A nightmare

I just had a dream that I still hadn’t finished my PhD and had to return to the Economics department to finish it. In actual fact I finished it five years ago and tend to avoid mentioning it because, well, it isn’t very good.
The stuff I wrote was based on Harsanyi’s various pieces of work on preferences and priors. Harsanyi (who won a Nobel prize) did some interesting work on the foundations of game theory under incomplete information – interesting in that it was a strange foray into the gap between game theory as a sparse-but-useful model of behaviour and game theory as a description of the way people actually think and behave in strategic situations.
Game theory is a peculiar but attractive branch of economics. Most people know about the ‘prisoners’ dilemma’ – a very simple game where the rational thing to do (Nash Equilibrium) is the worst option for both the participants, and has been used to suggest how rational actors can nevertheless, say, destroy themselves in a nuclear war. The rational in isolation becomes the irrational viewed from an external perspective. This tension between the perspective of the god-like observer of the game and the fictional participants led me and others into strange places.
Harsanyi used Bayesian decision theory to model the subjective beliefs and decisions of game-players, and to examine what happens when the players don’t know everything about the game they are playing. This too meanders into strange territory. Harsanyi proved that to attain equilibrium in games with uncertainty, players must have the same underlying understanding of the world before the game has started. This is the god-perspective in a different guise. But the problem is that before the game starts, there is nothing: all the information to do with the game is encoded in its mathematics. This means that the players are ciphers, voids…must they therefore have the same probability distribution over the possible set of outcomes? the same opinions? how can they have opinions at all?
These are the sorts of questions I contemplated over the three years.
Harsanyi pulled a similar trick in work on equitable distribution of income. Suppose, he argued, that everyone did not know who they would turn out to be in a future world with some distribution of wealth. Suppose then that they could choose the distribution of wealth in this future world. Wouldn’t they choose an equitable distribution? Well, perhaps. Economics describes these types of decisions in terms of utility theory which in turn depends on what the individuals prefer. In Harsanyi’s model however, the people relinquish their preferences: they choose over the preferences they might be assigned in the future world. Now isn’t that an odd perspective? How can they choose – in economics-wonderland – if they don’t have preferences? what is there left of them? the void-people return again.
John Broome, my supervisor for the first few months, argued that the void people would have preferences – had to within the economic model – over the future distribution of wealth, and so the agreement Harsanyi found could not exist. Made sense to me. There was little for me to add, despite the best efforts of my main supervisor, Paul Grout.
Harsanyi’s work in both areas poked holes in the shared fantasy that economics can describe people and their interactions. Economics is just models and to use it successfully you need to hum ‘lalalala’ in the places where the model does not mesh successfully with your perception of the world. But its simplicity is also its power. Von Neumann reportedly advocated a preemptive strike against the Soviet Union, perhaps believing his own game-theory (it’s said that Von Neumann was a model for Dr. Strangelove; another claim is that Robert McNamara was the inspiration; though McNamara, the ‘computer of death’ now emphasises the need for empathy with the enemy).
The attraction for me to game theory and related questions of public choice and income redistribution was the element of puzzle-solving and the moments where a complex problem dissolves into a tractable solution. Puzzles are fine, but I came to believe that I had indeed been contemplating the void for several years, and when the opportunity came to jump ship and play with computers instead (easier, more tractable puzzles) I took it gladly. I learned Java to try and create graphs of income distribution and had the great advantage of Dan Brickley as my housemate to teach me about html and the web.
Near the start of my PhD I went to a conference in Caen, France, and met Harsanyi, by then quite old (he died last year, suffering from Alzheimers). During that conference I drew a picture of him on the back of my notes, so I suppose I wasn’t greatly gripped even then. Our only interaction was when he asked me if I would order some icecream for him, so I went and asked the waiter (in English).