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The arrival of the new

机译：新品的到来

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摘要

In this work we present a number of urn models in which, contrary to standard Plya urns, the number of competing alternatives is not given from the outset but may increase with the arrival of innovations. We begin by describing a variant of Plya urns, first introduced by Fred Hoppe, in which balls of previously non-existing colors are added with some (declining) probability. We then propose new variants in which the probability of the arrival of new colors is itself subject to adaptive change depending on the success of past innovations and discuss applications to evolutionary models of technologies and industries. We numerically simulate different specifications of these urns with adaptively changing mutation rate and show that they can account for complex patterns of evolution in which periods of exploration and innovation are followed by periods in which the dynamics of the system is driven by selection among a stable set of alternatives.
机译：在这项工作中，我们提出了许多缸模型，与标准的Plya缸相反，竞争的替代方案从一开始就没有给出，但随着创新的到来可能会增加。我们首先描述一个由Fred Hoppe首次提出的Plya缸的变体，其中以一些（下降）的概率添加了以前不存在的颜色的球。然后，我们提出新的变体，其中取决于过去的创新成功，新颜色到达的可能性本身会进行适应性变化，并讨论在技术和产业进化模型中的应用。我们通过数值模拟这些骨灰盒的不同规格，并自适应地改变突变率，表明它们可以解释复杂的进化模式，其中探索和创新阶段紧随其后，系统动态由稳定集合中的选择驱动替代品。

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