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Stochastic revision opportunities in Markov decision problems

Author

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  • Yevgeny Tsodikovich

    (Tel-Aviv University)

  • Ehud Lehrer

    (Tel-Aviv University)

Abstract

We extend Markov Decision Processes to situations where the actions are binding and cannot be changed in every period. Instead, the decision maker can revise her actions at random times. We consider two slightly different models. In the first, the revision opportunity appears at a specific stage at which the decision maker can change her action, but is lost if not used. The action taken then remains constant until the next revision opportunity comes up. In the second model, the revision opportunity remains open and can be used at any time after it appears. Only when the action is changed, it becomes binding again for another random period. We compare between different stochastic revision processes and characterize when one is always preferred to another.

Suggested Citation

  • Yevgeny Tsodikovich & Ehud Lehrer, 2019. "Stochastic revision opportunities in Markov decision problems," Annals of Operations Research, Springer, vol. 279(1), pages 251-270, August.
    • Handle: RePEc:spr:annopr:v:279:y:2019:i:1:d:10.1007_s10479-019-03252-9
    DOI: 10.1007/s10479-019-03252-9
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    References listed on IDEAS

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    1. Ralf Dewenter & Ulrich Heimeshoff & Hendrik Lüth, 2017. "Less Pain at the Pump? The Effects of Regulatory Interventions in Retail Gasoline Markets," Applied Economics Quarterly (formerly: Konjunkturpolitik), Duncker & Humblot GmbH, Berlin, vol. 63(3), pages 259-274.
    2. Vivek F. Farias & Benjamin Van Roy, 2010. "Dynamic Pricing with a Prior on Market Response," Operations Research, INFORMS, vol. 58(1), pages 16-29, February.
    3. Libich, Jan & Stehlík, Petr, 2011. "Endogenous monetary commitment," Economics Letters, Elsevier, vol. 112(1), pages 103-106, July.
    4. Ming Chen & Zhi-Long Chen, 2015. "Recent Developments in Dynamic Pricing Research: Multiple Products, Competition, and Limited Demand Information," Production and Operations Management, Production and Operations Management Society, vol. 24(5), pages 704-731, May.
    5. Lipman, Barton L. & Wang, Ruqu, 2009. "Switching costs in infinitely repeated games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 292-314, May.
    6. Stephen M. Gilbert, 2000. "Coordination of Pricing and Multiple-Period Production Across Multiple Constant Priced Goods," Management Science, INFORMS, vol. 46(12), pages 1602-1616, December.
    7. Ashley, Richard A & Orr, Daniel, 1985. "Further Results on Inventories and Price Stickiness," American Economic Review, American Economic Association, vol. 75(5), pages 964-975, December.
    8. Beggs, Alan W & Klemperer, Paul, 1992. "Multi-period Competition with Switching Costs," Econometrica, Econometric Society, vol. 60(3), pages 651-666, May.
    9. Zhi-Long Chen & Nicholas G. Hall, 2010. "The Coordination of Pricing and Scheduling Decisions," Manufacturing & Service Operations Management, INFORMS, vol. 12(1), pages 77-92, April.
    10. Wedad Elmaghraby & P{i}nar Keskinocak, 2003. "Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions," Management Science, INFORMS, vol. 49(10), pages 1287-1309, October.
    11. Taylor, John B., 1999. "Staggered price and wage setting in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 15, pages 1009-1050, Elsevier.
    12. Yossi Aviv & Amit Pazgal, 2005. "A Partially Observed Markov Decision Process for Dynamic Pricing," Management Science, INFORMS, vol. 51(9), pages 1400-1416, September.
    13. Omar Besbes & Assaf Zeevi, 2009. "Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms," Operations Research, INFORMS, vol. 57(6), pages 1407-1420, December.
    14. Margaret E. Slade, 1992. "Vancouver's Gasoline-Price Wars: An Empirical Exercise in Uncovering Supergame Strategies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(2), pages 257-276.
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    Cited by:

    1. Yevgeny Tsodikovich, 2021. "The worst-case payoff in games with stochastic revision opportunities," Annals of Operations Research, Springer, vol. 300(1), pages 205-224, May.

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    More about this item

    Keywords

    Markov decision process; Stochastic dominance; Commitment; Exogenous timing;
    All these keywords.

    JEL classification:

    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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