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ryuxik
by ryuxik

gt_mechanism_gale_shapley

Finds a proposer-optimal stable matching using deferred acceptance. Accepts proposers and receivers with preferences and optional capacities, and checks for blocking pairs.

Instructions

Stable matching via deferred acceptance. Proposers/receivers each have {id, preferences} (and optional capacity for receivers). Returns a proposer-optimal stable matching plus a blocking-pair sanity check.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
proposersYes
receiversYes
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the disclosure burden. It explains the algorithm type and return value (proposer-optimal, sanity check). It does not explicitly state side effects (likely none) or authorization needs, but the description is transparent enough for a computation tool.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is two sentences, very concise, and front-loaded with the key algorithm name. Every sentence adds value, with no wasted words.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given no output schema, the description explains the return value. The two parameters are adequately described with required fields, and the scope of the tool is fully captured for an agent to use it correctly.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters5/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 0%, but the description compensates by specifying that proposers and receivers must have 'id' and 'preferences' fields, and receivers optionally a 'capacity' field. This adds critical meaning beyond the generic 'object' schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool performs stable matching via deferred acceptance (Gale-Shapley). It specifies inputs (proposers and receivers with preferences) and output (proposer-optimal matching and blocking-pair check), distinguishing it from sibling auction and negotiation tools.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description implicitly indicates usage for stable matching with proposer-optimal outcome. It does not explicitly exclude alternatives, but the context of sibling tools (auctions, negotiations) makes the domain clear.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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