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Non-existence of subgame-perfect $$\varepsilon $$ ε -equilibrium in perfect information games with infinite horizon

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Listed:
  • János Flesch
  • Jeroen Kuipers
  • Ayala Mashiah-Yaakovi
  • Gijs Schoenmakers
  • Eran Shmaya
  • Eilon Solan
  • Koos Vrieze

Abstract

Every finite extensive-form game with perfect information has a subgame-perfect equilibrium. In this note we settle to the negative an open problem regarding the existence of a subgame-perfect $$\varepsilon $$ ε -equilibrium in perfect information games with infinite horizon and Borel measurable payoffs, by providing a counter-example. We also consider a refinement called strong subgame-perfect $$\varepsilon $$ ε -equilibrium, and show by means of another counter-example, with a simpler structure than the previous one, that a game may have no strong subgame-perfect $$\varepsilon $$ ε -equilibrium for sufficiently small $$\varepsilon >0$$ ε > 0 , even though it admits a subgame-perfect $$\varepsilon $$ ε -equilibrium for every $$\varepsilon >0$$ ε > 0 . Copyright Springer-Verlag Berlin Heidelberg 2014

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  • János Flesch & Jeroen Kuipers & Ayala Mashiah-Yaakovi & Gijs Schoenmakers & Eran Shmaya & Eilon Solan & Koos Vrieze, 2014. "Non-existence of subgame-perfect $$\varepsilon $$ ε -equilibrium in perfect information games with infinite horizon," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 945-951, November.
    • Handle: RePEc:spr:jogath:v:43:y:2014:i:4:p:945-951
    DOI: 10.1007/s00182-014-0412-3
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    1. János Flesch & P. Jean-Jacques Herings & Jasmine Maes & Arkadi Predtetchinski, 2022. "Individual upper semicontinuity and subgame perfect $$\epsilon $$ ϵ -equilibria in games with almost perfect information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 695-719, April.
    2. Elena Parilina & Georges Zaccour, 2016. "Strategic Support of Node-Consistent Cooperative Outcomes in Dynamic Games Played Over Event Trees," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-16, June.
    3. Kutay Cingiz & János Flesch & P. Jean-Jacques Herings & Arkadi Predtetchinski, 2020. "Perfect information games where each player acts only once," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 965-985, June.
    4. János Flesch & Arkadi Predtetchinski, 2016. "Subgame-Perfect ϵ-Equilibria in Perfect Information Games with Common Preferences at the Limit," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1208-1221, November.
    5. J. Kuipers & J. Flesch & G. Schoenmakers & K. Vrieze, 2016. "Subgame-perfection in recursive perfect information games, where each player controls one state," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 205-237, March.
    6. János Flesch & Arkadi Predtetchinski, 2020. "Parameterized games of perfect information," Annals of Operations Research, Springer, vol. 287(2), pages 683-699, April.

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