IDEAS home Printed from https://ideas.repec.org/p/ter/wpaper/00160.html
   My bibliography  Save this paper

A Nash equilibrium for differential games with moving-horizon strategies

Author

Listed:
  • Di Bartolomeo Giovanni
  • Semmler Willi
  • Saltari Entrico

Abstract

Our paper aims to introduce a moving-horizon interaction in a strategic context. We assume that, in each instant, players can predict the effects of their actions and those of their opponents on a finite moving horizon. We define an equilibrium concept consistent in this setting and develop an appropriate algorithm to compute it using nonlinear model predictive control techniques. Focusing on the length of the forecasting horizon, we propose two economic interpretations for our equilibrium based on the limited rationality and political economy literature. Finally, we consider a debt stabilization game in a monetary union to provide some practical insights into our approach.

Suggested Citation

  • Di Bartolomeo Giovanni & Semmler Willi & Saltari Entrico, 2022. "A Nash equilibrium for differential games with moving-horizon strategies," wp.comunite 00160, Department of Communication, University of Teramo.
    • Handle: RePEc:ter:wpaper:00160
    as

    Download full text from publisher

    File URL: https://www.dipecodir.it/wpcom/data/wp_no_160_2022.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. Engwerda, Jacob & van Aarle, Bas & Plasmans, Joseph & Weeren, Arie, 2013. "Debt stabilization games in the presence of risk premia," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2525-2546.
    3. Adam, Klaus, 2011. "Government debt and optimal monetary and fiscal policy," European Economic Review, Elsevier, vol. 55(1), pages 57-74, January.
    4. Smart, Michael & Sturm, Daniel M., 2013. "Term limits and electoral accountability," Journal of Public Economics, Elsevier, vol. 107(C), pages 93-102.
    5. Hughes Hallett, A J, 1984. "Non-cooperative Strategies for Dynamic Policy Games and the Problem of Time Inconsistency," Oxford Economic Papers, Oxford University Press, vol. 36(3), pages 381-399, November.
    6. Reis, Ricardo, 2006. "Inattentive consumers," Journal of Monetary Economics, Elsevier, vol. 53(8), pages 1761-1800, November.
    7. Giovanni Di Bartolomeo & Debora Di Gioacchino, 2008. "Fiscal-monetary policy coordination and debt management: a two-stage analysis," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 35(4), pages 433-448, September.
    8. Stefan Niemann & Paul Pichler & Gerhard Sorger, 2013. "Central Bank Independence And The Monetary Instrument Problem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54, pages 1031-1055, August.
    9. Tabellini, Guido, 1986. "Money, debt and deficits in a dynamic game," Journal of Economic Dynamics and Control, Elsevier, vol. 10(4), pages 427-442, December.
    10. Engwerda, Jacob C. & van Aarle, Bas & Plasmans, Joseph E. J., 2002. "Cooperative and non-cooperative fiscal stabilization policies in the EMU," Journal of Economic Dynamics and Control, Elsevier, vol. 26(3), pages 451-481, March.
    11. Gennaioli, Nicola & Shleifer, Andrei & Vishny, Robert, 2012. "Neglected risks, financial innovation, and financial fragility," Journal of Financial Economics, Elsevier, vol. 104(3), pages 452-468.
    12. van Aarle, B. & Bovenberg, A.L. & Raith, M., 1995. "Monetary and fiscal policy interaction and government debt stabilization," Discussion Paper 1995-1, Tilburg University, Center for Economic Research.
    13. Michael Woodford, 2019. "Monetary Policy Analysis When Planning Horizons Are Finite," NBER Macroeconomics Annual, University of Chicago Press, vol. 33(1), pages 1-50.
    14. Grüne, Lars & Semmler, Willi & Stieler, Marleen, 2015. "Using nonlinear model predictive control for dynamic decision problems in economics," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 112-133.
    15. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    16. Niemann, Stefan, 2011. "Dynamic monetary–fiscal interactions and the role of monetary conservatism," Journal of Monetary Economics, Elsevier, vol. 58(3), pages 234-247.
    17. Ricardo Reis, 2006. "Inattentive Producers," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(3), pages 793-821.
    18. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    19. Alberto Alesina & Guido Tabellini, 1990. "A Positive Theory of Fiscal Deficits and Government Debt," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(3), pages 403-414.
    20. van Aarle, Bas & Lans Bovenberg, A. & Raith, Matthias G., 1997. "Is there a tragedy of a common central bank? A dynamic analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 417-447.
    21. Grune, Lars & Semmler, Willi, 2004. "Using dynamic programming with adaptive grid scheme for optimal control problems in economics," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2427-2456, December.
    22. Tabellini, Guido & La Via, Vincenzo, 1989. "Money, Deficit and Public Debt in the United States," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 15-25, February.
    23. Reinhard Neck & Dmitri Blueschke, 2014. "“Haircuts” for the EMU periphery: virtue or vice?," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 41(2), pages 153-175, May.
    24. Stefan Niemann & Paul Pichler & Gerhard Sorger, 2013. "Central Bank Independence And The Monetary Instrument Problem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(3), pages 1031-1055, August.
    25. Benjamin Hébert & Michael Woodford, 2017. "Rational Inattention and Sequential Information Sampling," NBER Working Papers 23787, National Bureau of Economic Research, Inc.
    26. Hebert, Benjamin & Woodford, Michael, 2017. "Rational Inattention with Sequential Information Sampling," Research Papers repec:ecl:stabus:3457, Stanford University, Graduate School of Business.
    27. Rieth, Malte, 2014. "Myopic governments and welfare-enhancing debt limits," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 250-265.
    28. van den Broek, W. A., 2002. "Moving horizon control in dynamic games," Journal of Economic Dynamics and Control, Elsevier, vol. 26(6), pages 937-961, June.
    29. Ghadimi, Noradin & Akbarimajd, Adel & Shayeghi, Hossein & Abedinia, Oveis, 2018. "Two stage forecast engine with feature selection technique and improved meta-heuristic algorithm for electricity load forecasting," Energy, Elsevier, vol. 161(C), pages 130-142.
    30. van Aarle, Bas & Engwerda, Jacob & Weeren, Arie, 2018. "Effects of debt mutualization in a monetary union with endogenous risk premia: Can Eurobonds contribute to debt stabilization?," Structural Change and Economic Dynamics, Elsevier, vol. 44(C), pages 100-114.
    31. Buchanan, James M, 1976. "Barro on the Ricardian Equivalence Theorem," Journal of Political Economy, University of Chicago Press, vol. 84(2), pages 337-342, April.
    32. Bas Aarle & Lans Bovenberg & Matthias Raith, 1995. "Monetary and fiscal policy interaction and government debt stabilization," Journal of Economics, Springer, vol. 62(2), pages 111-140, June.
    33. Jacob Engwerda & Bas van Aarle & Arie Weeren & Bas Van Aarle, 2015. "Debt Stabilization and Debt Mutualization in a Monetary Union with Endogenous Risk Premia," CESifo Working Paper Series 5564, CESifo.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Semmler, Willi & Di Bartolomeo, Giovanni & Minooei Fard, Behnaz & Braga, Joao Paulo, 2022. "Limit pricing and entry game of renewable energy firms into the energy sector," Structural Change and Economic Dynamics, Elsevier, vol. 61(C), pages 179-190.
    2. De Grauwe, Paul & Foresti, Pasquale, 2023. "Interactions of fiscal and monetary policies under waves of optimism and pessimism," Journal of Economic Behavior & Organization, Elsevier, vol. 212(C), pages 466-481.
    3. Behnaz Minooei Fard & Willi Semmler & Giovanni Di Bartolomeo, 2023. "Rare Earth Elements: A game between China and the rest of the world," Working Papers in Public Economics 235, University of Rome La Sapienza, Department of Economics and Law.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Giovanni Di Bartolomeo & Marco Di Pietro & Enrico Saltari & Willi Semmler, 2018. "Public debt stabilization: the relevance of policymakers’ time horizons," Public Choice, Springer, vol. 177(3), pages 287-299, December.
    2. Di Bartolomeo, Giovanni & Saltari, Enrico & Semmler, Willi, 2019. "The effects of political short-termism on transitions induced by pollution regulations," EconStor Preprints 200143, ZBW - Leibniz Information Centre for Economics.
    3. Jacob Engwerda & Davoud Mahmoudinia & Rahim Dalali Isfahani, 2016. "Government and Central Bank Interaction under Uncertainty: A Differential Games Approach," Iranian Economic Review (IER), Faculty of Economics,University of Tehran.Tehran,Iran, vol. 20(2), pages 225-259, Spring.
    4. Christos Mavrodimitrakis, 2022. "Debt stabilization and financial stability in a monetary union: Market versus authority‐based preventive solutions," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(2), pages 2582-2599, April.
    5. Willi Semmler & Alexander Haider, 2018. "Cooperative Monetary and Fiscal Policies in the Euro Area," Southern Economic Journal, John Wiley & Sons, vol. 85(1), pages 217-234, July.
    6. Z. Nikooeinejad & M. Heydari & M. Saffarzadeh & G. B. Loghmani & J. Engwerda, 2022. "Numerical Simulation of Non-cooperative and Cooperative Equilibrium Solutions for a Stochastic Government Debt Stabilization Game," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 775-801, February.
    7. Xavier Gabaix, 2017. "Behavioral Inattention," NBER Working Papers 24096, National Bureau of Economic Research, Inc.
    8. Engwerda, Jacob & van Aarle, Bas & Anevlavis, Tzanis, 2019. "Debt stabilization games in a monetary union: What are the effects of introducing eurobonds?," Journal of Macroeconomics, Elsevier, vol. 59(C), pages 78-102.
    9. Valeria De Bonis & Pompeo Della Posta, 2005. "Strategic interactions between monetary and fiscal authorities in a monetary union," Working Papers de Economia (Economics Working Papers) 26, Departamento de Economia, Gestão e Engenharia Industrial, Universidade de Aveiro.
    10. Di Bartolomeo Giovanni & Saltari Enrico & Semmler Willi, 2017. "Inattention and pollution regulation policies," wp.comunite 00130, Department of Communication, University of Teramo.
    11. Caglayan, Mustafa & Pham, Tho & Talavera, Oleksandr & Xiong, Xiong, 2020. "Asset mispricing in peer-to-peer loan secondary markets," Journal of Corporate Finance, Elsevier, vol. 65(C).
    12. Barucci, Emilio & Brachetta, Matteo & Marazzina, Daniele, 2023. "On the feasibility of a debt redemption fund," Economic Modelling, Elsevier, vol. 119(C).
    13. D. Masciandaro, 2019. "What Bird Is That? Central Banking And Monetary Policy In The Last Forty Years," BAFFI CAREFIN Working Papers 19127, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    14. Engwerda, Jacob & van Aarle, Bas & Plasmans, Joseph & Weeren, Arie, 2013. "Debt stabilization games in the presence of risk premia," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2525-2546.
    15. Reis, Ricardo, 2006. "Inattentive consumers," Journal of Monetary Economics, Elsevier, vol. 53(8), pages 1761-1800, November.
    16. Niemann, Stefan & Pichler, Paul, 2011. "Optimal fiscal and monetary policies in the face of rare disasters," European Economic Review, Elsevier, vol. 55(1), pages 75-92, January.
    17. Pasquale Foresti, 2015. "Monetary and debt-concerned fiscal policies interaction in monetary unions," International Economics and Economic Policy, Springer, vol. 12(4), pages 541-552, October.
    18. Engwerda, J.C., 1998. "On the Scalar Feedback Nash Equilibria in the Infinite Horizon LQ-Game," Other publications TiSEM 3142d140-f18c-4699-be28-9, Tilburg University, School of Economics and Management.
    19. Olivier Coibion & Yuriy Gorodnichenko, 2012. "What Can Survey Forecasts Tell Us about Information Rigidities?," Journal of Political Economy, University of Chicago Press, vol. 120(1), pages 116-159.
    20. Lucidi, Francesco Simone & Semmler, Willi, 2023. "Long-run scarring effects of meltdowns in a small-scale nonlinear quadratic model," Journal of Macroeconomics, Elsevier, vol. 75(C).

    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ter:wpaper:00160. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Giovanni Di Bartolomeo (email available below). General contact details of provider: http://wp.comunite.it/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.