The paper studies the existence of equilibrium in price setting oligopoly. In particular, the question is addressed whether the non-existence of pure strategy equilibria in capacity constrained price games results from an artificial restriction of the strategy space. While in special cases this conjecture is true we find that the non-existence is a fairly general phenomenon for static games. It stems from the inherent conflict between competitors.
Models of dynamic competition give rise for implicit coordination possibilities. Thus, existence of pure strategy equilibria is possible, as we demonstrate at two natural extensions of the static game. However, the conflict of coordination is not fully resolved and a wide multiplicity of equilibria is found
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