Every few weeks, some big new contest arrives. This month, Overstock.com, the online retailer, announced that it would sponsor a competition paying $1 million to the person or team who comes up with new technology that most improves its product recommendations. And Qualcomm and the X Prize Foundation — a group known for its huge prizes for grand challenges, like private space flight — announced a $10 million competition for a smartphone application that could diagnose health problems as accurately as human physicians could. Last month, the Heritage Provider Network, a medical group in California, supplied details and data for its $3 million prize. It will go to the team with the best algorithm for predicting which patients are most likely to be admitted to hospitals in the next year. Perhaps the most far-reaching effort, however, comes from the federal government. Legislation passed in December, the America Competes Act, gives government agencies far greater freedom to sponsor prize contests with purses of up to $50 million. Last September, even before the legislation, the Obama administration put up a Web site, challenge.gov, listing government challenges, some with prize money and some without, as part of its goal of tapping innovative ideas from citizens. The proliferation of prizes, says Josh Lerner, a professor at the Harvard Business School, is part of the larger trend of opening corporations and government to wider networks of people with fresh ideas by using the Internet. Crowdsourcing and open-source software — computer programs developed and debugged by far-flung groups of contributors — are other examples of the “open innovation” approach, he says.