The regular prices for the two sections are $40 and $30 for games against the Nationals on July 23 and Houston on Aug. 6. Each homer Hart hits over the course of the competition will be subtracted from the price.
If Hart eclipses the price of the tickets, they will be free.
The team ran a similar promotion last year when Prince Fielder won the competition in St. Louis.
Fielder hit 23 homers and $28 tickets were reduced to $5 for three games against the Padres. Those tickets sold out in 15 minutes.