The transition to open, distributed Multi-Agent Systems (MAS) promises scalable intelligence but introduces a non-trivial tension: maximizing global efficiency requires cooperative, resource-aware scheduling, yet autonomous agents may be self-interested and cannot be managed by a centralized controller. Prior approaches fall short in two key areas: they typically focus on single-query routing, neglecting long-term resource reuse (e.g., KV-caching) and the complexities of system-level many-to-many matching; furthermore, they rely on generic incentive mechanisms that ignore the distinct characteristics of LLM inference. To bridge this gap, we propose IEMAS (Incentive-Efficiency Mechanism for Multi-Agent Systems), a distributed framework that aligns economic incentives with system performance. IEMAS integrates a probabilistic predictive model to estimate Quality of Service (QoS) under uncertainty, which feeds into a VCG-based bipartite matching mechanism. This design guarantees truthful capability reporting and social optimality while explicitly leveraging KV cache-affinity to minimize computational redundancy. We implement IEMAS on top of vLLM and evaluate it via extensive simulations. Results demonstrate that our incentive-efficiency co-design reducing average service cost by 35% and end-to-end latency by up to 2.9 compared to baselines.