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Strategic Optimisation of Rank

Wednesday 5 November 2014
John Howard
4pm - 5pm, 32L.G.20

Abstract

In many competitive situations (including nearly all sports) a player's aim is not simply to maximize his score but to maximize its rank among all scores. Examples include sales contests (where the salesman with highest monthly sales gets a bonus) and patent races (where lowest time is best). We assume a player's score is obtained costlessly, so that his utility is the probability of having the best score. This gives a constant-sum game. All that matters for a player is the distribution of his score, so we assume he chooses from a given convex set of distributions. We prove that such games, called Distribution Ranking Games, under certain assumptions have an equilibrium solution in pure strategies. We characterize their solution for various classes of distributions, such as distributions with given mean or moment, where we extend a result of Bell and Cover. Our model was stimulated by an intriguing game of E. J. Anderson: we modify his game to a setting in which several players go into separate casinos with given starting capital, and the one who stops with the highest amount wins.

This is joint work with Professor Steve Alpern.

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John Howard