This paper demonstrates that the Bertrand paradox does not hold if cost functions are strictly convex. Instead, multiple equilibria exist which can be Pareto-ranked. The paper shows that the Pareto-dominant equilibrium may imply profus higher than in Cournot competition or may even sustain perfect cartelization. The potential scope for implicit collusion is discussed for the case that the Pareto-dominant noncooperative equilibrium does not support perfect cartelization. Due to multiple non-cooperative equilibria, the discussion involves finitely repeated Bertrand games as well. The paper discusses several strategies which may support implicit collusion. 1t develops the notion of punishment-proofness, and it demonstrates that strongly renegotiationproof equilibria exist for sujficiently high discount factors. Finally, extensions are discussed which cover Stackeiberg leadership, fixed and sunk costs and endogenous market structures.