Multi-agent LLM systems decompose complex tasks across specialist agents, yet joint prompt optimization remains difficult because agents are coupled through structured information handoffs. We identify interface mismatch as a structural failure mode that existing optimizers cannot diagnose: their scalar attribution signals conflate reasoning quality with format incompatibility, and the inter-agent contract is left entirely implicit. We propose BID-SPO (Bidding-based Shapley Prompt Optimization), which makes the inter-agent contract an explicit optimization variable. Each agent declares an Output Bid and an Input Demand, and a contract-aware cooperative-game characteristic function yields an attribution signal whose Shapley decomposition exposes three interpretable dimensions (global task contribution, downstream interface alignment, and upstream adaptation cost), turning attribution into a targeted diagnosis for prompt repair. A bid-conformance constraint keeps declared contracts feasible with respect to actual agent behavior throughout optimization. Across seven benchmarks and different model configurations, BID-SPO outperforms MASPO and AgentDropout, with accuracy gains of +2.93% under the Qwen3-8B + Gemini-2.5-pro configuration and +4.38% under the DeepSeek-v4 flash / pro configuration. Our findings emphasize that reliable multi-agent LLM optimization requires optimizing inter-agent interfaces as explicit objects, not just improving agents in isolation.