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Abstract

This thesis is a collection of studies about ratings and rankings and a study about pricing of cryptocurrencies.

In the first chapter, jointly with Peter Duersch and Jörg Oechssler we develop a universal measure of skill and chance in games. Online and offline gaming has become a multibillion dollar industry, yet, games of chance (in contrast to games of skill) are prohibited or tightly regulated in many jurisdictions. Thus, the question whether a game predominantly depends on skill or chance has important legal and regulatory implications. We suggest a new empirical criterion for distinguishing games of skill from games of chance. All players are ranked according to a “best-fit” Elo algorithm. The wider the distribution of player ratings are in a game, the more important is the role of skill. Most importantly, we provide a new benchmark (“50%-chess”) that allows to decide whether games predominantly depend on chance, as this criterion is often used by courts. We apply the method to large datasets of various games (e.g. chess, poker, backgammon). Our findings indicate that most popular online games, including poker, are below the threshold of 50% skill and thus depend predominantly on chance. In fact, poker contains about as much skill as chess when 75% of the chess results are replaced by a coin flip. The second chapter aims to measure skill and chance in different versions of online poker, using the best-fit Elo algorithm established in the first chapter. While Texas Hold’em arguably is the most popular version being played, the amount of skill involved might differ from other versions like Omaha Hold’em. Many platforms offer faster procedures to play (e.g. ”hyper turbo”), as well as different levels of stakes. Given the richness of online poker data, it is possible to isolate the impact of these variations individually. The heterogeneity of best-fit Elo ratings decreases in quicker competitions or with higher stakes. Meanwhile, Omaha seems to contain more elements of skill than Texas Hold’em, as its analysis shows a wider distribution of skill levels of players. The third chapter motivates the introduction of the notion of Independece of Alternatives (IoA) in the context of ranking models. IoA postulates a property of independence which seems intuitively reasonable but does not exclusively hold in models where Luce’s Choice Axiom applies. Assuming IoA, expected ranks in the ranking of multiple alternatives can be determined from pairwise comparisons. The result can significantly simplify the calculation of expected ranks in practice and potentially facilitate analytic methods that build on more general approaches to model the ranking of multiple alternatives. The fourth chapter describes an experimental study on cryptocurrency markets. Jointly with Andis Sofianos and Yilong Xu we focus on potential effects of mining on pricing. Recent years have seen an emergence of decentralized cryptocurrencies that were initially devised as a payment system, but are increasingly being recognized as investment instruments. The price trajectories of cryptocurrencies have raised questions among economists and policy makers, especially since such markets can have spillover effects on the real economy. We focus on two key properties of cryptocurrencies that may contribute to their pricing. In a controlled lab setting, we test whether pricing is influenced by costly mining, as well as entry barriers to mining technology. Our mining design resembles the proof-of-work algorithm employed by the majority of cryptocurrencies, such as bitcoin. In our second treatment, half of the traders have access to the mining technology, while the other half can only participate in the market. This is designed to resemble the high entry cost to initiate cryptocurrency mining. In the absence of mining, no bubbles or crashes occur. When costly mining is introduced, assets are traded at prices more than 300% higher than fundamental value and the bubble peaks relatively late in the trading periods. When only half of the traders can mine, prices surge much earlier and reach values of more than 400% higher than fundamental value at the peak of the market. Overall, the proof-of-work algorithm seems to fuel overpricing, which in conjunction with entry barriers to mining is intensified.