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  • 1Department of Mathematics and Statistics, University of Agriculture, Faisalabad, Pakistan. profarshad@yahoo.com.

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Designing fair blockchain reward mechanisms needs to consider miner behavior. Our simulation framework shows the Adaptive strategy best balances rewards, reducing entropy and improving fairness in decentralized systems.

Keywords:
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Area of Science:

  • Blockchain Technology
  • Computer Science
  • Economics

Background:

  • Designing effective blockchain reward mechanisms is complex.
  • Existing methods often overlook behavioral variability among miners.
  • Fairness and stability are critical for decentralized systems.

Purpose of the Study:

  • To develop and evaluate a simulation framework for blockchain reward mechanisms.
  • To assess reward fairness and stability using entropy as a key metric.
  • To compare the performance of different reward allocation strategies.

Main Methods:

  • A simulation framework was developed to model miner behavior with log-normal execution times and varying task complexity.
  • Three reward strategies were evaluated: a traditional baseline, Mining-X, and Adaptive-X.
  • Reward distributions were analyzed using Kernel Density Estimation (KDE) and Empirical Cumulative Distribution Functions (ECDF).
  • Entropy metrics (Shannon, Rényi, Tsallis, normalized Shannon) were computed on discretized reward distributions.
  • An interactive Shiny application was created for reproducible analysis.

Main Results:

  • The Adaptive-X strategy demonstrated superior performance, yielding the most behavior-sensitive and equitable reward allocations.
  • Adaptive-X achieved the lowest entropy across all four measured metrics compared to the baseline and Mining-X.
  • Relative to the traditional baseline, Adaptive-X significantly reduced entropy, with Shannon entropy decreasing by 41.5% and Normalized Shannon entropy by 35.2%.

Conclusions:

  • The proposed simulation framework provides a robust method for evaluating blockchain reward mechanisms.
  • The Adaptive-X strategy emerges as a highly effective approach for enhancing fairness and stability in decentralized systems.
  • This work offers an evidence-based, deployable solution for optimizing reward allocation in blockchains.