TY - JOUR
T1 - Implementability of correlated and communication equilibrium outcomes in incomplete information games
AU - Milchtaich, Igal
PY - 2014/5
Y1 - 2014/5
N2 - In a correlated equilibrium, the players' choice of actions is directed by correlated random messages received from an outside source, or mechanism. These messages allow for more equilibrium outcomes than without any messages (pure-strategy equilibrium) or with statistically independent ones (mixed-strategy equilibrium). In an incomplete information game, the messages may also reflect the types of the players, either because they are affected by extraneous factors that also affect the types (correlated equilibrium) or because the players themselves report their types to the mechanism (communication equilibrium). Mechanisms may be further differentiated by the connections between the messages that the players receive and their own and the other players' types, by whether the messages are statistically dependent or independent, and by whether they are random or deterministic. Consequently, whereas for complete information games there are only three classes of equilibrium outcomes, with incomplete information the corresponding number is 14 or 15 for correlated equilibria and even larger-15, 16 or 17-for communication equilibria. For both solution concepts, the implication relations between the different kinds of equilibria form a two-dimensional lattice, which is considerably more intricate than the single-dimensional one of the complete information case.
AB - In a correlated equilibrium, the players' choice of actions is directed by correlated random messages received from an outside source, or mechanism. These messages allow for more equilibrium outcomes than without any messages (pure-strategy equilibrium) or with statistically independent ones (mixed-strategy equilibrium). In an incomplete information game, the messages may also reflect the types of the players, either because they are affected by extraneous factors that also affect the types (correlated equilibrium) or because the players themselves report their types to the mechanism (communication equilibrium). Mechanisms may be further differentiated by the connections between the messages that the players receive and their own and the other players' types, by whether the messages are statistically dependent or independent, and by whether they are random or deterministic. Consequently, whereas for complete information games there are only three classes of equilibrium outcomes, with incomplete information the corresponding number is 14 or 15 for correlated equilibria and even larger-15, 16 or 17-for communication equilibria. For both solution concepts, the implication relations between the different kinds of equilibria form a two-dimensional lattice, which is considerably more intricate than the single-dimensional one of the complete information case.
KW - Bayesian games
KW - Communication equilibrium
KW - Correlated equilibrium
KW - Implementation
KW - Incomplete information
KW - Mechanism
UR - http://www.scopus.com/inward/record.url?scp=84899971934&partnerID=8YFLogxK
U2 - 10.1007/s00182-013-0381-y
DO - 10.1007/s00182-013-0381-y
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AN - SCOPUS:84899971934
SN - 0020-7276
VL - 43
SP - 283
EP - 350
JO - International Journal of Game Theory
JF - International Journal of Game Theory
IS - 2
ER -