Paranoid algorithm

In combinatorial game theory, the paranoid algorithm is a game tree search algorithm designed to analyze multi-player games using a two-player adversarial framework.^[1] The algorithm assumes all opponents form a coalition to minimize the focal player’s payoff, transforming an n-player non-zero-sum game into a zero-sum game between the focal player and the coalition.

The paranoid algorithm significantly improves upon the maxⁿ algorithm by enabling the use of alpha-beta pruning and other minimax-based optimization techniques that are less effective in standard multi-player game analysis.^[2] By treating opponents as a unified adversary whose payoff is the opposite of the focal player’s payoff, the algorithm can apply branch and bound techniques and achieve substantial performance improvements over traditional multi-player algorithms.^[3]

While the paranoid assumption may not accurately reflect the true strategic interactions in all multi-player scenarios—where players typically optimize their own payoffs—the algorithm has proven effective in practice for artificial intelligence applications in board games and other combinatorial multi-player games.^[3] The algorithm is particularly valuable in computer game AI where computational efficiency is crucial and the simplified opponent model provides adequate performance for real-time applications.

References

^ Sturtevant, Nathan; Korf, Richard (30 July 2000). "On Pruning Techniques for Multi-Player Games" (PDF). AAAI-00 Proceedings: 201–207.
^ Sturtevant and Korf, 2000
^ ^a ^b Sturtevant, Nathan (2003). "A Comparison of Algorithms for Multi-player Games". Lecture Notes in Computer Science. Vol. 2883. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 108–122. doi:10.1007/978-3-540-40031-8_8. ISBN 978-3-540-20545-6.

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