When the New York Giants play the New York Jets in preseason, it’s for “bragging rights”—the right to brag about being the best team in New York City, even if the game itself is actually meaningless. The term “bragging rights” was popularized by Texas land deals in the 1950s.
 
When the Giants played the Jets in preseason in August 1970, New York Jets head coach Weeb Ewbank (1907-1998) said:
 
“I’m not preparing for it any differently than other exhibition games, but the players probably will play ita lot differently, though. They’ve got a lot of pride. They like to have bragging rights.”
 
The term “bragging rights” has been used for competitions involving many other sporting rivalries.
   
     
Wiktionary: bragging rights
Noun
bragging rights (plural only)
1. (idiomatic) The prerogative to praise oneself for an accomplishment or for possession of a superior characteristic.
 
Merriam-Webster Dictionary
bragging rights
noun
: a good reason to talk with pride about something you have done
 
Google Books
Flat Top Ranch,
The Story of a Grassland Venture
By B. W. Allred, Jeff Dykes and Louis Bromfield
Norman, OK: University of Oklahoma Press
1957
Pg. XIX:
Bragging about the Alamo, San Jacinto, and Adobe Walls will be hollow indeed if Texas land will not support the ever increasing population. The bragging rights of future generations of Texans are in jeopardy.
 
23 August 1970, Boston (MA) Herald Traveler, “Revenge vs. Pride in Yale Bowl: Giants 6 1/2-Point Pick To Defeat Jets Today” by George Sullivan, sec. 4, pg. 1, col. 5:
“I’m not preparing for it any differently than other exhibition games,” insists the Jets’ Weeb Ewbank. ‘But the players probably will play ita lot differently, though. They’ve got a lot of pride.THey like to have bragging rights.”
 
23 August 1970, Sunday Herald-Leader (Lexington, KY), pg. 33, col. 1:
‘Bragging Rights’ On Line
In Giants-Jets Exhibitiion
By VITO STELLINO
NEW HAVEN, Conn. (UPI)—Pros are supposed to play for money but Sunday at old Yale Bowl, something different wil be at stake—“bragging rights.”
 
Google News Archive
22 August 1971, TUscaloosa (AL) News, pg. 2B, col. 1:
New York’s Giants, Jets
Clash For ‘Brag Rights’
By THE ASSOCIATED PRESS
The New York Giants and the New York Jets will clash at New Haven, Conn. in one of four exhibition games scheduled for Sunday to decide, as Jet Coach Weeb Ewbank has described it, who gets “the bragging rights to the city” for 1971.
   
New York (NY) Times
Sports of The Times; Giants-Jets Private ‘Playoff’
By DAVE ANDERSON
Published: December 12, 1988
EAST RUTHERFORD, N.J.— AT last, in their 19th season as National Football League lodge brothers, the Giants and the Jets will collide Sunday in a regular-season game with something at stake other than what Weeb Ewbank always described as the ‘‘bragging rights’’ to the New York area.
   
OCLC WorldCat record
Bragging rights : a season inside the SEC, football’s toughest conference
Author: Richard Ernsberger
Publisher: New York : M. Evans and Co., ©2000.
Edition/Format:   Print book : English
 
Urban Dictionary
bragging rights
They are the rights granted to a person that allow said person to boast on themselves to a certain extent without being looked down on for it.

Bragging rights may be granted to a person for (but not limited to) the following reasons:
 
-An Amazing Achievement
-Attaining something greatly desired by many people
-An unfortunate event that can be viewed as positive for different reasons
(...)
by Zen Master Alvey August 24, 2007
 
OCLC WorldCat record
Bragging rights : the Dallas-Houston rivalry
Author: Carolyn Kneese; John DeMers; Lynn Ashby
Publisher: Houston : Bright Sky Press 2014.
Edition/Format:   Print book : English