Symmetries in the lab

Here is slight modification of the example Christoph presented in the last MEDS lunch (I don’t remember the attribution). I am going to describe three games, and, because for my main point I need to think of the game as taking place in the laboratory, I will call the game `an experiment’ and the players `subjects’, denoted S1 and S2. Below are full descriptions of three experiments. These descriptions are also given to the subjects.

Experiment 1: S2 leaves the room. S1 faces a disk divided into two sides and has to chose one side. His choice is recorded (say, marked on the back of the disk). Then the disk is randomly rotated. Then S2 returns and has to chose a side. If both subjects chose the same side, they get one dollar each. Otherwise, they are cast into the lake of fire.

Experiment 2: Same as Experiment 1, except that the disk is not rotated.

Experiment 3: The Experiment is called `Driving in Illinois’. The rest of the game is as in Experiment 2.

Ariel’s afterword

Via Jeff, from Ariel Rubinstein’s afterword (pdf) for a reprinting of von-Neumann and Morgenstern’s book in which Ariel states his opinion about the usefulness of game theory for real-life strategic interactions (emphasis mine)

According to this opinion, Game theory does not have normative implications and its empirical significance is very limited.  Game theory is viewed as a cousin of logic.  Logic does not allow us to screen out true statements from false ones and does not help us distinguish right from wrong.  Game theory does not tell us which action is preferable or predict what other people will do.  If game theory is nevertheless useful or practical, it is only indirectly so.   In any case, the burden of proof is on those who use game theory to make policy recommendations, not on those who doubt the practical value of game theory in the first place.

And, by the way, I sometimes wonder why people are so obsessed in looking for “usefulness” in economics generally and game theory in particular.  Should academic research be judged by its usefulness ?

Readers of this blog can hopefully guess my view on this issue. I don’t view game theory as a mathematical or logical exercise (I am not sure that’s Ariel’s view either), but I have never found it useful in my own interactions with fellow human beings. As Rubinstein says, the burden of proof is on those who use game theory to make policy recommendations, and I have never seen such a proof: I have never came across any example in which a theorem or a definition or an insight from game theory turned out to be useful in policy recommendation or in predicting human behavior in strategic situations. But that doesn’t say much since I have little patience to look into such proclaimed proofs and I usually just shrug them off without studying them carefully. The reason is that even if there were situations in which game theory would turn out to be useful in this sense, it wouldn’t make game theory more exciting for me.

Which brings me to Rubistein’s question about judgding academic research. To be sure, some academic enterprises have practical usefulness, sometimes even in a way that was not originally foreseen. The applicability of number theory to encryption protocols is a wonderful example. But that’s not the reason why prime numbers are so fascinating, nor is building bridges the reason we are curious about the laws of the universe. Similarly, while I can see several reasons to be driven to study game theory, I doubt if any of us has done so to improve their performance in strategic situations. So why do so many game theorist feel the need to justify their interest in game theory by appealing to real life applicability ?

Btw, my feeling is that most of our seniors don’t agree with Ariel here. You can see this in the round table discussions in conferences. While not everyone actually claim that game theory is useful for policy making right now, the premise is always that this is our ultimate goal. But I believe Ariel’s position is relatively popular among juniors. Read into this what you will.