The Nash solution concept was not a drama scripted by Luigi Pirandello or a novel by Robert Musil; it was much closer to a novella by Thomas Pynchon. Just as von Neumann’s minimax solution is best grasped as the psychology of the reluctant duelist, the Nash solution is best glossed as the rationality of the paranoid. Nash appropriated the notion of a strategy as an algorithmic program and pushed it to the nth degree.
From these paranoid premises where all trust is eliminated and all action taken on the basis of perpetual fear, Nash then slips in an assumption that completes the circle and makes his vision of the economic agent truly in line by assuming telepathy on the part of the actor. From Modern Political Economics:
[Nash’s proof] only holds water if we can assume that [the economic agents] can potentially share common knowledge of the probability of no agreement [taking place when one agents threatens another]. But how can they, given that [each agent] has an incentive to overrepresent it [in order to strengthen their bargaining position]? As rationality alone cannot bring about such common knowledge, something closer to telepathy is necessary.[Author’s emphasis]
Or, Mirowski again:
In the grips of paranoia, the only way to elude the control of others is unwavering eternal vigilance and hyperactive simulation of the thought processes of the Other. Not only must one monitor the relative ‘dominance’ of one’s own strategies, but vigilance demands the complete and total reconstruction of the thought processes of the Other – without communication, without interaction, without cooperation – so that one could internally reproduce (or simulate) the very intentionality of the opponent as a precondition for choosing the best response. An equilibrium point is attained when the solitary thinker has convinced himself that the infinite regress of simulation, dissimulation, and countersimulation has reached a fixed point, a situation where his simulation of the response of the Other coincides with the other’s own understanding of his optimal choice. Everything must fit into a single interpretation, come hell or high water.[My emphasis]
Welcome to the concentration camp in which telepathy reigns and all privacy melts into ether!
We should, of course, take this as a powerful critique of the game theoretic foundations of modern neoclassical doctrine – foundations which were then built upon by Nobel prize winners Kenneth Arrow and Gérard Debreu and many others. But we should also see this as something more.
Those who came before Nash recognised that the economy – inhabited as it is by people whose decisions are impossible to pin down – cannot be wholly reduced to some model or others. Keynes’ theories were the most eloquent expression of this, but even von Neumann who did develop game theoretic and general equilibrium models which he deployed for the purpose of economic explanation recognised the limits of this axiomatic way of portraying a capitalist economy. And yet, after the war, the neoclassicals pursued their closed, autistic models with gusto.
What we should see in this example is something about the very nature of trying to apply mathematical models to systems that are created and inhabited by humans. Modelling these systems is equivalent to trying to model those around us. And while many neoclassicals (we hope) would not try to write equations to explain their spouse’s or their child’s behaviours, they seem perfectly content to do so for everybody else – absurdity be damned!
