A Retrograde Approximation Algorithm for Multi-player Can't Stop
نویسندگان
چکیده
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 threeand four-player Can’t Stop are presented.
منابع مشابه
A Retrograde Approximation Algorithm for One-Player Can't Stop
A one-player, finite, probabilistic game with perfect information can be presented as a bipartite graph. For one-player Can’t Stop, the graph is cyclic and the challenge is to determine the game-theoretical values of the positions in the cycles. In this article we prove the existence and uniqueness of the solution to one-player Can’t Stop, and give an efficient approximation algorithm to solve ...
متن کاملA Retrograde Approximation Algorithm for Two-Player Can’t Stop
A two-player, finite, probabilistic game with perfect information can be presented as a four-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. In a previous paper we have presented our success on tackling one-player Can’t Stop. In this paper we prove the existence and uniqueness of the solution to two...
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Can’t Stop is a jeopardy stochastic game played on an octagonal game board with four six-sided dice. Optimal strategies have been computed for some simplified versions of Can’t Stop by employing retrograde analysis and value iteration combined with Newton’s method. These computations result in databases that map game positions to optimal moves. Solving the original game, however, is infeasible ...
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