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A Time-Inconsistent Dynkin Game: from Intra-personal to Inter-personal Equilibria
Optimization and Control · Submitted 2 Jan 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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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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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This paper studies a nonzero-sum Dynkin game in discrete time under non-exponential discounting. | contribution 0.83 | 0.85 | 0.03 | asserted 0.96 |
| s1 | For both players, there are two levels of game-theoretic reasoning intertwined. | method 0.55 | 0.40 | 0.03 | asserted 1.00 |
| s2 | 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. | method 0.77 | 0.31 | 0.04 | asserted 0.99 |
| s3 | Next, given the other player's chosen stopping policy, each player selects a best response among her intra-personal equilibria. | method 0.86 | 0.31 | 0.04 | asserted 0.95 |
| s4 | 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. | method 0.66 | 0.30 | 0.16 | asserted 0.99 |
| s5 | Under appropriate conditions, we show that an inter-personal equilibrium exists, based on concrete iterative procedures along with Zorn's lemma. | result 0.95 | 0.95 | 0.45 | asserted 1.00 |
| s6 | 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. | contribution 0.54 | 0.89 | 0.03 | asserted 0.93 |
| s7 | By deriving inter-personal equilibria explicitly, we find that coercive power in negotiation depends crucially on the impatience levels of the two firms. | result 0.71 | 0.96 | 0.49 | asserted 1.00 |
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Original 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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This includes the classical framework in discrete time that relies on a straightforward backward sequential optimization detailed in [ref] , as well as the more recent development in continuous time that employs the spike variation technique introduced in Ekeland and Lazrak [ref] .
Being serious about non-commitment: subgame perfect equilibrium in continuous time · Introduction · 0.81
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