We study a competition among two contests, where each contest designer aims to attract as much effort as possible. Such a competition exists in reality, e.g., in crowd-sourcing websites. Our results are phrased in terms of the ``relative prize power'' of a contest, which is the ratio of the total prize offered by this contest designer relative to the sum of total prizes of the two contests. When contestants have a quasi-linear utility function that captures both a risk-aversion effect and a cost of effort, we show that a simple contest attracts a total effort which approaches the relative prize power of the contest designer assuming a large number of contestants. This holds regardless of the contest policy of the opponent, hence providing a ``safety level'' which is a robust notion similar in spirit to the max-min solution concept.