coordinationB. Return B/(A+B), AB/(A+B), and that modeled mixed payoff minus outsidePayoff.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coordinationA | Coordination A | Required. Finite number; strictly above 0. |
| coordinationB | Coordination B | Required. Finite number; strictly above 0. |
| outsidePayoff | Outside Payoff | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| mixProbability | Mix Probability | Required. Finite number. |
| mixedPayoff | Mixed Payoff | Required. Finite number. |
| outsideGap | Outside Gap | Required. Finite number. |
{
"input": {
"coordinationA": 4,
"coordinationB": 2,
"outsidePayoff": 1
},
"output": {
"mixProbability": 0.3333333333333333,
"mixedPayoff": 1.3333333333333333,
"outsideGap": 0.33333333333333326
}
}Limitations and assumptions
- The formulas assume the supplied diagonal coordination-payoff model with zero off-diagonal payoffs. They do not solve an arbitrary payoff matrix or select an outside action.
- 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
- Mixed Strategy Two Action Indifference
Return (d-b)/(a-b-c+d) as opponentFirstProbability and whether it lies in [0, 1].
- Battle Of Sexes Mixed Probability Term
Return columnPreferred/(columnPreferred+columnOther) for row's first-action probability and rowOther/(rowPreferred+rowOther) for column's.