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2 results

  • WINNER PLAYS COMPETITION MODELS

  • Yang Cao, Sheldon M. Ross
  • Journal:
    Probability in the Engineering and Informational Sciences / Volume 35 / Issue 2 / April 2021
    Published online by Cambridge University Press:
    18 October 2019, pp. 236-241

  • Suppose there are n players in an ongoing competition, with player i having value vi, and suppose that a game between i and j is won by i with probability vi/(vi + vj). Consider the winner plays competition where in each stage two players play a game, and the winner keeps playing in the next game. We consider two models for choosing its opponent, analyze both models as Markov chains, and determine their stationary probabilities as well as other quantities of interest.

  • WINNER PLAYS STRUCTURE IN RANDOM KNOCKOUT TOURNAMENTS

  • Yang Cao, Sheldon M. Ross
  • Journal:
    Probability in the Engineering and Informational Sciences / Volume 33 / Issue 4 / October 2019
    Published online by Cambridge University Press:
    05 December 2018, pp. 500-510

  • Suppose there are n players, with player i having value vi > 0, and suppose that a game between i and j is won by i with probability vi/(vi + vj). In the winner plays random knockout tournament, we suppose that the players are lined up in a random order; the first two play, and in each subsequent game the winner of the last game plays the next in line. Whoever wins the game involving the last player in line, is the tournament winner. We give bounds on players’ tournament win probabilities and make some conjectures. We also discuss how simulation can be efficiently employed to estimate the win probabilities.