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This clip is a great example of the principle of reciprocity in two ways. First, Tyrion is planning to use Princess Myrcella as a way of forging an alliance between House Lannister and House Arryn, therefore making it easier for them to win the war; second, he is offering Petyr Baelish Harrenhal and one of the most powerful positions in the whole realm to persuade him to head off and try to secure the marriage pact.
Reciprocity works by doing someone a favour, which they then feel the need to pay you back for. In a study carried out by Kunz and Woolcott (1976) most strangers who were sent Christmas cards by the researchers sent cards back even though they didn't know them, showing that if someone has done something for you, you're more likely to do something for them. In this situation, Tyrion is trying to get Petyr to go and negotiate a marriage pact and to do so, offers him a castle and a title.
The reason this technique is going to work on Petyr is that Tyrion is an authority figure, he wears the Hand of the King pin, a position that gives him the power to hand out titles, and this solidifies his offer of Harrenhal, meaning that Petyr already feels like he's been given something, rather than it be an exchange. This pin, worn by Tyrion, is a little like a uniform, and Bickman (1974) showed that people comply much more readily when people are wearing a guard's uniform than when dressed in other clothing. So it could be that this pin has given Tyrion legitimate social power over Petyr.
The reciprocity principle is also the reason behind the marriage pact, if the princess is promised to Lysa Arryn's son, she will then feel indebted to Tyrion and his house and so be more likely to send troops in the case of war.
Of course, this whole exchange between Petyr and Tyrion is a pretence, Tyrion is trying to work out which of the three members of the council is feeding secrets to the queen, and so tricks them by each telling them of a different marriage pact, and Petyr isn't best pleased when he finds out.
Bickman, L. (1974). The social power of a uniform. Journal of Applied Social Psychology, 4, 47-61.
Kunz, P. R., & Woolcott, M. (1976). Season's greetings: From my status to yours. Social Science Research, 5, 269-278.
Xenia Millar (Blog 5)