On reading about John Nash passing away, I spent some quiet time mulling over stories I’ve heard about him, incidences from the “Beautiful Mind” that touched my heart and have stayed with me and obviously, thinking and re-thinking the many applications of game theory in general and Nash equilibrium, in particular. Unknowingly, but perhaps unresistingly too, I was also drawn to other philosophical issues that always crop up when Nash is being discussed. Yes, philosophy. Because I’ve often felt that the beauty of Nash’s work is that it gives us a mathematical tool to look more logically at deeper, more soul searching, non-mathematical issues.
I cannot help going back to Laches, that famous dialogue between Socrates and two men (Nicias and Laches) on why children should be trained in warfare. In this dialogue, there is a very interesting story that Socrates narrates. There is a soldier on the border, who is observing the war. He observes that his side is winning without his intervention. It now becomes unimportant for him to actively engage in combat and increase the probability of his own death, especially given that his side is winning. He does not engage in combat. If he observes that the opposition is winning, the chances of his getting injured go up even more than earlier and so he decides to run away. Socrates argues that here, running away is something that every soldier would want to practice, immaterial of who wins the war. This is “prudence”. In Nash’s terms, folks, we have now seriously identified dominant strategies.
Prudence demands that soldiers wouldn’t want to fight; yet they do. So there could be a bigger motive to this; perhaps it is not always rational to be only selfish. The moment you say that, you have opened THE Pandora’s box. There are uncontrolled number of opinions that take off from this point, each irresistible in its appeal and yet, aggressive in its persuasion. There would be Plato, Mill, Kant, all arguing that ethics are larger than selfish acts of prudence. And then of course, there would be Charles Darwin holding the opposite end of the spectrum. Nature, in its raw form, supports only survival of the fittest. And that implies that the game of life is so created to support only and only rational individual self-interest. And where do we go from here? Where else can we go from here? We can, only and only move to individualism, supported by Rand and followers. The only rationality lies in selfish focus; you can pretty much discard any other notion of altruism with a shrug.
Very close, so close that you may be tempted to call him the economic version of Ayn Rand, is Adam Smith. Smith, the father of Economics, with his utterances on how a laissez faire economy will automatically promote the best possible outcomes. However, careful here; there are significant differences between Ayn Rand and Adam Smith. In the Theory of Moral Sentiments, Smith admits “How selfish soever man may be supposed, there are evidently some principles in his nature, which interest him in the fortune of others, and render their happiness necessary to him, though he derives nothing from it except the pleasure of seeing it”. And it is here perhaps that Smith scores rather heavily over Rand. While Smith agrees that self focus would lead to profitable outcomes, he does not always presume that the self is the center of the rational human universe. And this is perhaps his biggest departure from Rand, who goes so far as to say that the only God is “I”. “The word “We” is as lime poured over men, which sets and hardens to stone, and crushes all beneath it, and that which is white and that which is black are lost equally in the grey of it. It is the word by which the depraved steal the virtue of the good, by which the weak steal the might of the strong, by which the fools steal the wisdom of the sages. I am done with the monster of “We,” the word of serfdom, of plunder, of misery, falsehood and shame. And now I see the face of god… This god, this one word: “I.”
But if people only focus on their own individual strategies, then there could be a case where greed brings in anarchy. So Thomas Hobbes, in his unparalleled and rather unconvincing work Leviathan, brings in “tyranny” as a whiplash over anarchy. Since individuals may be so blinded by their self-interest, it perhaps makes sense to have an intervention in place…perhaps, a tyrant, called as the Government?
The main point however is: Why do I write about Plato and Smith and Rand and Hobbes, when my musings are primarily about Nash? Well you see, Nash gives me the tool with which I can connect the philosophies of all these thinkers onto one platform. A platform called Game Theory.
In the prisoner’s dilemma, each prisoner decides to choose that strategy that minimizes the sentence given to him, irrespective of the strategy used by his opponent. What every prisoner is really doing is that he is employing his own dominant strategy; he focuses on the self.
As all players employ self centered strategies, the game settles to a stable Nash equilibrium. Ayn Rand would rejoice in this choice and would perhaps like to call it the God equilibrium.
Plato, Mill and Kant would perhaps not be so convinced. Their point was that stable equilibria are not always the most ethical equilibria. And fortunately, people don’t always behave in a self centered manner, do they? Nash would interpret this to say that there are other altruistic pay-offs that we would need to incorporate in the game. Further, its not always possible for us to have dominant strategies. People do reciprocate an act of kindness; in Nash’s world, strategies are at times reactive.
Enter Hobbes and Nash will show that the presence of the Government will change the equilibrium from a competitive one to a co-opetitive one. It could be a law or a cartel or a mafia or a Government that could affect this change.
Every philosophical idea can be equated to a change in pay-offs as perceived by the players. Or it could be equated to introduction of new strategies being made available to the players. Or it could be equated to introduction of a new player altogether. Whatever be your philosophy, the theory of games and the dilemma offers us the perfect mathematical tool with which to view it.
The vision is entirely yours. The choice of philosophy is entirely yours too. John Nash is the name of the binocular through which you suddenly see things close by.