Three-player nim with podium rule

If a combinatorial game involves more than two players, the problem of coalitions arises. To avoid the problem, Shuo-Yen Robert Li analyzed three-player nim with the podium rule, that is, if a player cannot be last, he should try to be last but one. With that simplification, he proved that a disjunc...

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Bibliographic Details
Published in:International journal of game theory 2021-09, Vol.50 (3), p.623-633
Main Authors: Nowakowski, Richard J., Santos, Carlos P., Silva, Alexandre M.
Format: Article
Language:English
Subjects:
Behavioral/Experimental Economics
Canonical forms
Combinatorial analysis
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Equality
Equivalence classes
Game Theory
Games
Operations Research/Decision Theory
Original Paper
Simplification
Social and Behav. Sciences
Citations: Items that this one cites
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Summary:If a combinatorial game involves more than two players, the problem of coalitions arises. To avoid the problem, Shuo-Yen Robert Li analyzed three-player nim with the podium rule, that is, if a player cannot be last, he should try to be last but one. With that simplification, he proved that a disjunctive sum of nim piles is a P -position if and only if the sum modulo 3 of the binary representations of the piles is equal to zero. In this paper, we extend the result in order to understand the complete characterization of the outcome classes, the possible reductions of the game forms, the equivalence classes under the equality of games and related canonical forms.
ISSN:0020-7276
1432-1270
DOI:10.1007/s00182-019-00702-3