A Role of Constraint in Self-Organization
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Practical Algorithms for On-line Sampling
DS '98 Proceedings of the First International Conference on Discovery Science
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We consider a natural generalization of the classical ruin problem to more than two parties. Our "ruin" problem, which we will call the (k, I)-game, starts with k players each having I units as its initial capital. At each round of the game, all remaining k′ players pay 1/k′th unit as game fee, play the game, and one of the players wins and receives the combined game fees of 1 unit. A player who cannot pay the next game fee goes bankrupt, and the game terminates when all players but one are bankrupt.We analyze the length of the game, that is, the number of rounds executed until the game terminates, and give upper and lower bounds for the expected game length.