Abstract
We consider the Chainmail Jousting game by Gygax and Perren (1971), a symmetric game of pure skill for two players. Preliminary analysis produces a payoff matrix with only zero and unit values. We find that this matrix is too large to be solved by existing software tools, such that IEDS of weakly-dominated strategies is needed to find solutions. We then apply the lrs solver by Avis et. al. (2010), and find a trio of critical mixed strategies which form the Nash equilibria for the game, including one composed of a simple coin flip between two of the permitted moves. We further consider ways to distinguish the various Nash equilibria, and also some variants of the game.
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References
Gygax, G., Perren, J.: Chainmail: Rules for Medieval Miniatures. 2nd edn. Guidon Games, Belfast Maine (1972)
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Avis, D., Rosenberg, G., Savani, R., von Stengel, B.: Enumeration of nash equilibria for two-player games. Econ. Theory 42, 9–37 (2010). https://doi.org/10.1007/s00199-009-0449-x
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Acknowledgments
The author wishes to thank Nataniel Greene and Stephen Wendell for encouragement in writing this paper.
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Collins, D.R. (2023). Solving Chainmail Jousting. In: Browne, C., Kishimoto, A., Schaeffer, J. (eds) Computers and Games. CG 2022. Lecture Notes in Computer Science, vol 13865. Springer, Cham. https://doi.org/10.1007/978-3-031-34017-8_4
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DOI: https://doi.org/10.1007/978-3-031-34017-8_4
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