Abstract
The Seat Arrangement Problem is a problem of finding a desirable seat arrangement for given preferences of agents and a seat graph that represents a configuration of seats. In this paper, we consider decision problems of determining if an envy-free arrangement exists and an exchange-stable arrangement exists, when a seat graph is an ℓ × m grid graph. When ℓ=1, the seat graph is a path of length m and both problems have been known to be NP-complete. In this paper, we extend it and show that both problems are NP-complete for any integer ℓ ≥ 2.