| Sumario: | I show equilibrium existence for a price‐setting game among multi‐product firms facing a nested logit/CES demand. As opposed to previous research I allow arbitrary firm/nest overlap, making the result relevant for applied work. Additionally, under easy‐to‐verify conditions, I show that there exist extreme equilibria, which are the most and least preferred by consumers, and provide an algorithm to find them. This allows researcher to numerically verify equilibrium uniqueness in applications, that is, if the extreme equilibria are equal to each other. As a by‐product, I show that inverting FOCs correctly identifies the marginal costs that rationalize observed prices.
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