Parrondo’s effects with aperiodic protocols

ArXiv ID: 2410.02987 “View on arXiv”

Authors: Unknown

Abstract

In this work, we study the effectiveness of employing archetypal aperiodic sequencing – namely Fibonacci, Thue-Morse, and Rudin-Shapiro – on the Parrondian effect. From a capital gain perspective, our results show that these series do yield a Parrondo’s Paradox with the Thue-Morse based strategy outperforming not only the other two aperiodic strategies but benchmark Parrondian games with random and periodical ($AABBAABB\ldots$) switching as well. The least performing of the three aperiodic strategies is the Rudin-Shapiro. To elucidate the underlying causes of these results, we analyze the cross-correlation between the capital generated by the switching protocols and that of the isolated losing games. This analysis reveals that a strong anticorrelation with both isolated games is typically required to achieve a robust manifestation of Parrondo’s effect. We also study the influence of the sequencing on the capital using the lacunarity and persistence measures. In general, we observe that the switching protocols tend to become less performing in terms of the capital as one increases the persistence and thus approaches the features of an isolated losing game. For the (log-)lacunarity, a property related to heterogeneity, we notice that for small persistence (less than 0.5) the performance increases with the lacunarity with a maximum around 0.4. In respect of this, our work shows that the optimization of a switching protocol is strongly dependent on a fine-tuning between persistence and heterogeneity.

Keywords: Parrondo’s Paradox, Aperiodic Sequencing, Capital Gain Analysis, Cross-correlation, Optimization Strategies, Algorithmic Strategy

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced mathematical concepts from stochastic processes, number theory, and nonlinear dynamics, including aperiodic sequences and correlation analysis, but its empirical testing is limited to theoretical simulation without any real financial data, backtesting protocols, or implementation details.

  flowchart TD
    A["Research Goal: Analyze Parrondo's effects<br>with aperiodic protocols<br>(Fibonacci, Thue-Morse, Rudin-Shapiro)"] --> B["Methodology: Capital Gain Analysis"]
    B --> C["Inputs: Aperiodic Sequences & Isolated Losing Games"]
    C --> D["Computational Process: Cross-correlation,<br>Lacunarity, and Persistence Analysis"]
    D --> E{"Key Findings"}
    E --> F["Thue-Morse Outperforms<br>Random & Periodic Switching"]
    E --> G["Rudin-Shapiro is Least Effective"]
    E --> H["Optimization requires balance<br>between Persistence & Heterogeneity"]