A Generalization of Berry’s Probability Function

Abstract

In a multi-prize contest, we consider the space of all outcomes and define a probability on it by hypothesizing the probability of an outcome to depend on resources expended by all the players. In this probability space, we then derive the probability of an individual player winning. It turns out that this probability is a generalized Berry (1993) probability function. Specifically, when 0 weight is attached to the resources spent by the "unsuccessful players" (losers), the probability of winning of an individual player is proposed exactly by Berry (1993). Such a formulation also helps to alleviate charges against the probability function of Berry levied by Clark and Riis (1996) in the context of sequential distribution of prizes since prizes by our very hypothesis, are awarded simultaneously.