A rare alliance of healthcare rivals -- a giant insurance company, a major hospital chain and a large doctors group -- has managed to reduce healthcare costs through a radical new strategy: working together. The collaboration among Blue Shield of California, Catholic Healthcare West and Hill Physicians Medical Group shaved more than $20 million in costs last year and prevented an insurance rate hike for public sector workers in Northern California. The three partners cite evidence that the quality of care also improved: Hospital stays were shorter, readmissions dropped and doctors and nurses kept closer tabs on patients. Relationships between these kinds of companies are typically adversarial, with doctors and hospitals trying to negotiate higher prices for their services as insurers strive to limit what they pay out. But driven by a mutual interest to cut costs and to be more competitive, the three devised a strategy they believed would deliver medical care more efficiently.