부산대학교 도서관

The authors study the Zeckendorf Game (introduced by P. Baird-Smith et al. [Fibonacci Quart. {\bf 57} (2019), no.~5, 1--14; MR4034342]). The game is based on the Zeckendorf decomposition of a natural number $n$ in terms of nonadjacent Fibonacci numbers. Starting with $n$ ones, players take turns combining numbers in one of three ways. A player wins the game when the terms add to $n$ and are the Zeckendorf distribution of $n$. The authors prove that when the number of players is at least three, then none of the players have a winning strategy for $n\geq 5$. They extend this result to multialliance games, where more than two teams play. For instance, they prove that if each team has exactly $k$ consecutive players, then no team has a winning strategy for $n\geq 2k^2+4k$ and $k\geq 2$. There are several other results proved in the paper involving larger alliances.