A Retrograde Approximation Algorithm for Multi-player Can't Stop

Authors:
James Glenn;Haw-Ren Fang;Clyde P. Kruskal
Affiliations:
Department of Computer Science, Loyola College in Maryland, USA MD 21210;Department of Computer Science and Engineering, University of Minnesota, Minnesota, USA 55455;Department of Computer Science, University of Maryland, Maryland, USA 20742
Venue:
CG '08 Proceedings of the 6th international conference on Computers and Games
Year:
2008

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Abstract

An n-player, finite, probabilistic game with perfect information can be presented as a 2n-partite graph. For Can't Stop, the graph is cyclic and the challenge is to determine the game-theoretical values of the positions in the cycles. We have presented our success on tackling one-player Can't Stop and two-player Can't Stop. In this article we study the computational solution of multi-player Can't Stop (more than two players), and present a retrograde approximation algorithm to solve it by incorporating the multi-dimensional Newton's method with retrograde analysis. Results of experiments on small versions of three- and four-player Can't Stop are presented.