You would think that’s why society invented money, but A&E is doing a reality series about the “thriving subculture of cashless trading.” Barter Kings, which has been picked up for 13 half-hour episodes to premiere this summer, features teams of entrepreneurs pursuing items they want by trading other items that they currently own without the use of cash. The series is produced by Brownstone Entertainment, with Drew Brown, Bob Gillan and James Flint executive producing.