TY - JOUR
T1 - Non-existence of subgame-perfect ε-equilibrium in perfect information games with infinite horizon
AU - Flesch, János
AU - Kuipers, Jeroen
AU - Mashiah-Yaakovi, Ayala
AU - Schoenmakers, Gijs
AU - Shmaya, Eran
AU - Solan, Eilon
AU - Vrieze, Koos
N1 - Funding Information:
The research of Mashiah-Yaakovi has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ ERC Grant agreement n [249159]. The research of Solan was supported in part by the Israel Science Foundation (Grant number 212/09) and by the Google Inter-university center for Electronic Markets and Auctions.
Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
PY - 2014/11
Y1 - 2014/11
N2 - 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 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 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 ε-equilibrium for sufficiently smallε>0, even though it admits a subgame-perfect ε-equilibrium for every ε>0.
AB - 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 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 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 ε-equilibrium for sufficiently smallε>0, even though it admits a subgame-perfect ε-equilibrium for every ε>0.
KW - Infinite horizon
KW - Non-existence
KW - Perfect-information games
KW - Subgame-perfect equilibrium
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U2 - 10.1007/s00182-014-0412-3
DO - 10.1007/s00182-014-0412-3
M3 - Article
AN - SCOPUS:84893637518
SN - 0020-7276
VL - 43
SP - 945
EP - 951
JO - International Journal of Game Theory
JF - International Journal of Game Theory
IS - 4
ER -