Do LLM Agents Negotiate Rationally? A Mechanism-Design Framework for Verifiable Multi-Agent Interaction over A2A/MCP

Modern LLM-agent frameworks increasingly interoperate through standards such as Anthropic's Model Context Protocol (MCP) for agent-to-tool access and Google's Agent2Agent (A2A) protocol for agent delegation and negotiation. However, these protocols specify transport and discovery rather than strategic correctness and do not guarantee efficient, individually rational, or strategy-proof outcomes. We introduce a framework that (i) encodes classical negotiation mechanisms, including alternating-offers bargaining and Vickrey-Clarke-Groves-style auctions, as constraints over A2A message schemas; (ii) provides a lightweight runtime verification and repair layer that checks messages against protocol invariants; and (iii) offers a benchmark of negotiation and allocation tasks with known optimal solutions for measuring deviations from game-theoretic predictions. We evaluate multiple LLM backbones using unstructured dialogue, structured protocols, and structured protocols with verification. Across negotiation trials (N=30 per condition), verification reduces outcome variance, while structured protocols achieve 100 percent success for both models. After correcting parser artifacts, audited unstructured baselines achieve approximately 97 percent and 93.3 percent success. In auction experiments (N=30 per model), both models achieve 100 percent efficient allocation but differ sharply in truthful bidding: one bids its exact valuation in every trial, whereas the other does so in only 3.3 percent of trials. Thus, mechanism-level incentive compatibility does not automatically transfer to LLM-agent behavior. A three-party fair-allocation task produced only 4.2 percent usable outcomes; we report this negative result with a diagnosis. This work bridges classical multi-agent systems theory and modern LLM-agent infrastructure and defines verifiable interaction at the A2A protocol layer.