生产经济的普遍增长
Universal Growth in Production Economies
摘要：
我们考虑一个扩展经济的冯·诺依曼模型的简单变体，其中多个生产者根据他们的生产函数生产商品。玩家在市场上交易他们的货物，然后在下一轮中使用获得的捆包进行生产。我们研究了一个简单的去中心化动态-被称为比例响应-在这个过程中，参与者根据上一轮投资的有用程度按比例更新他们的出价。我们表明，这种动态导致了经济的长期增长（只要增长是可能的），但也创造了无限的不平等，即非常富有和非常贫穷的球员出现。我们还分析了其他一些现象，如一个球员与其他人的关系如何影响其发展和基尼系数的系统。其中一个关键的技术发现是，参与者以分散的方式学习网络的全局特征（最优循环），同时与其直接邻居进行本地交互。我们通过研究由此产生的动力系统中的体积来获得这一点，并表明每个循环的体积在每一轮中以恒定的因子膨胀或收缩。
英文摘要：
We consider a simple variant of the von Neumann model of an expanding economy, in which multiple producers make goods according to their production function. The players trade their goods at the market and then use the bundles acquired for the production in the next round. We study a simple decentralized dynamic---known as proportional response---in which players update their bids proportionally to how useful the investments were in the past round. We show this dynamic leads to growth of the economy in the long term (whenever growth is possible) but also creates unbounded inequality, i.e. very rich and very poor players emerge. We analyze several other phenomena, such as how the relation of a player with others influences its development and the Gini index of the system. One of the key technical findings is that the players learn a global feature of the network (the optimal cycle) in a decentralized way, while interacting locally with their direct neighbors. We obtain this by studying the volume in the resulting dynamical system and showing that the volume of each cycle expands or contracts by a constant factor in each round.
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