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Equilibrium pricing of securities in the co-presence of cooperative and non-cooperative populations

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  • Masaaki Fujii

Abstract

In this work, we develop an equilibrium model for price formation of securities in a market composed of two populations of different types: the first one consists of cooperative agents, while the other one consists of non-cooperative agents. The trading of every cooperative member is assumed to be coordinated by a central planner. In the large population limit, the problem for the central planner is shown to be a conditional extended mean-field control. In addition to the convexity assumptions, if the relative size of the cooperative population is small enough, then we are able to show the existence of a unique equilibrium for both the finite-agent and the mean-field models. The strong convergence to the mean-field model is also proved under the same conditions.

Suggested Citation

  • Masaaki Fujii, 2022. "Equilibrium pricing of securities in the co-presence of cooperative and non-cooperative populations," Papers 2209.12639, arXiv.org, revised Jun 2023.
    • Handle: RePEc:arx:papers:2209.12639
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    References listed on IDEAS

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    1. Olivier Féron & Peter Tankov & Laura Tinsi, 2020. "Price Formation and Optimal Trading in Intraday Electricity Markets with a Major Player," Risks, MDPI, vol. 8(4), pages 1-21, December.
    2. David Evangelista & Yuri Saporito & Yuri Thamsten, 2022. "Price formation in financial markets: a game-theoretic perspective," Papers 2202.11416, arXiv.org.
    3. Olivier F'eron & Peter Tankov & Laura Tinsi, 2020. "Price formation and optimal trading in intraday electricity markets with a major player," Papers 2011.07655, arXiv.org.
    4. Boualem Djehiche & Julian Barreiro-Gomez & Hamidou Tembine, 2020. "Price Dynamics for Electricity in Smart Grid Via Mean-Field-Type Games," Dynamic Games and Applications, Springer, vol. 10(4), pages 798-818, December.
    5. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    6. Philippe Casgrain & Sebastian Jaimungal, 2020. "Mean‐field games with differing beliefs for algorithmic trading," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 995-1034, July.
    7. René Aïd & Roxana Dumitrescu & Peter Tankov, 2021. "The entry and exit game in the electricity markets: A mean-field game approach," Post-Print hal-03215763, HAL.
    8. Alexander Schied & Tao Zhang, 2013. "A market impact game under transient price impact," Papers 1305.4013, arXiv.org, revised May 2017.
    9. Guanxing Fu & Ulrich Horst, 2018. "Mean-Field Leader-Follower Games with Terminal State Constraint," Papers 1809.04401, arXiv.org.
    10. Fu, Guanxing & Horst, Ulrich, 2018. "Mean-Field Leader-Follower Games with Terminal State Constraint," Rationality and Competition Discussion Paper Series 129, CRC TRR 190 Rationality and Competition.
    11. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," Papers 2102.10756, arXiv.org, revised Feb 2022.
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    Cited by:

    1. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field Equilibrium Price Formation with Exponential Utility," CIRJE F-Series CIRJE-F-1210, CIRJE, Faculty of Economics, University of Tokyo.
    2. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field equilibrium price formation with exponential utility," CARF F-Series CARF-F-559, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Gianmarco Del Sarto & Marta Leocata & Giulia Livieri, 2024. "A Mean Field Game approach for pollution regulation of competitive firms," Papers 2407.12754, arXiv.org.
    4. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field equilibrium price formation with exponential utility," Papers 2304.07108, arXiv.org, revised Oct 2023.

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