TY - JOUR

T1 - The complexity of computing a best response automaton in repeated games with mixed strategies

AU - Ben-porath, Elchanan

PY - 1990/3

Y1 - 1990/3

N2 - I examine the complexity of computing a best response automaton in a two-person repeated game when there is uncertainty about the automaton selected by the other player. There are two versions of this problem: (1) Finding a best response automaton; (2) Deciding if a given automaton is a best response. It is shown that these problems are "difficult" (i.e., not polynomial). Next it is shown that if the size of the support of the distribution of the other player's automata is known in advance (for example, when it is known that the other player is restricted to automata of a certain size), the problems are polynomial. The problems are polynomial even if there is uncertainty in the game that will be played (i.e., even if it is a repeated game with incomplete information).

AB - I examine the complexity of computing a best response automaton in a two-person repeated game when there is uncertainty about the automaton selected by the other player. There are two versions of this problem: (1) Finding a best response automaton; (2) Deciding if a given automaton is a best response. It is shown that these problems are "difficult" (i.e., not polynomial). Next it is shown that if the size of the support of the distribution of the other player's automata is known in advance (for example, when it is known that the other player is restricted to automata of a certain size), the problems are polynomial. The problems are polynomial even if there is uncertainty in the game that will be played (i.e., even if it is a repeated game with incomplete information).

UR - http://www.scopus.com/inward/record.url?scp=0011471586&partnerID=8YFLogxK

U2 - 10.1016/0899-8256(90)90010-R

DO - 10.1016/0899-8256(90)90010-R

M3 - Article

AN - SCOPUS:0011471586

SN - 0899-8256

VL - 2

SP - 1

EP - 12

JO - Games and Economic Behavior

JF - Games and Economic Behavior

IS - 1

ER -