by The limits of game theory If you read Binmore’s Essays on the foundations of game theory (1990) you will find a section where he says that, unfortunately, we get into a kind of impasse. We get this infinite regress linked to the common knowledge problem. For example, I drive frequently from Aix to Marseille. You have the autoroute and parallel to it is the routenationale. Say there is, one day, congestion on the autoroute and nobody on the nationale. I think: “Tomorrow I will take the nationale. But, wait a minute, these other drivers are intelligent too, so they will take thenationale tomorrow, I would do better to stay over here. But, wait a minute, these drivers are pretty intelligent so they can make that step too…” It is actually not logically possible to reason to the solution of these kinds of problems that people are supposed to be solving in game theory. You can surely define an equilibrium, and say that if we were there nobody would want to move. But then you get to the problem of how we get to this equilibrium—the exact same problem that we have with general equilibrium … For certain specific, local problems, game theory is a very nice way of thinking about how people might try to solve them, but as soon as you are dealing with a general problem like an economy or a market, I think it is difficult to believe that there is full strategic interaction going on.
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The limits of game theory
If you read Binmore’s Essays on the foundations of game theory (1990)
you will find a section where he says that, unfortunately, we get into a
kind of impasse. We get this infinite regress linked to the common
knowledge problem. For example, I drive frequently from Aix to
Marseille. You have the autoroute and parallel to it is the route
nationale. Say there is, one day, congestion on the autoroute and nobody
on the nationale. I think: “Tomorrow I will take the nationale. But, wait
a minute, these other drivers are intelligent too, so they will take the
nationale tomorrow, I would do better to stay over here. But, wait a
minute, these drivers are pretty intelligent so they can make that step
too…” It is actually not logically possible to reason to the solution of
these kinds of problems that people are supposed to be solving in game
theory.
You can surely define an equilibrium, and say that if we were there
nobody would want to move. But then you get to the problem of how we
get to this equilibrium—the exact same problem that we have with
general equilibrium …For certain specific, local problems, game theory is a very nice way
of thinking about how people might try to solve them, but as soon as
you are dealing with a general problem like an economy or a market,
I think it is difficult to believe that there is full strategic interaction
going on. It is just asking too much of people. Game theory imposes a
huge amount of abstract reasoning on the part of people …That is why I think game theory, as an approach to large scale interaction, is probably not the right way to go.