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<p>In this article, we prove that exponential measures are invariant under the replicator dynamics defined on symmetric bilinear games with one-dimensional strategy sets and provide the differential equation that governs the evolution of the rate parameters of these measures. The results are then extended to asymmetric games and those with multi-dimensional strategy sets.</p>

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Invariance of exponential measures under the replicator dynamics on bilinear games

  • 期刊论文

  • 发表日期：

    2026年1月15日

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  • Karl D. Lewis,
  • A. J. Shaiju

摘要

In this article, we prove that exponential measures are invariant under the replicator dynamics defined on symmetric bilinear games with one-dimensional strategy sets and provide the differential equation that governs the evolution of the rate parameters of these measures. The results are then extended to asymmetric games and those with multi-dimensional strategy sets.