"Dead Rubber" definitive etymology
A rubber is a series that consists of an odd number of matches where a majority of wins takes the series.  For example, in baseball, the World Series is an example of a rubber; the team that wins 4 games out of 7 wins the series.  Rubber bridge is a form of contract bridge where the teams play best out of three games.  (Wiktionary lists this the etymology of this definition of rubber as "unknown."  If you want more information, English Language &amp; Usage would be a good place to ask.)

The rubber match is a match that decides a series after a tie.  For example, in this year's World Series, after 6 games the San Francisco Giants and the Kansas City Royals were tied 3-3.  The last game on October 29 was the rubber match, and the winner, San Francisco, won the series.  In rubber bridge, the rubber match is the third game.

A dead rubber is a match in a series that has already been decided, but the match is still played.  In the World Series, this doesn't happen; once a team has four wins, no more games are played.  However, this term is used in other sports, such as some tennis tournaments, cricket, or the FIFA World Cup.  For example, in the group stage of the FIFA World Cup, you might have a match at the end of the group stage where it is already known which teams will advance to the knockout stage before the match begins.  This is a dead rubber match, and no matter who wins, the result of the tournament doesn't change.

In rubber bridge, the rubber is over when one team has won two games, so I don't think that "dead rubber" is a bridge term.