Sentence examples for joint reply from inspiring English sources
After Doreen Lawrence accused the Government of ignoring race relations issues, the Prime Minister and his deputy sent a joint reply paying tribute to her work and insisting they "care a great deal" about the subject.
Mr. Adler and Mr. Draper issued a joint reply: "We have done our best as artists and do not intend to let anything stop us from doing our best as citizens".
In a joint reply to the judge, prosecutor Brandon L. Van Grack and Flynn attorney Kelner had said that although they still wanted to postpone sentencing and could update Sullivan again about timing on Aug. 24, they had asked to launch the pre-sentence investigation because it would eventually help the court move more quickly.
Please see our joint reply.
We agree with both reviewers that we went overboard in our usage of terminology from speciation and have cleaned up our language accordingly (please see our joint reply to Reviewer 2).
Proof Let F ( ⋅, t ) be the joint best reply correspondence of the game Γ t.
Then, by Theorem 3, the set of fixed points of the joint best reply correspondence, that is, the Nash equilibrium set is a CPO.
Then, by Theorem 2, there exists the least fixed point of the joint best reply correspondence, which is the least Nash equilibrium of the game.
Games with strategic complementarities in which the joint best reply correspondence is Veinott increasing (Veinott [5], Calciano [6]) rely on Zhou's [7] extension of Tarski fixed point theorem (Tarski [8]) to set-valued maps.
Theorem 6 Let T be a partially ordered set, and ( Γ t ) t ∈ T be a collection of games with extended weak general complementarities such that the joint best reply correspondence F ( ⋅, t ) is lower increasing in ( x, t ) on X × T and has a bottom element for every ( x, t ) ∈ X × T. Then the least Nash equilibrium is increasing in t.
Definition 3 A game Γ has extended weak general complementarities on CPOs (hence, is a GEWGC) if (i) each strategy set X i (a subset of a complete lattice Y) is a CPO; (ii) ∀ x ∈ X : the joint best reply correspondence F is nonempty and has a least element; and (iii) F is lower increasing.
