Abstract
Alesia is a two-player zero-sum game which is quite similar to the rock-paper-scissors game: the two players simultaneously move and do not know what the opponent plays at a given round. The simultaneity of the moves implies that there is no deterministic good strategy in this game, otherwise one would anticipate the moves of the opponent and easily win the game. We explore how to build a family of one-dimensional stochastic cellular automata to play this game. The rules are built in an iterative way by progressively increasing the complexity of the transitions. We show the possibility to construct a family of rules with interesting results, including a good performance when confronted to the Nash-equilibrium strategy.
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Cook, M., Larsson, U., Neary, T.: A cellular automaton for blocking queen games. Nat. Comput. 16(3), 397–410 (2017)
Fraenkel, A.S.: Two-player games on cellular automata. More Games Chance 42, 279–306 (2002)
Grilo, C., Correia, L.: Effects of asynchronism on evolutionary games. J. Theor. Biol. 269(1), 109–122 (2011). https://doi.org/10.1016/j.jtbi.2010.022
Meyer, C., Ganascia, J.G., Zucker, J.D.: Learning strategies in games by anticipation. In: Proceedings of IJCAI (1), pp. 698–707 (1997)
Perolat, J., Scherrer, B., Piot, B., Pietquin, O.: Approximate dynamic programming for two-player zero-sum Markov games. In: Proceedings of International Conference on Machine Learning 2015, Lille, France, vol. 37, pp. 1321–1329 (2015)
Szabó, G., Fáth, G.: Evolutionary games on graphs. Phys. Rep. 446(4–6), 97–216 (2007). https://doi.org/10.1016/j.physrep.2007.04.004
Acknowledgements
We express our sincere gratitude to Bruno Scherrer for introducing us to the game of Alesia and for providing us with an optimal Nash player program. We thank Irène Marcovici for her valuable comments on the manuscript.
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Fatès, N. (2018). A Pedagogical Example: A Family of Stochastic Cellular Automata that Plays Alesia. In: Mauri, G., El Yacoubi, S., Dennunzio, A., Nishinari, K., Manzoni, L. (eds) Cellular Automata. ACRI 2018. Lecture Notes in Computer Science(), vol 11115. Springer, Cham. https://doi.org/10.1007/978-3-319-99813-8_35
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DOI: https://doi.org/10.1007/978-3-319-99813-8_35
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