I stumbled upon a paper by Anna Dreber, David Rand, Drew Fudenberg and Martin Nowak, whose title is the title of this post. This paper reports on the following experiment: players play the repeated prisoner’s dilemma, where there is an additional action: punish the opponent. At every period each player has to decide whether to cooperate (I lose 1, you get 2), to defect (I get 1, you lose 1), or to punish (I lose 1, you lose 4). The game is discounted: after each period an unfair coin is tossed: with probability 25% the game ends, with probability 75% it continues. In particular, the expected length of the game is 4 periods.
Results: the players who had the highest gains did not punish each other. The players who came next are those who punished but were not punished, and the players who fared worse are those who were punished. When you look at the expected length of the game and at the payoffs, you realize why this happens. The authors run more correlation tests to derive additional conclusions; you can press this link (or the one above) and read it for yourselves.
Why do I tell you about this paper? Because I do not like experiments. I do not see what we gain from them. The title of this paper, for example, is “Winners Don’t Punish”. Is this the right conclusion? I do not think so. Because the game is short, there is not much time for learning, for using a punishment. If you were punished, you lose 4, and there is hardly any time to regain your losses. And even if the game were longer, and players could teach each other that defection leads to punishment and is therefore not profitable, will an experiment on $10 teach us anything about decisions in the real world? The Roman Empire used to punish heavily. And it worked, as long as it was the strongest. Most dictators punish, and some last decades. So in real life, if you are strong, you can punish as much as you wish. I still wait to see the experiment that will convince me that it reveals some insight on real life.