Abstract
We study the group Russian roulette problem, also known as the
shooting problem, defined as follows. We have n armed people in a room. At
each chime of a clock, everyone shoots a random other person. The persons shot
fall dead and the survivors shoot again at the next chime. Eventually, either
everyone is dead or there is a single survivor. We prove that the probability p_n
of having no survivors does not converge as n → ∞, and becomes asymptotically
periodic and continuous on the log n scale, with period 1.
shooting problem, defined as follows. We have n armed people in a room. At
each chime of a clock, everyone shoots a random other person. The persons shot
fall dead and the survivors shoot again at the next chime. Eventually, either
everyone is dead or there is a single survivor. We prove that the probability p_n
of having no survivors does not converge as n → ∞, and becomes asymptotically
periodic and continuous on the log n scale, with period 1.
| Original language | English |
|---|---|
| Pages (from-to) | 35-66 |
| Number of pages | 32 |
| Journal | Markov Processes and Related Fields |
| Volume | 23 |
| Issue number | 1 |
| Publication status | Published - 2017 |
Keywords
- group Russian roulette
- shooting problem
- non-convergence
- coupling
- asymptotic periodicity and continuity