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On time-inconsistent stopping problems and mixed strategy stopping times |
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| Affiliation: | 1. Department of Mathematics, Wayne State University, Detroit, MI 48202, United States;2. School of Mathematics, Beijing Institute of Technology, Beijing 100081, China;1. Department of Economics, University of Bologna, Strada Maggiore 45, 40125 Bologna, Italy;2. ENCORE, University of Amsterdam, Roeterstraat 11, WB1018 Amsterdam, The Netherlands;3. MEMOTEF, Sapienza University of Rome, Via del Castro Laurenziano 9, 00161 Rome, Italy;1. Department of Virtual Material Design, Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Schloss Birlinghoven, 53754 Sankt Augustin, Germany;2. Institute for Numerical Simulation, Universität Bonn, Wegelerstr. 6, 53115 Bonn, Germany |
| Abstract: | A game-theoretic framework for time-inconsistent stopping problems where the time-inconsistency is due to the consideration of a non-linear function of an expected reward is developed. A class of mixed strategy stopping times that allows the agents in the game to jointly choose the intensity function of a Cox process is introduced and motivated. A subgame perfect Nash equilibrium is defined. The equilibrium is characterized and other necessary and sufficient equilibrium conditions including a smooth fit result are proved. Existence and uniqueness are investigated. A mean–variance and a variance problem are studied. The state process is a general one-dimensional Itô diffusion. |
| Keywords: | Cox process Mean–variance criterion Mixed strategies Optimal stopping Subgame perfect nash equilibrium Time-inconsistency |
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