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arXiv · 2101.00343

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

Yu-Jui Huang·Zhou Zhou
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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.

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Yu-Jui Huang, Zhou Zhou. 2021-01-02. A Time-Inconsistent Dynkin Game: from Intra-personal to Inter-personal Equilibria. https://doi.org/10.1007/s00780-021-00468-1

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