 Solution

Include all four positions and a turn marker:The initial marker is $\mathrm{R}$. There are at most $2n^8$ such states before terminal compression. The two robots form one maximizing team in the adversarial search representation. At an R state their actions are joint legal moves, including waiting, with deterministic successor positions and marker M. At an M state the monster outcome is a pair of legal cardinal moves, producing marker R.

Check termination initially and after each simultaneous pair of moves. A state is a failure if $\{p,q\}\cap \{z_1,z_2\}\ne \varnothing$. Otherwise it is a success if $p=q$. Collision takes priority over meeting, so meeting on an occupied room fails. A safe meeting ends immediately, before a further monster response. Room swaps without a shared position at a checked boundary are neither capture nor meeting.

The monsters move randomly, so their nodes are chance nodes, not minimizing decisions. Under independent uniform legal moves, if monster $j$ currently has $d_j$ available destinations, each joint outcome has probability $1/(d_1{d}_2)$. If several commands produce the same state, add their probabilities. This specifies a stochastic game tree, equivalently a Markov decision process for the robot team. Uniform legal moves and independent monsters are explicit boundary/joint-law conventions; uniform attempted directions with blocked moves staying put is another convention, with different boundary transition probabilities but the same search method. For the one-cell grid, a monster with no legal move stays; all four initial positions then coincide and the instance immediately fails.