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Corrigendum to: “Discounted Stochastic Games with No Stationary Nash Equilibrium: Two Examples

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Abstract

Levy (2013) presents examples of discounted stochastic games that do not have stationary equilibria. The second named author has pointed out that one of these examples is incorrect. In addition to describing the details of this error, this note presents a new example by the first named author that succeeds in demonstrating that discounted stochastic games with absolutely continuous transitions can fail to have stationary equilibria.

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  • Yehuda John Levy & Andrew McLennan, 2014. "Corrigendum to: “Discounted Stochastic Games with No Stationary Nash Equilibrium: Two Examples," Discussion Papers Series 527, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uq2004:527
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    File URL: https://economics.uq.edu.au/files/46020/527.pdf
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    1. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    2. Yehuda Levy, 2013. "Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples," Econometrica, Econometric Society, vol. 81(5), pages 1973-2007, September.
    3. McLennan, Andrew, 2014. "Fixed points of parameterized perturbations," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 186-189.
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    1. Page, Frank, 2016. "Stationary Markov equilibria for approximable discounted stochastic games," LSE Research Online Documents on Economics 67808, London School of Economics and Political Science, LSE Library.
    2. Hülya Eraslan & Kirill S. Evdokimov & Jan Zápal, 2022. "Dynamic Legislative Bargaining," Springer Books, in: Emin Karagözoğlu & Kyle B. Hyndman (ed.), Bargaining, chapter 0, pages 151-175, Springer.
    3. Page, Frank, 2016. "On K-Class discounted stochastic games," LSE Research Online Documents on Economics 67809, London School of Economics and Political Science, LSE Library.
    4. Qingda Wei & Xian Chen, 2022. "Discounted stochastic games for continuous-time jump processes with an uncountable state space," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 187-218, April.
    5. McLennan, Andrew, 2014. "Fixed points of parameterized perturbations," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 186-189.
    6. Subir K. Chakrabarti, 2021. "Stationary equilibrium in stochastic dynamic models: Semi-Markov strategies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 177-194, October.
    7. Eunmi Ko, 2024. "Stationary Bayesian–Markov Equilibria in Bayesian Stochastic Games with Periodic Revelation," Games, MDPI, vol. 15(5), pages 1-17, September.
    8. Page, Frank, 2015. "Stationary Markov equilibria for K-class discounted stochastic games," LSE Research Online Documents on Economics 65103, London School of Economics and Political Science, LSE Library.
    9. Wei He, 2022. "Discontinuous stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 827-858, June.
    10. Kimmo Berg, 2016. "Elementary Subpaths in Discounted Stochastic Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 304-323, September.
    11. He, Wei & Sun, Yeneng, 2017. "Stationary Markov perfect equilibria in discounted stochastic games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 35-61.
    12. Anna Jaśkiewicz & Andrzej S. Nowak, 2016. "Stationary Almost Markov Perfect Equilibria in Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 430-441, May.
    13. Vivek S. Borkar, 2022. "Learning to cooperate in agent-based control of queueing networks," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 513-515, April.

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