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A Time-Inconsistent Dynkin Game: from Intra-personal to Inter-personal Equilibria

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  • Yu-Jui Huang
  • Zhou Zhou

Abstract

This paper studies a nonzero-sum Dynkin game in discrete time under non-exponential discounting. For both players, there are two levels of game-theoretic reasoning intertwined. First, each player looks for an intra-personal equilibrium among her current and future selves, so as to resolve time inconsistency triggered by non-exponential discounting. Next, given the other player's chosen stopping policy, each player selects a best response among her intra-personal equilibria. A resulting inter-personal equilibrium is then a Nash equilibrium between the two players, each of whom employs her best intra-personal equilibrium with respect to the other player's stopping policy. Under appropriate conditions, we show that an inter-personal equilibrium exists, based on concrete iterative procedures along with Zorn's lemma. To illustrate our theoretic results, we investigate a two-player real options valuation problem: two firms negotiate a deal of cooperation to initiate a project jointly. By deriving inter-personal equilibria explicitly, we find that coercive power in negotiation depends crucially on the impatience levels of the two firms.

Suggested Citation

  • Yu-Jui Huang & Zhou Zhou, 2021. "A Time-Inconsistent Dynkin Game: from Intra-personal to Inter-personal Equilibria," Papers 2101.00343, arXiv.org, revised Dec 2021.
    • Handle: RePEc:arx:papers:2101.00343
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    References listed on IDEAS

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    1. Yu‐Jui Huang & Adrien Nguyen‐Huu & Xun Yu Zhou, 2020. "General stopping behaviors of naïve and noncommitted sophisticated agents, with application to probability distortion," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 310-340, January.
    2. Erhan Bayraktar & Song Yao, 2015. "On the Robust Dynkin Game," Papers 1506.09184, arXiv.org, revised Sep 2016.
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    9. Yu-Jui Huang & Zhenhua Wang, 2020. "Optimal Equilibria for Multi-dimensional Time-inconsistent Stopping Problems," Papers 2006.00754, arXiv.org, revised Jan 2021.
    10. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
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