This paper studies collusive behavior in a repeated oligopoly model with localized competition, also reinterpreted as a model of multimarket operation. Private information about the rivals' past actions naturally arises from these product market structures. The resulting communication problems imply that firms should not adopt strategies with too severe punishments. Infinite grim punishments may be too severe, for large discount factors. The standard stick-and-carrot punishments from the perfect public information model are always too severe, for all discount factors. Modified stick-and-carrot punishments can still be used, though for a smaller range of discount factors than the standard stick-and-carrot punishments