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  <front xmlns:xlink="http://www.w3.org/1999/xlink">
    <journal-meta>
      <journal-title-group>
        <journal-title>Technoeconomics</journal-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Technoeconomics</trans-title>
        </trans-title-group>
      </journal-title-group>
      <issn pub-type="epub">2949-1290</issn>
    </journal-meta>
    <article-meta xmlns:xlink="http://www.w3.org/1999/xlink">
      <article-id pub-id-type="publisher-id">4</article-id>
      <article-id pub-id-type="doi">10.57809/2026.5.2.17.3</article-id>
      <title-group>
        <article-title>Endogenous Token Supply Stability in Algorithmic Blockchain Protocols</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Эндогенная устойчивость предложения токена в алгоритмических блокчейн-протоколах</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Kislyuk</surname>
            <given-names>Lev</given-names>
          </name>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
      </contrib-group>
      <aff id="aff1">Moscow Financial and Industrial University "Synergy"</aff>
      <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-06-30">
        <day>30</day>
        <month>06</month>
        <year>2026</year>
      </pub-date>
      <volume>5</volume>
      <issue>2</issue>
      <issue-id pub-id-type="publisher-id">17</issue-id>
      <fpage>31</fpage>
      <lpage>46</lpage>
      <self-uri xmlns:xlink="http://www.w3.org/1999/xlink" content-type="pdf" xlink:href="https://technoeconomics.spbstu.ru/userfiles/files/Issues/17/3_kisluk.pdf"/>
      <abstract xml:lang="en">
        <p>Three flows govern token supply in blockchain protocols: issuance, burning, and staking lock-ups. We study this supply adjustment mechanism in isolation from price dynamics, treating market returns and on-chain activity as predetermined observables. This design permits analytical examination of supply-side feedbacks without modeling price endogeneity. A representative staker's utility maximization problem yields an equilibrium staking function with a linearly decreasing dependence on market return. From this microeconomic foundation we derive a first-order ordinary differential equation (ODE) for circulating supply with endogenous feedbacks from all three supply channels.</p>
      </abstract>
      <kwd-group xml:lang="en">
        <kwd>tokenomics</kwd>
        <kwd>blockchain</kwd>
        <kwd>circulating supply</kwd>
        <kwd>staking</kwd>
        <kwd>stability analysis</kwd>
        <kwd>Lyapunov function</kwd>
        <kwd>stochastic differential equation</kwd>
        <kwd>Ethereum</kwd>
        <kwd>EIP-1559</kwd>
        <kwd>algorithmic monetary policy</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <back>
    <ref-list>
      <title>References</title>
      <ref id="ref1">
        <mixed-citation publication-type="journal">Asimakopoulos S., Lorusso M., Ravazzolo F. 2023. A Bayesian DSGE approach to modelling cryptocurrency. Review of Economic Dynamics, 51, pp. 1012–1035. https://doi.org/10.1016/j.red.2023.09.006</mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation publication-type="journal">Briola A., Vidal-Tomás D., Wang Y., Aste T. 2023. Anatomy of a stablecoin's failure: the Terra-Luna case. Finance Research Letters, 51, 103358. https://doi.org/10.1016/j.frl.2022.103358</mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation publication-type="journal">Caginalp C. 2018. A dynamical systems approach to cryptocurrency stability. arXiv:1805.03143[q-fin.MF]. https://doi.org/10.48550/arXiv.1805.03143</mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation publication-type="journal">Chemeris O.S., Kitanin S., Tinyakova V., Pushkin A., Kalyazina S. 2025. Application of blockchain technology in the power sector. In: Chemeris, O.S. (ed.) Innovations in Energy Systems, vol. 1124. Springer, Cham, pp. 315–330. https://doi.org/10.1007/978-3-031-80710-7_24</mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation publication-type="journal">Cong L.W., He Z., Tang K. 2025. The tokenomics of staking. NBER Working Paper 33640. https://doi.org/10.3386/w33640</mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation publication-type="journal">Cong L.W., Li Y., Wang N. 2021. Tokenomics: dynamic adoption and valuation. Review of Financial Studies, 34(3), pp. 1105–1155. https://doi.org/10.1093/rfs/hhaa089</mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation publication-type="journal">Dong H., Weber M., Xiao Y. 2026. Valuation of proof-of-stake and smart contract cryptocurrencies. Finance Research Letters, 100, 110003. https://doi.org/10.1016/j.frl.2026.110003</mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation publication-type="journal">Jermann U., Xiang H. 2025. Tokenomics: optimal monetary and fee policies. Journal of Monetary Economics, 155, 103808. https://doi.org/10.1016/j.jmoneco.2025.103808</mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation publication-type="journal">Katsiampa P. 2017. Volatility estimation for Bitcoin: a comparison of GARCH models. Economics Letters, 158, pp. 3–6. https://doi.org/10.1016/j.econlet.2017.06.023</mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation publication-type="journal">Khasminskii R.Z. 2012. Stochastic Stability of Differential Equations, 2nd edn. Springer, Berlin. https://doi.org/10.1007/978-3-642-23280-0</mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation publication-type="journal">Kochergin D.A. 2021. Central bank digital currencies: world experience. World Economy and International Relations, 65(5), pp. 68–77. https://doi.org/10.20542/0131-2227-2021-65-5-68-77</mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation publication-type="journal">Leonardos S., Monnot B., Reijsbergen D., Skoulakis E., Piliouras, G. 2021. Dynamical analysis of the EIP-1559 Ethereum fee market. In: Proceedings of the 3rd ACM Conference on Advances in Financial Technologies (AFT '21). ACM, New York, pp. 114–126. https://doi.org/10.1145/3479722.3480993</mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation publication-type="journal">Lyons R.K., Viswanath-Natraj G. 2023. What keeps stablecoins stable? Journal of International Money and Finance, 131, 102777. https://doi.org/10.1016/j.jimonfin.2022.102777</mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation publication-type="journal">Oderbolz N., Marosvölgyi B., Hafner M. 2024. Towards an optimal staking design: balancing security, user growth, and token appreciation. arXiv:2405.14617 [econ.GN]. https://doi.org/10.48550/arXiv.2405.14617</mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation publication-type="journal">Phinney Dominguez J.E. 2025. Decay-weighted fair price for Solana blockchain token buyback. Technoeconomics, 4.3(14), pp. 64–77. https://doi.org/10.57809/2025.4.3.14.7</mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation publication-type="journal">Roughgarden T. 2020. Transaction fee mechanism design for the Ethereum blockchain: an economic analysis of EIP-1559. arXiv:2012.00854 [cs.GT]. https://doi.org/10.48550/arXiv.2012.00854</mixed-citation>
      </ref>
      <ref id="ref17">
        <mixed-citation publication-type="journal">Saito K., Iwamura M. 2019. How to make a digital currency on a blockchain stable. Future Generation Computer Systems, 100, pp. 58–69. https://doi.org/10.1016/j.future.2019.05.019</mixed-citation>
      </ref>
      <ref id="ref18">
        <mixed-citation publication-type="journal">Schilling L., Uhlig H. 2019. Some simple Bitcoin economics. Journal of Monetary Economics, 106, pp. 16–26. https://doi.org/10.1016/j.jmoneco.2019.07.002</mixed-citation>
      </ref>
      <ref id="ref19">
        <mixed-citation publication-type="journal">Shin H.S. 2026. Tokenomics and blockchain fragmentation. BIS Working Paper 1335. Available at: https://www.bis.org/publ/work1335.htm (Accessed: 2026/05/01)</mixed-citation>
      </ref>
      <ref id="ref20">
        <mixed-citation publication-type="journal">Silva L., Maciel L. 2025. Cryptocurrency price returns volatility modeling and forecasting with GARCH models. RAUSP Management Journal, 60(1), pp. 225–239. https://doi.org/10.1108/RAUSP-04-2023-0056</mixed-citation>
      </ref>
      <ref id="ref21">
        <mixed-citation publication-type="journal">Sockin M., Xiong W. 2023. A model of cryptocurrencies. Management Science, 69(11), pp. 6684–6707. https://doi.org/10.1287/mnsc.2023.4756</mixed-citation>
      </ref>
      <ref id="ref22">
        <mixed-citation publication-type="journal">Werner S.M., Perez D., Gudgeon L., Klages-Mundt A., Harz D., Knottenbelt W.J. 2022. SoK: decentralized finance (DeFi). In: Proceedings of the 4th ACM Conference on Advances in Financial Technologies (AFT '22). ACM, New York, pp. 30–46. https://doi.org/10.1145/3558535.3559780</mixed-citation>
      </ref>
      <ref id="ref23">
        <mixed-citation publication-type="journal">Zhang Z., Zargham M., Preciado V.M. 2020. On modeling blockchain-enabled economic networks as stochastic dynamical systems. Applied Network Science, 5, 19. https://doi.org/10.1007/s41109-020-0254-9</mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>
