Description
Evaluate a blocking-pair condition from explicitly supplied matching preferences.
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.
Evaluate a blocking-pair condition from explicitly supplied matching preferences.
When to use this tool
Use Matching Game Blocking Pair Flag when checking the stated local payoff, strategy, matching or repeated-game condition.
How to use the tool and how it works
- Enter alreadyPaired, firstStrictlyPrefers, secondStrictlyPrefers. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read blockingPair. Inspect blockingPair before interpreting the associated values.
Return blockingPair exactly when not alreadyPaired and both supplied strict-preference flags are true.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| alreadyPaired | Already Paired | Required. Boolean. |
| firstStrictlyPrefers | First Strictly Prefers | Required. Boolean. |
| secondStrictlyPrefers | Second Strictly Prefers | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| blockingPair | Blocking Pair | Required. Boolean. |
{
"input": {
"alreadyPaired": false,
"firstStrictlyPrefers": true,
"secondStrictlyPrefers": true
},
"output": {
"blockingPair": true
}
}Limitations and assumptions
- Preferences and current matching are asserted; one pair does not establish overall stability, feasible matching or a real allocation policy.
- 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.
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
- Pure Strategy Best Response Flag
Check whether a chosen action lies within supplied tolerance of the best payoff.
- Transferable Utility Core Coalition Slack
Check one transferable-utility coalition's payoff-allocation inequality.