Just come across a question regarding sequential maximization and simultaneous maximization, and I do not recall whether there are any established conditions for the equivalence. Anyone has some idea? max x max y f ( x , y ) = max y max x f ( x , y ) ?

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Just come across a question regarding sequential maximization and simultaneous maximization, and I do not recall whether there are any established conditions for the equivalence. Anyone has some idea?      max    x        max    y    f  (  x  ,  y  )  =      max    y        max    x    f  (  x  ,  y  )  ?

lisicw2 · Accepted Answer

max    x        max    y    f  (  x  ,  y  )  =      max    y        max    x    f  (  x  ,  y  )  ?Let   (  x  ,  y  )  ∈  X  ×  Y.  f  (  x  ,  y  )  ≤      max    x    f  (  x  ,  y  )  ≤      max    y        max    x    f  (  x  ,  y  )  ;as this is true for every   y  ∈  Y,      max    y    f  (  x  ,  y  )  =      max    y        max    x    f  (  x  ,  y  )  ;and as this is true for every   x  ∈  X:      max    x        max    y    f  (  x  ,  y  )  ≤      max    y        max    x    f  (  x  ,  y  )  .Now use the symetry to get the conclusion.

Just come across a question regarding sequential maximization and simultaneous maximization, and I d

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