The current peer review system suffers from two key problems: promotion of an in-crowd whose methods, opinions and innovations it protects; and failure to represent the opinions and interests of non-peer clients. As a result, whole disciplines orient themselves toward navel-gazing research questions of little import to society or even science as a whole, and new methods and concepts must be unusually persuasive to break through. We thus suggest a more efficient and integrity-preserving system based on an open two-sided market in which buyers and sellers of peer review services would both be subject to a set of recursive quality indicators. We lay out key features we think would be important to reduce the opportunities for gaming and that improve the signals about the societal value of a contribution. Our suggestions include a level of reward offered by the author of a paper to get refereed and a level of desired quality of the referee. They include randomly selecting from a group of referees that express a willingness to accept the offered contract. They include the possibility that papers are put up by non-authors for peer-review for assessment on different criteria, such as societal relevance. And they finally include the possibility that referee reports themselves become refereed by other referees. What we envisage is that such an open market in which all elements are subject to peer review will over time lead to specialized reviewers in different criteria, and more useful signals about the nature and quality of any individual piece of work. Our incentivized market set-up would both professionalize the peer review process and make it completely transparent, an innovation long overdue.