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arXiv · 1604.03161

Friendly frogs, stable marriage, and the magic of invariance

Maria Deijfen·Alexander E. Holroyd·James B. Martin
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Abstract

We introduce a two-player game involving two tokens located at points of a fixed set. The players take turns to move a token to an unoccupied point in such a way that the distance between the two tokens is decreased. Optimal strategies for this game and its variants are intimately tied to Gale-Shapley stable marriage. We focus particularly on the case of random infinite sets, where we use invariance, ergodicity, mass transport, and deletion-tolerance to determine game outcomes.

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Maria Deijfen, Alexander E. Holroyd, James B. Martin. 2016-04-11. Friendly frogs, stable marriage, and the magic of invariance. https://arxiv.org/abs/1604.03161

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