A time-inconsistent Dynkin game: from intra-personal to inter-personal equilibria

Yu-Jui Huang () and Zhou Zhou ()
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Yu-Jui Huang: University of Colorado
Zhou Zhou: University of Sydney

Finance and Stochastics, 2022, vol. 26, issue 2, No 5, 334 pages

Abstract: Abstract This paper studies a nonzero-sum Dynkin game in discrete time under non-exponential discounting. For both players, there are two intertwined levels of game-theoretic reasoning. 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 theoretical results, we investigate a two-player real options valuation problem where 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.

Keywords: Dynkin games; Time inconsistency; Non-exponential discounting; Intra-personal equilibrium; Inter-personal equilibrium; Alternating fixed-point iterations; 60J20; 91A05; 91A07; 03E75 (search for similar items in EconPapers)
JEL-codes: C73 D91 G31 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00780-021-00468-1

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