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I am only looking for an intuitive answer, so I won't provide any specific equations.

In this model: firm A and firm B compete on prices. Firm A is always better off choosing a smaller price than firm B. So firm A behaves similar to the firms in the standard Bertrand model.

Firm B is different. If firm A chooses a large enough price (say, $p_A > c$ for some boundary $c$), then firm B also starts to behave like firm A and wants to undercut the price of firm A. However, if $p_A < c$, then firm B doesn't care about firm $A$ and simply sets its monopoly price.

In this model, I cannot find a pure-strategy Nash equilibrium, because for any price chosen by the second firm B, firm A will find it optimal to undercut firm B's price. So there is no "unique" best-response by firm A.

Does there intuitively exist some sort of mixed-strategy equilibrium? If so, how might it be characterized? Who will be mixing, and over what range?


marked as duplicate by Herr K., Bayesian, Giskard, BB King, Maarten Punt Apr 11 at 9:39

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    $\begingroup$ It is very difficult, perhaps even impossible to answer this without specific profit functions. $\endgroup$ – Giskard Mar 27 at 4:36

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