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Time Inconsistency and Self-Control Optimization Problems: Progress and Challenges

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Optimization and Control for Systems in the Big-Data Era

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 252))

Abstract

Time inconsistency has been an important issue in many stochastic decision problems arisen in real life and financial decision making, especially in the dynamic investment area. When a stochastic decision problem is time inconsistent, the decision maker would be puzzled by his/her conflicting decisions “optimally” derived from his/her time-varying preferences at different time instants. In the literature, the time inconsistent problem is also called the self-control problem, as the decision maker needs to exert proper self-control to resist present temptation and then achieve a better long-term performance. Different approaches dealing with time inconsistency in the literature are reviewed in this paper. After that, the open questions and challenges are also discussed.

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Notes

  1. 1.

    More time inconsistency examples can be found in Gul and Pesendorfer (2001), Grenadier and Wang (2007), Björk and Murgoci (2010), Basak and Chabakauri (2010) and Cui et al. (2012).

  2. 2.

    This policy is also termed “strategy of pre commitment” in Strotz (1956).

  3. 3.

    In the United States, a 401(k) plan is the tax-qualified, defined-contribution pension account defined in section 401(k) of the Internal Revenue Code. The Internal Revenue Code imposes severe restrictions on withdrawals of pre-tax or Roth contributions while a person remains in service with the company and is under the age of 59.5. Any withdrawal that is permitted before the age of 59.5 is subject to an excise tax equal to ten percent of the amount distributed (on top of the ordinary income tax that has to be paid).

  4. 4.

    This policy is also termed the “strategy of consistent planning” in Strotz (1956), and the decision maker who adopts this policy is called the sophisticated decision maker in O’Donoghue and Rabin (1999, 2001) and Grenadier and Wang (2007).

  5. 5.

    In Gul and Pesendorfer (2001, 2004), the preference of such a type of decision maker is called “preference with self-control”. In O’Donoghue and Rabin (1999, 2001) and DellaVigna and Malmendier (2004, 2006), the decision maker who takes this type of policy is classified as partially naive. In Fudenberg and Levine (2006, 2012), this policy is termed “SR-Perfect equilibrium strategy”.

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Acknowledgements

This work is dedicated to the 65th birthday of the authors’ supervisor, Professor Duan Li. Both the authors are in debt to Professor Duan Li for his invaluable guidances and advices during the authors’ studies, career developments and lives. This work was partially supported by National Natural Science Foundation of China under Grants 71601107, 71671106, 71201094, by the State Key Program in the Major Research Plan of National Natural Science Foundation of China under Grant 91546202, by Shanghai Pujiang Program under Grant 15PJC051, by Program for Innovative Research Team of Shanghai University of Finance and Economics.

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Authors and Affiliations

  1. School of Management, Shanghai University, Shanghai, People’s Republic of China

    Yun Shi

  2. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, People’s Republic of China

    Xiangyu Cui

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  1. Yun Shi
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  2. Xiangyu Cui
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Correspondence to Xiangyu Cui .

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Editors and Affiliations

  1. Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Tsan-Ming Choi

  2. School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai, China

    Jianjun Gao

  3. Department of Systems and Information Engineering, University of Virginia, Charlottesville, Virginia, USA

    James H. Lambert

  4. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    Chi-Kong Ng

  5. Department of Management Science and Engineering, Business School, Qingdao University, Shandong, China

    Jun Wang

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Shi, Y., Cui, X. (2017). Time Inconsistency and Self-Control Optimization Problems: Progress and Challenges. In: Choi, TM., Gao, J., Lambert, J., Ng, CK., Wang, J. (eds) Optimization and Control for Systems in the Big-Data Era. International Series in Operations Research & Management Science, vol 252. Springer, Cham. https://doi.org/10.1007/978-3-319-53518-0_3

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