Analyze surprising aspect of human behavior using Game Theory

Insight

Asking favors to friends is very common and we genuinely expect them to cooperate and say yes without following up with a number of questions. However, in the odd case the answer is a no, we’d like them to first ask us questions in order to soften the no with reasons. Although this seems very different when comparing yourselves with significant others, the result from The Envelop Game shows otherwise. They both differ in “degrees of manipulation and preferential interaction” (Paiste 2017). 

Background

Alfonso Pérez-Escudero, a doctor at MIT and his colleagues has proven that “The Envelope Game” helps play out the manipulation and interactions. The game was developed by Harvard University researchers Martin Nowak, Erez Yoeli, and Moshe Hoffman. They have developed a generalization that describes both manipulative mechanisms and preferential interactions. 

The Game

The game is originally played with players who know each other very well and have some sort of trust between one another. Specifically in our case, there are two players involved in the making of the envelope game in which the second player’s payout depends solely on the decisions made by the first player. Player 1 can first choose whether to look at an envelope that may be valued high or low. Regardless of if player 1 looked or not, they can now either “cooperate”, resulting in both players receiving the same payout, or to choose “defeat”, where player 1 gets the payout while player 2 gets nothing. In either case, player 2’s next move is to continue the game or quit. 

It is clear to see that the player who is making the decision to cooperate has all the power. However, it would be surprising to see player 2 ending the game given player 1 has chosen to cooperate. Similarly, player 2 ending the game given that player 1 has chosen defeat; in which player 2 walks out with nothing. 

If you have watched “Let’s make a deal”, the envelope game is very similar to pretty much most of the games played on the show.  This influences viewers’ attention rate as the games are very manipulative between players who would like to receive the best prize; and makes a thrilling experience.  

The Intuition(s)

If player 1 decides to open up the envelope, player 2 receives the message that player 1 is unreliable and should not be trusted. This is because player 1 was hesitant to cooperate when deciding on opening the envelope. Thus player 2 is more lenient in ending the game as player 1 was not confident in themselves. If player 1 decides to cooperate without having the need to peek at the envelope, player 2 will obviously vote to continue the game to receive a greater payout. However, do note that even though we said the game is played with players who trust each other, there is always uncertainty in the real world. Player 2 can manipulate player 1 by threatening to end the game if player 1 chooses to open the envelope, hence going back to the manipulation mechanism of the game and having a Sequential Equilibrium. 

Sequential Equilibrium 

Although we focused on Nash Equilibrium, Sequential Equilibrium is just as important. At each stage of the game, a player is said to be sequentially rational if he maximizes his expected utility given his beliefs at the information presented to him.   

Real Life Applications 

Both manipulation and preferential interaction mechanisms were displayed by the envelope game. Take for example you are in a relationship and decide to flirt with other people, you’d expect your girlfriend to get angry, and possibly leave you. At this stage, she has the manipulative power over you as she holds the true decisions of your actions. However, suppose your girlfriend is not angry but realizes that you are not emotionally invested into the relationship; showcasing the preferential interaction based on the same scenario. 

Conclusion

My point of view regarding personal relations has widened as the results from the envelope game have made me consider previous situations I’ve encountered; embracing the manipulation and preferential interaction mechanisms concept that I’ve been reluctant to think about.

Truly a great game.

Links

Denis Paiste | Materials Processing Center. “Using EvolutionaryDynamics and Game Theory to Understand Personal Relations.” MIT News | Massachusetts Institute of Technology, https://news.mit.edu/2017/using-evolutionary-dynamics-game-theory-to-understand-personal-relations-0105.