A hunger game is a greedy dynamical process associated with a finite Markov chain. Each state 
has a real hunger 
.
At each step, a state of maximum hunger is selected, with ties resolved by a fixed
priority order. Firing state 
subtracts 1 from 
and adds 
to every 
, where 
is the transition matrix. Total
hunger is conserved.
For an irreducible transition matrix 
with rational entries and
stationary distribution 
, let 
be the least positive integer
such that 
has integer coordinates. Huang and Tian (2026) proved
that every periodic orbit has least period 
, with state 
firing exactly 
times. The set of periodic states with total hunger zero
tiles the hyperplane 
by translations of a lattice.
Huang and Tian (2026) credit GPT-5.6 Sol with completing the least-period proof from their proposed return map and report further human-AI collaboration.
