Tuesday, January 27, 2015

Game theory and anger

As a child, I recall learning the Latin tag “Ira furor brevis est” (Anger is a brief madness). It makes the point that anger is irrational; really, as game theorists we ought never to get angry. On the other hand, emotional modelling is important for us as computer scientists: the article Computationally Modeling Human Emotion was highlighted on the front cover of the December issue of the CACM. A recent article, The Commitment Function of Angry Facial Expressions, by Lawrence Ian Reed, Peter DeScioli, and Steven A. Pinker (RDP in what follows), provides a satisfying game-theoretic explanation. The clue is in the Latin tag: you may benefit from being irrational, if you can convince your opponent that you are irrational. This helps you get better payoff in the ultimatum game.

Recall that in the ultimatum game, player 1 gets (provisionally) a sum of money that he is to share with player 2. He does this by offering player 2 some percentage of the money, and if player 2 accepts, the money is divided accordingly, but if player 2 rejects, neither player gets anything. This means that a rational player 2 should accept even a derisory offer from player 1, but in experiments the money tends to be split more evenly. If player 2 can convince player 1 that he is not rational (will reject a derisory offer) he stands to do better.

The RDP paper tested the ultimatum game on several hundred players (over Amazon’s Mechanical Turk), in which player 1 got to see a video clip, purporting to come from player 2, announcing what player 2 would accept, either with or without an angry expression. A one-sentence summary of results is that the angry expression helps player 2 get a better offer from player 1. Player 2 wins by convincing player 1 he is irrational.

As a usage of game theory, does this still fall foul of Ariel Rubinstein’s critique of game theory, in which he says that some of the arguments for game theory do nothing more than attach labels to real life situations? I feel like it does help to justify the study of game theory, e.g. study of the ultimatum game for its own sake, since it would be hard to just devise it on ad ad-hoc basis, in the context of the RDP paper.

Finally, while the RDP paper concentrates on the appearance of anger, as opposed to its reality, it seems like a basis for explaining the existence of anger in the first place. That is, in a world where we worry that undervaluing someone else’s welfare may cause them to succumb to a “furor brevis” and do something you’ll both regret, we all cooperate more. There are articles like this one that seek to explain anger and advise people on how to deal with it, that miss this game-theoretic point. So next time you see someone lose their temper, explain to them that their behaviour is not a bug but a feature, that is against the interest of the individual but in the interest of the tribe. Then duck for cover.

1 comment:

Anonymous said...

Might find this interesting...
This was part of my Thesis a long time a go now!

Morrison, William G. "Instincts as reflex choice: does loss of temper have strategic value?." Journal of Economic Behavior & Organization 31, no. 3 (1996): 335-356.