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New Keynesian models of price setting under monopolistic competition involve two kinds of inefficiency: the price level is too high because firms ignore an aggregate demand externality, and when there are costs of changing prices, price stickiness may be an equilibrium response to changes in nominal money even when all agents would be better off if all adjusted prices. This paper models the consequences of allowing firms to coordinate, enforcing the coordination by punishing deviators; this is equivalent to modeling firms as an implicit cartel playing a punishment game. We show that coordination can partially or fully eliminate the first kind of inefficiency, depending on the magnitude of the punishment, but cannot always remove the second. The response of prices to a monetary shock will depend on the magnitude of the punishment, and may be asymmetric. Implications for the welfare cost of fluctuations also differ from the standard monopolistic competition case.