Duopolies are one of the simplest economic situations where interactions between firms determine market behavior. The standard model of a price-setting duopoly is the Bertrand model, which has the unique solution that both firms set their prices equal to their costs—a paradoxical result where both firms obtain zero profit, which is generally not observed in real market duopolies. Here we propose a new game theory model for a price-setting duopoly, which we show resolves the paradoxical behavior of the Bertrand model and provides a consistent general model for duopolies.

中文翻译：

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伯特兰双头垄断的演化动力学

双头垄断是最简单的经济情况之一，在这种情况下，公司之间的相互作用决定了市场行为。定价双头垄断的标准模型是 Bertrand 模型，它具有独特的解决方案，即两家公司都将价格设定为其成本——这是一个矛盾的结果，即两家公司都获得零利润，这在实际市场双头垄断中通常不会观察到。在这里，我们为定价双头垄断提出了一种新的博弈论模型，该模型解决了 Bertrand 模型的悖论行为，并为双头垄断提供了一致的一般模型。