Game Theory in Crazy Rich Asians
https://www.vox.com/first-person/2018/8/17/17723242/crazy-rich-asians-movie-mahjong
Warning: spoilers ahead!
In the climax of Crazy Rich Asians, Rachel plays an intense game of mahjong with her boyfriend’s disapproving mother, Eleanor. The game is a metaphor for the characters’ conflicting ideas toward love, duty, and family. Since a lot of articles about the scene throw around the word game casually and the two characters are effectively making strategic decisions, I wondered if I could represent Rachel and Eleanor’s choices in a payoff matrix. It seemed especially appropriate given that Rachel is an economics professor who teaches game theory.
Before she faces Eleanor for the mahjong game, Rachel has two choices. She can choose to stay with Nick or leave Nick. Similarly, Eleanor also has two choices. She can choose whether or not she gives the couple her blessing. If Rachel stays and Eleanor gives her blessing, Rachel’s payoff is a happy marriage to rich and kind man. However, Eleanor loses her son because he will stay in America with Rachel. If Rachel leaves and Eleanor chooses to give her blessing (a very unlikely scenario), both woman lose Nick because presumably Nick will go back to New York City to find Rachel. However, the payoffs become a bit more complicated for the other two payoffs. It’s clear that Eleanor has an erroneous expectation of what Rachel’s payoffs will be since she does not see Rachel as deserving and does not understand how much Rachel loves her son. Without her blessing, Eleanor thinks that Rachel’s payoff for staying is happiness since she gets to marry Nick, and Rachel’s payoff for leaving is heartbreak. For either choice Rachel makes, Eleanor thinks she gets to keep Nick in Singapore. To summarize, their payoff matrices look like this:
The payoff matrices show that there are actually two different Nash equilibriums due to their differed perceptions. In the end, Rachel’s expectation ends up happening as Eleanor really does not understand her. Rachel is not willing to keep Nick away from the family and she wants Eleanor’s respect. Since Rachel knows that Eleanor’s dominant strategy is to not give her blessing, she chooses to leave because leaving gives her the higher payoff.
There is one more catch in this game. Eleanor finally realizes that she might lose her son forever by not accepting Rachel. “If [Nick] chooses his family, he might spend the rest of his life resenting you,” Rachel says to Eleanor. This exchange combined with Rachel’s self-sacrifice changes Eleanor’s payoffs again to the following:
Eleanor realizes that giving her blessing is the only way she can keep her son, so it is her new dominant strategy. Upon realizing Eleanor’s change of heart when Nick proposes to her with his mother’s ring, Rachel accepts and gets her happy ending. This is a rather simplified analysis of the movie, but it does show that people (or characters in this case) are always playing strategic games.
fun analysis