Executing an important prisoner can destroy bargaining power. In the Game of Thrones example, killing Ned Stark and losing Arya leaves the Lannisters with only Sansa to exchange for Jaime. Ned and Jaime had broadly comparable importance to their respective families. With only Sansa available, the Starks could seek additional concessions because Jaime mattered more to the opposing side.
Notable Point ยท 43:59-45:26
Hostages and bargaining power in Game of Thrones
The fictional loss of two Stark hostages weakens the Lannisters' bargaining position and illustrates the diplomatic value of keeping prisoners alive.