TY - UNPB
T1 - Best response cycles in perfect information games
AU - Herings, P.J.J.
AU - Predtetchinski, A.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - We consider n-player perfect information games with payofffunctions having a finite image. We do not make any further assumptions, so in particular we refrain from making assumptions on the cardinality or the topology of the set of actions and assumptions like continuity or measurability of payofffunctions. We show that there exists a best response cycle of length four, that is, a sequence (σ0, σ1, σ2, σ3, σ0) of pure strategy profiles where every successive element is a best response to the previous one. This result implies the existence of point-rationalizable strategy profiles. When payoffs are only required to be bounded, we show the existence of an ϵ-best response cycle of length four for every ϵ > 0.
AB - We consider n-player perfect information games with payofffunctions having a finite image. We do not make any further assumptions, so in particular we refrain from making assumptions on the cardinality or the topology of the set of actions and assumptions like continuity or measurability of payofffunctions. We show that there exists a best response cycle of length four, that is, a sequence (σ0, σ1, σ2, σ3, σ0) of pure strategy profiles where every successive element is a best response to the previous one. This result implies the existence of point-rationalizable strategy profiles. When payoffs are only required to be bounded, we show the existence of an ϵ-best response cycle of length four for every ϵ > 0.
U2 - 10.26481/umagsb.2015017
DO - 10.26481/umagsb.2015017
M3 - Working paper
T3 - GSBE Research Memoranda
BT - Best response cycles in perfect information games
PB - Maastricht University, Graduate School of Business and Economics
CY - Maastricht
ER -