What studies isolate back-and-forth LLM interaction from one-way sharing and self-refinement [D]

A developer is seeking existing research on whether back-and-forth interaction between two different LLMs improves task success more than one-way sharing or self-refinement, especially under a controlled resource budget. They have designed an experiment involving GPT-4.1 and Claude Sonnet 4.6 across twelve tasks and eight families, with 576 planned pipelines. The developer is trying to avoid a $110 API cost for this personal project if the question is already settled by prior studies.