We theoretically did that with our University system. We made the top price about £9,000 per year but gave Universities the capacity to charge whatever they pleased. They all rocketed up to the maximum and nobody budged from there - charging lower was seen as a drop off in quality. I fear you'd have to legislate against it and put a market cap on rental prices in a given postcode. People (landlords) are often greedy and try to get the most money they can.