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Glicksberg's theorem : ウィキペディア英語版
Glicksberg's theorem

In the study of zero sum games, Glicksberg's theorem (also Glicksberg's existence theorem) is a result that shows certain games have a minimax value
.
If ''A'' and ''B'' are compact sets, and ''K'' is an upper semicontinuous or lower semicontinuous function on A\times B, then
:
\sup_\inf_\int\int K\,df\,dg = \inf_\sup_\int\int K\,df\,dg

where ''f'' and ''g'' run over Borel probability measures on ''A'' and ''B''.
The theorem is useful if ''f'' and ''g'' are interpreted as mixed strategies of two players in the context of a continuous game. If the payoff function ''K'' is upper semicontinuous, then the game has a value.
The continuity condition may not be dropped: see example of a game with no value.
== References ==



抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Glicksberg's theorem」の詳細全文を読む



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