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The Kelly mechanism is a proportional allocation auction widely adopted in decentralized resource allocation systems to share an infinitely divisible resource among competing agents. We analyze the sequential game it induces when agents have \(\alpha \) -fair utilities and behave strategically. Our main result proves that synchronous best-response updates drive bids to the unique Nash equilibrium at a linear rate for \(\alpha \in \{0,1,2\}\) . Extensive simulations reveal that best-response dynamics reach equilibrium significantly faster than previously proposed no-regret learning algorithms.

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Best-Response Learning in Budgeted \(\alpha \) -Fair Kelly Mechanisms

  • 会议论文

  • 发表日期：

    2026年

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  • Cleque Marlain Mboulou-Moutoubi,
  • Younes Ben Mazziane,
  • Francesco De Pellegrini,
  • Eitan Altman

摘要

The Kelly mechanism is a proportional allocation auction widely adopted in decentralized resource allocation systems to share an infinitely divisible resource among competing agents. We analyze the sequential game it induces when agents have \(\alpha \) -fair utilities and behave strategically. Our main result proves that synchronous best-response updates drive bids to the unique Nash equilibrium at a linear rate for \(\alpha \in \{0,1,2\}\) . Extensive simulations reveal that best-response dynamics reach equilibrium significantly faster than previously proposed no-regret learning algorithms.