A Generalization of Berry’s Probability Function

Affiliation(s)

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Economics and Social Science Area, Indian Institute of Management Bangalore (IIMB), Bangalore, India.

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Economics and Social Science Area, Indian Institute of Management Bangalore (IIMB), Bangalore, India.

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 Berrylevied by Clark and Riis (1996) in the context of sequential distribution of prizes since prizes by our very hypothesis, are awarded simultaneously.

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 Berrylevied by Clark and Riis (1996) in the context of sequential distribution of prizes since prizes by our very hypothesis, are awarded simultaneously.

KEYWORDS

Probability Function in Multi-Prize Contests; Generalization of Tullock’s Contest Success Function

Probability Function in Multi-Prize Contests; Generalization of Tullock’s Contest Success Function

Cite this paper

A. Palma and S. Munshi, "A Generalization of Berry’s Probability Function,"*Theoretical Economics Letters*, Vol. 3 No. 5, 2013, pp. 12-16. doi: 10.4236/tel.2013.35A2003.

A. Palma and S. Munshi, "A Generalization of Berry’s Probability Function,"

References

[1] S. K. Berry, “Rent-seeking with Multiple Winners,” Public Choice, Vol. 77, No. 2, 1993, pp. 437-443. doi:10.1007/BF01047881

[2] D. J. Clark and C. Riis, “A Multi-Winner Nested Rent-Seeking Contest,” Public Choice, Vol. 87, No. 1-2, 1996, pp. 177-184.doi:10.1007/BF00151735

[3] D. J. Clark and C. Riis, “Influence and the discretionary allocation of several prizes,” European Journal of Political Economy, Vol. 14, No. 4, 1998, pp. 605-625. doi:10.1016/S0176-2680(98)00028-7

[1] S. K. Berry, “Rent-seeking with Multiple Winners,” Public Choice, Vol. 77, No. 2, 1993, pp. 437-443. doi:10.1007/BF01047881

[2] D. J. Clark and C. Riis, “A Multi-Winner Nested Rent-Seeking Contest,” Public Choice, Vol. 87, No. 1-2, 1996, pp. 177-184.doi:10.1007/BF00151735

[3] D. J. Clark and C. Riis, “Influence and the discretionary allocation of several prizes,” European Journal of Political Economy, Vol. 14, No. 4, 1998, pp. 605-625. doi:10.1016/S0176-2680(98)00028-7