In a two-manufacturer supply chain with discrete price grids and price-sensitive, partly loyal customers, positive-margin Nash equilibria exist and are non-unique, but disappear when the price step is small.
Beckmann’s Bertrand–Edgeworth Duopoly Model: New Pure Strategy Equilibria
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Price equilibria with positive margins in loyal-strategic markets with discrete prices
In a two-manufacturer supply chain with discrete price grids and price-sensitive, partly loyal customers, positive-margin Nash equilibria exist and are non-unique, but disappear when the price step is small.