A pedagogical example: a family of stochastic cellular automata that plays Alesia
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 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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