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Friendly frogs, stable marriage, and the magic of invariance

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.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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10.4169/amer.math.monthly.124.5.387

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Department:
Oxford, MPLS, Statistics
Role:
Author
Publisher:
Mathematical Association of America Publisher's website
Journal:
American Mathematical Monthly Journal website
Volume:
124
Issue:
5
Pages:
387-402
Publication date:
2017-05-05
Acceptance date:
2016-10-20
DOI:
Pubs id:
pubs:616377
URN:
uri:a53f7432-882f-48b7-87ae-74bacbed16a6
UUID:
uuid:a53f7432-882f-48b7-87ae-74bacbed16a6
Local pid:
pubs:616377
Keywords:

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