Memory and long-range correlations in chess games

In this paper we report the existence of long-range memory in the opening moves of a chronologically ordered set of chess games using an extensive chess database. We used two mapping rules to build discrete time series and analyzed them using two methods for detecting long-range correlations; rescaled range analysis and detrented fluctuation analysis. We found that long-range memory is related to the level of the players. When the database is filtered according to player levels we found differences in the persistence of the different subsets. For high level players, correlations are stronger at long time scales; whereas in intermediate and low level players they reach the maximum value at shorter time scales. This can be interpreted as a signature of the different strategies used by players with different levels of expertise. These results are robust against the assignation rules and the method employed in the analysis of the time series.Comment: 12 pages, 5 figures. Published in Physica

A study of memory effects in a chess database

A series of recent works studying a database of chronologically sorted chess games --containing 1.4 million games played by humans between 1998 and 2007-- have shown that the popularity distribution of chess game-lines follows a Zipf's law, and that time series inferred from the sequences of those game-lines exhibit long-range memory effects. The presence of Zipf's law together with long-range memory effects was observed in several systems, however, the simultaneous emergence of these two phenomena were always studied separately up to now. In this work, by making use of a variant of the Yule-Simon preferential growth model, introduced by Cattuto et al., we provide an explanation for the simultaneous emergence of Zipf's law and long-range correlations memory effects in a chess database. We find that Cattuto's Model (CM) is able to reproduce both, Zipf's law and the long-range correlations, including size-dependent scaling of the Hurst exponent for the corresponding time series. CM allows an explanation for the simultaneous emergence of these two phenomena via a preferential growth dynamics, including a memory kernel, in the popularity distribution of chess game-lines. This mechanism results in an aging process in the chess game-line choice as the database grows. Moreover, we find burstiness in the activity of subsets of the most active players, although the aggregated activity of the pool of players displays inter-event times without burstiness. We show that CM is not able to produce time series with bursty behavior providing evidence that burstiness is not required for the explanation of the long-range correlation effects in the chess database.Comment: 18 pages, 7 figure

Confidence building in emerging stock markets

Investor confidence in reliable property rights and stable, market-oriented policies are a necessary condition for financial integration and the development of emerging stock markets. Announced market-oriented policies may be reversed, however, and are initially not fully credible. We argue that sustained privatization and liberalization programmes represent a major test of political commitment to safer private property rights. We investigate whether successful privatization has a significant effect on emerging stock market development through the resolution of policy risk, i.e. the risk of ex post policy changes with redistributive impact on investment returns. The evidence from our panel study suggests that progress in privatization gradually leads to increased confidence. Moreover, increased confidence has a strong effect on local market development and is a significant determinant of excess returns. We conclude that financial liberalization and the resolution of policy risk resulting from successful privatization has been an important source for the broadening and deepening of emerging stock markets

Innovation and Nested Preferential Growth in Chess Playing Behavior

Complexity develops via the incorporation of innovative properties. Chess is one of the most complex strategy games, where expert contenders exercise decision making by imitating old games or introducing innovations. In this work, we study innovation in chess by analyzing how different move sequences are played at the population level. It is found that the probability of exploring a new or innovative move decreases as a power law with the frequency of the preceding move sequence. Chess players also exploit already known move sequences according to their frequencies, following a preferential growth mechanism. Furthermore, innovation in chess exhibits Heaps' law suggesting similarities with the process of vocabulary growth. We propose a robust generative mechanism based on nested Yule-Simon preferential growth processes that reproduces the empirical observations. These results, supporting the self-similar nature of innovations in chess are important in the context of decision making in a competitive scenario, and extend the scope of relevant findings recently discovered regarding the emergence of Zipf's law in chess.Comment: 8 pages, 4 figures, accepted for publication in Europhysics Letters (EPL

Capital regulation and tail risk

The paper studies risk mitigation associated with capital regulation, in a context when banks may choose tail risk assets. We show that this undermines the traditional result that higher capital reduces excess risk-taking driven by limited liability. When capital raising is costly, poorly capitalized banks may limit risk to avoid breaching the minimal capital ratio. A bank with higher capital has less chance of breaching the ratio, so may actually take more risk. As a result, banks which have access to tail risk projects may take greater risk when highly capitalized. The results are consistent with stylized facts about pre-crisis bank behavior, and suggest implications for the optimal design of capital regulation