A more interesting (and perhaps more relevant) competition would be a customer acquisition competition.
People think that starting a business looks like this: 1. Come up with an idea 2. Build a product or service 3. Sell the product or service
When, in reality, it often looks like this: 1. See what you can sell (and sell it if you can) 2. Build it
There is certainly a case to be made for business plans in specific instances, such as businesses that require substantial capital, but in most cases, formal business plans are not the best way to invest precious time, and the competitions are poor predictors of future business success.