Shapiro-Shapley introduce their 1961 memorandum (published 17 years later as Shapiro-Shapley (1978)) with the remark that \institutions having a large number of competing participants are common in political and economic life, and cite as examples \markets, exchanges, corporations (from the shareholders viewpoint), Presidential nominating conventions and legislatures. They observe, however, that \game theory has not yet been able so far to produce much in the way of fundamental principles of \mass competition that might help to explain how they operate in practice, and that it might be \worth while to spend a little e_ort looking at the behavior of existing n-person solution concepts, as n becomes very large. In this, they echo both von Neumann-Morgenstern (1944) and Kuhn-Tucker (1950), and anticipate Mas-Colell (1998).