TY - JOUR TI - Hypergraph NIM DO - https://doi.org/doi:10.7282/t3-95k0-0506 PY - 2019 AB - NIM is a game in which two players take turns removing tokens from piles. There are usually several non overlapping piles each of which can have any amount of tokens in it. In a turn a player selects a nonempty pile and removes any positive number of tokens from it. The player that removed the last token(s) wins the game. This thesis focused on a generalization of the game NIM in which players on their turn instead of selecting a particular pile, they select a subset of piles and then proceed to remove and positive amount of tokens from each pile i.e. at least on token from each pile. Not all subsets of piles can be selected though, the available options are usually given as a hypergraph H. Also if any of the piles are empty then the corresponding moves that include that pile are no longer legal. If not specifically said otherwise we assume the base set of H is V i.e. H ⊆ 2V This generalization we named Hypergraph NIM and it is a very broad generalization as it also includes other NIM generalizations like Moore’s NIM [25]. KW - NIM KW - Operations Research KW - Game theory LA - eng ER -