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Martingale theory for Dynkin games with asymmetric information

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  • Tiziano De Angelis
  • Jan Palczewski
  • Jacob Smith

Abstract

This paper provides necessary and sufficient conditions for a pair of randomised stopping times to form a saddle point of a zero-sum Dynkin game with partial and/or asymmetric information across players. The framework is non-Markovian and covers essentially any information structure. Our methodology relies on the identification of suitable super and submartingales involving players' equilibrium payoffs. Saddle point strategies are characterised in terms of the dynamics of those equilibrium payoffs and are related to their Doob-Meyer decompositions.

Suggested Citation

  • Tiziano De Angelis & Jan Palczewski & Jacob Smith, 2025. "Martingale theory for Dynkin games with asymmetric information," Papers 2510.15616, arXiv.org.
    • Handle: RePEc:arx:papers:2510.15616
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    References listed on IDEAS

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    1. Tiziano De Angelis & Erik Ekström & Kristoffer Glover, 2022. "Dynkin Games with Incomplete and Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 560-586, February.
    2. Touzi, N. & Vieille, N., 1999. "Continuous-Time Dynkin Games with Mixed Strategies," Papiers d'Economie Mathématique et Applications 1999.112, Université Panthéon-Sorbonne (Paris 1).
    3. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 1999. "Stopping Games with Randomized Strategies," Discussion Papers 1258, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
    5. Erik Ekstrom & Stephane Villeneuve, 2006. "On the value of optimal stopping games," Papers math/0610324, arXiv.org.
    6. Stéphane Villeneuve & Erik Ekstrom, 2006. "On the Value of Optimal Stopping Games," Post-Print hal-00173182, HAL.
    7. repec:dau:papers:123456789/6927 is not listed on IDEAS
    8. Tiziano De Angelis & Fabien Gensbittel & Stephane Villeneuve, 2021. "A Dynkin Game on Assets with Incomplete Information on the Return," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 28-60, February.
    9. Banas, Lubomir & Ferrari, Giorgio & Randrianasolo, Tsiry Avisoa, 2025. "Numerical approximation of Dynkin games with asymmetric information," Center for Mathematical Economics Working Papers 733, Center for Mathematical Economics, Bielefeld University.
    Full references (including those not matched with items on IDEAS)

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