A retrograde approximation algorithm for multi-player can't stop

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. © 2008 Springer-Verlag Berlin Heidelberg.