Modifying variability and correlations in winner-take-all contests

We consider contests with a fixed proportion of winners based on relative performance. Special attention is paid to winner-take-all contests, which we define as contests with relatively few winners receiving relatively large awards, but we consider the full range of values of the proportion of winners. If a contestant has the opportunity to modify the distribution of her performance, what strategy is advantageous? When the proportion of winners is less than one-half, a riskier performance distribution is preferred; when this proportion is greater than one-half, it is better to choose a less risky distribution. Using a multinormal model, we consider modifications in the variability of the distribution and in correlations with the performance of other contestants. Increasing variability and decreasing correlations lead to improved chances of winning when the proportion of winners is less than one-half, and the opposite directions should be taken for proportions greater than one-half. Thus, it is better to take chances and to attempt to distance oneself from the other contestants (i.e., to break away from the herd) when there are few winners; a more conservative, herding strategy makes sense when there are many winners. Our analytical and numerical results indicate that the probability of winning can change substantially as variability and/or correlations are modified. Furthermore, in a game-theoretic setting in which all contestants can make modifications, choosing a riskier (less risky) performance distribution when the proportion of winners is low (high) is the dominant best-response strategy. We briefly consider some practical issues related to the recommended strategies and some possible extensions.