TY - JOUR
T1 - Non-Existence of Subgame-Perfect ε-Equilibrium in Perfect Information Games with Infinite Horizon
AU - Flesch, Janos
AU - Kuipers, Jeroen
AU - Mashiah-Yaakovi, A.
AU - Schoenmakers, Gijsbertus
AU - Shmaya, E.
AU - Solan, E.
AU - Vrieze, Okko
PY - 2014
Y1 - 2014
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 e e\varepsilon -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 e e\varepsilon -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 e e\varepsilon -equilibrium for sufficiently small e>0 e>0\varepsilon >0, even though it admits a subgame-perfect e e\varepsilon -equilibrium for every e>0 e>0\varepsilon >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 e e\varepsilon -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 e e\varepsilon -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 e e\varepsilon -equilibrium for sufficiently small e>0 e>0\varepsilon >0, even though it admits a subgame-perfect e e\varepsilon -equilibrium for every e>0 e>0\varepsilon >0.
U2 - 10.1007/s00182-014-0412-3
DO - 10.1007/s00182-014-0412-3
M3 - Article
SN - 0020-7276
VL - 43
SP - 945
EP - 951
JO - International Journal of Game Theory
JF - International Journal of Game Theory
IS - 4
ER -