Nash equilibrium bleg
Updated with an expanded quote:
"If we expand are small world [of the Edgeworth Box], we meet with considerably more difficulties. This expansion goes as follows. Suppose we had Albert's possession of money taken as a starting point, instead of his possession of cheese. And suppose that, after some bargaining, Beatrice is willing to give up to over bottles of wine in exchange for 100 of Albert's guilders. If Albert agrees, the border has resulted in the price of 50 guilders per bottle. That is the so-called equilibrium price. Other individuals, with the same convex characteristics as those of Albert and Beatrice, can now enter our small world and also bid for Beatrice's wine. We can also continue this process by exchanging money against all other goods. Thus, ultimately, it appears that it can be mathematically proven that, where there is free barter, equilibrium prices can be established for all goods. This is the so-called Nash equilibrium..." -- Arnold Merkies, quoted in Mary Morgan, The World in the Model, p. 102
I have never seen Nash equilibrium connected with general price equilibrium before. Economists, does this make sense?
"If we expand are small world [of the Edgeworth Box], we meet with considerably more difficulties. This expansion goes as follows. Suppose we had Albert's possession of money taken as a starting point, instead of his possession of cheese. And suppose that, after some bargaining, Beatrice is willing to give up to over bottles of wine in exchange for 100 of Albert's guilders. If Albert agrees, the border has resulted in the price of 50 guilders per bottle. That is the so-called equilibrium price. Other individuals, with the same convex characteristics as those of Albert and Beatrice, can now enter our small world and also bid for Beatrice's wine. We can also continue this process by exchanging money against all other goods. Thus, ultimately, it appears that it can be mathematically proven that, where there is free barter, equilibrium prices can be established for all goods. This is the so-called Nash equilibrium..." -- Arnold Merkies, quoted in Mary Morgan, The World in the Model, p. 102
I have never seen Nash equilibrium connected with general price equilibrium before. Economists, does this make sense?
It definitely sounds like nonsense to me, especially because he's not saying, "This is a case of..." but instead makes it look like the very definition of Nash equilibrium.
ReplyDeleteBut can you give a few more sentences from before and after for fuller context? I hesitate to render judgment when I don't know what the guy is *trying* to say.
OK now that you've augmented the quote, I can confidently say it's wrong, both in letter and in spirit.
ReplyDeleteIn letter, it's wrong because a Nash equilibrium is a profile of strategy choices (one from each player in the game). In a normal general equilibrium model, the individual agents would be choosing quantities in response to exogenous price vectors. So to say a list of prices would be a "Nash equilibrium" is ungrammatical, at the very least.
But in terms of the spirit: The discussion above makes it sound like "Nash equilibrium" is equivalent to general equilibrium in a decentralized price-taking market. But no, Nash equilibrium is a much more general concept. You could define the Nash equilibrium in Tic Tac Toe.
I think part of the problem might be a translation though from a foreign language? In any event, Gene, I wouldn't "learn" anything about economic theory from this book if I were you.