ABSTRACTThis paper examines two‐dimensional spatial competition, with Bertrand price determination. With a block metric, equilibrium prices are significantly lower when market areas are squares than when they are diamonds (rotated squares) of the same size. If demand density grows, waves of entry occur, and the shapes of market areas change from squares to diamonds and back to squares again. The former change leaves prim unchanged, whereas the latter cuts prices in half. Results are also derived for a Euclidean metric, with square and hexagonal market areas. Optimal waves of entry are examined with the block metric. With either metric, the socially optimal market shape becomes suboptimal if market areas are constrained to be of the zero‐profit s