sol2_1

sol2_1 - ORIE 4350 (Shmoys 1:25): Problem Set #2 1. 1....

This preview shows pages 1–2. Sign up to view the full content.

ORIE 4350 (Shmoys 1:25): Problem Set #2 1. 1. (Binmore, Section 2.12, Number 19) Notice that ( s,t 0 ) is in the column corresponding to t 0 and the row corresponding to s ; ( s 0 ,t ) is in the column corresponding to t and the row corresponding to s 0 . By the deﬁnition of saddle point , [ 10pt ] ( s,t ) 1 ( s 0 ,t ) , ( s,t ) 1 ( s,t 0 ) ( s 0 ,t 0 ) 1 ( s,t 0 ) , ( s 0 ,t 0 ) 1 ( s 0 ,t ) which results in ( s,t ) 1 ( s 0 ,t ) 1 ( s 0 ,t 0 ) 1 ( s,t 0 ) 1 ( s,t ) Hence it has to be the case that [ 5pt ] ( s,t ) 1 ( s 0 ,t ) 1 ( s 0 ,t 0 ) 1 ( s,t 0 ) 1 ( s,t ) To show that( s,t 0 ) is also a saddle point, consider any outcome (ˆ s,t 0 ) in the column corresponding to t 0 and any outcome ( s, ˆ t ) in the row corresponding to s . By the fact that ( s,t ) and ( s 0 ,t 0 ) are saddle points, [ 5pt ] ( s,t 0 ) ( s 0 ,t 0 ) s,t 0 ) ( s,t 0 ) ( s,t ) ( s, ˆ t ) which says exactly that ( s,t 0 ) is a saddle point. [ 5pt ] The Same argument applies to ( s 0 ,t ). 2.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/06/2011 for the course ORIE 4350 at Cornell.

Page1 / 3

sol2_1 - ORIE 4350 (Shmoys 1:25): Problem Set #2 1. 1....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online