Queen reflections: a modification of Wythoff Nim

Wythoff Nim is a classical combinatorial game of queen moves on a chessboard. There are many ways to describe its P-positions (safe positions to move to). One way is to code them by the Fibonacci word 010010100100101.., which is the unique fixed point of the substitution of 0 by 01, and of 1 by 0. The coordinates of the n-th P-position are encoded by the location of the n-th zero and the n-th one in the Fibonacci word. We show that a minor modification of the rules of Wythoff Nim leads to a game with P-positions that are coded by 010010010010100100.. This word can be derived by deleting all 2’s from the Tribonacci word, which is the unique fixed point of the substitution of 0 by 01, of 1 by 02, and of 2 by 0.Applied Probabilit

The structure of trajectories

Electrical Engineering, Mathematics and Computer Scienc

Multiplayer boycotts in convex games

We extend the notion of boycotts between players in cooperative games to boycotts between coalitions. We prove that convex games offer a proper setting for studying these games. Boycotts have a heterogeneous effect. Individual players that are targeted by many-on-one boycotts suffer most, while non-participating players may actually benefit from a boycott.Applied ProbabilityElectrical Engineering, Mathematics and Computer Scienc