Abstract
We study a variation of Nim-type subtraction games, called Cumulative Subtraction (CS). Two players alternate in removing pebbles out of a joint pile, and their actions add or remove points to a common score. We prove that the zero-sum outcome in optimal play of a CS with a finite number of possible actions is eventually periodic, with period 2s, where s is the size of the largest available action. This settles a conjecture by Stewart in his Ph.D. thesis (2011). Specifically, we find a quadratic bound, in the size of s, on when the outcome function must have become periodic. In case of exactly two possible actions, we give an explicit description of optimal play.
Original language | English |
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Article number | P4.52 |
Journal | Electronic Journal of Combinatorics |
Volume | 26 |
Issue number | 4 |
DOIs | |
State | Published - 2019 |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics