Invertibility modulo dead-ending no- $$\mathcal {P}$$ P -universes

Invertibility modulo dead-ending no- $$\mathcal {P}$$ P -universes In combinatorial game theory, under normal play convention, all games are invertible, whereas only the empty game is invertible in misère play. For this reason, several restricted universes of games were studied, in which more games are invertible. Here, we study combinatorial games under misère play, in particular universes where no player would like to pass their turn. In these universes, we prove that having one extra condition makes all games become invertible. We then focus our attention on a specific quotient, called $${\mathcal {Q}_{\mathbb {Z}}}$$ Q Z , and show that all sums of universes whose quotient is $${\mathcal {Q}_{\mathbb {Z}}}$$ Q Z also have $${\mathcal {Q}_{\mathbb {Z}}}$$ Q Z as their quotient. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Game Theory Springer Journals

Invertibility modulo dead-ending no- $$\mathcal {P}$$ P -universes

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Economics; Economic Theory/Quantitative Economics/Mathematical Methods; Game Theory, Economics, Social and Behav. Sciences; Behavioral/Experimental Economics; Operations Research/Decision Theory
ISSN
0020-7276
eISSN
1432-1270
D.O.I.
10.1007/s00182-018-0629-7
Publisher site
See Article on Publisher Site

Abstract

In combinatorial game theory, under normal play convention, all games are invertible, whereas only the empty game is invertible in misère play. For this reason, several restricted universes of games were studied, in which more games are invertible. Here, we study combinatorial games under misère play, in particular universes where no player would like to pass their turn. In these universes, we prove that having one extra condition makes all games become invertible. We then focus our attention on a specific quotient, called $${\mathcal {Q}_{\mathbb {Z}}}$$ Q Z , and show that all sums of universes whose quotient is $${\mathcal {Q}_{\mathbb {Z}}}$$ Q Z also have $${\mathcal {Q}_{\mathbb {Z}}}$$ Q Z as their quotient.

Journal

International Journal of Game TheorySpringer Journals

Published: Jun 5, 2018

References

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