We show that the playing sequence-the order in which players update their actions-is a crucial determinant of whether the best-response dynamic converges to a Nash equilibrium. Specifically, we analyze the probability that the best-response dynamic converges to a pure Nash equilibrium in random n-player m-action games under three distinct playing sequences: clockwork sequences (players take turns according to a fixed cyclic order), random sequences, and simultaneous updating by all players. We analytically characterize the convergence properties of the clockwork sequence best-response dynamic. Our key asymptotic result is that this dynamic almost never converges to a pure Nash equilibrium when n and m are large. By contrast, the random sequence bestresponse dynamic converges almost always to a pure Nash equilibrium when one exists and n and m are large. The clockwork best-response dynamic deserves particular attention: we show through simulation that, compared to random or simultaneous updating, its convergence properties are closest to those exhibited by three popular learning rules that have been calibrated to human game-playing in experiments (reinforcement learning, fictitious play, and replicator dynamics).

We study the correlation structure of firm growth rates. We show that most firms are correlated because of their exposure to a common factor but that firms linked through the supply chain exhibit a stronger correlation on average than firms that are not. Removing this common factor significantly reduces the average correlation between two firms with no relationship in the supply chain while maintaining a significant correlation between two firms that are linked. We then demonstrate how this observation can be used to reconstruct the topology of a supply chain network using Gaussian Markov Models.

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Since the introduction of Bitcoin in 2009, the dramatic and unsteady evolution of the cryptocurrency market has also been driven by large investments by traditional and cryptocurrency-focused hedge funds. Notwithstanding their critical role, our understanding of the relationship between institutional investments and the evolution of the cryptocurrency market has remained limited, also due to the lack of comprehensive data describing investments over time. In this study, we present a quantitative study of cryptocurrency institutional investments based on a dataset collected for 1324 currencies in the period between 2014 and 2022 from Crunchbase, one of the largest platforms gathering business information. We show that the evolution of the cryptocurrency market capitalization is highly correlated with the size of institutional investments, thus confirming their important role. Further, we find that the market is dominated by the presence of a group of prominent investors who tend to specialise by focusing on particular technologies. Finally, studying the co-investment network of currencies that share common investors, we show that assets with shared investors tend to be characterized by similar market behavior. Our work sheds light on the role played by institutional investors and provides a basis for further research on their influence in the cryptocurrency ecosystem.