I am sorry but that's like the opposite of economic logic. Ceritus paribus, more competition means lower prices.
Regarding the actual topic, I've long maintained that a single payer system in America would be much more expensive than a single payer system in Europe because of different priorities of the American consumers (for instance, old people demographic in America, the pro-life nature where a big part of our insurance expenses goes towards saving premature newborn babies). The only way a single payer in America (or in any country) could be cheaper is by offering a different product to the consumers.