T. M. A. Fink et al 2008 EPL 83 60010 doi:10.1209/0295-5075/83/60010
T. M. A. Fink1,2,3,5, J. B. Coe1,3,5 and S. E. Ahnert4
Show affiliationsWe study a simple model of competition in which each player has a fixed strength: randomly selected pairs of players compete, the stronger one wins and the loser is eliminated. We show that the best indicator of future success is not the number of wins but a player's wealth: the accumulated wealth of all defeated players. We calculate the distributions of strength and wealth for two versions of the problem: in the first, the loser is replaced; in the second, the loser is not. The probability of attaining a given wealth is shown to be path-independent. We illustrate our model with the popular game of conkers and discuss an extension to round-robin sports competition.
01.50.Rt Physics tournaments and contests
02.50.-r Probability theory, stochastic processes, and statistics
Issue 6 (September 2008)
Received 12 January 2008, accepted for publication 1 August 2008
Published 15 September 2008
T. M. A. Fink et al 2008 EPL 83 60010
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