Dilworth’s theorem

L’Espresso, No. 10, March 12, 2009, pp. 112–116, published an article-interview — titled “Scacco matematico” (“Mathematical check”) — by Piergiorgio Odifreddi with Robert Mundell, a Nobel laureate in Economic Science and the so-called “Father of the Euro”, with whom he shared a passion for chess. “Result: a journey from Keynes through Bobby Fischer to us”. Here is an excerpt from the passage in question:

— I know that you met Bobby Fischer, exiled from the United States for violating the embargo against Yugoslavia in 1992, and then lived in Iceland as a somewhat paranoid man... — I went in Iceland to a conference, a couple of years ago, and I found a friend who knew a friend of his. Thus we arranged a meeting at my hotel. — And how did it go? — After we were introduced, he noticed that we bore the same name. For some reason we hit it off immediately, and spent hours together in one of his favourite bars, where people let him stay in peace. Then, whenever I returned to Reykjavík I saw him again, often along with his wife and some friends of his. — What were you talking about? — I about chess with him, and he about economics with me. We exchanged information, in our respective domains. We spent a lot of time discussing the history of chess and ranking the players. — What was his interest in the economics? — Its applications to Iceland, for example: he thought it was going in the wrong direction, and that sooner or later it would get into trouble. And he wasn’t all wrong, given that Iceland was one of the first countries to feel the effects of the current financial crisis, in October 2008, and one of the most strongly affected by it. A skillful chess player also understands economics. It is the rationality. — Did you ever play chess with Fischer? — Once. On one of my visits, I invited him, his wife and their friends to my hotel for lunch, but when they arrived the restaurant was still not ready. So we went up to my suite, I asked him if he wanted to play, and he accepted. But first he asked me what my Elo rating was. I had to confess I had none at all. He played with White, and made his favourite opening: the Ruy López, with the King’s Pawn. At one point I captured one of his Pawn with my Knight, and he warned me that this way I would lose a piece. I answered him that I knew it. Indeed I lost the Knight, but I gained two Pawns, finding myelf in a great position and threatening a check. — How did he take it? — He leaned back in his chair and said to me: “You play much better than I thought! I believed you were just a woodpusher”. Then he studied the board for a minute or two, and resumed playing. After a while his King managed to escape to the central squares, and I remained a Pawn down, albeit with a slight advantage in position. At that time, we were told that the lunch was served, and I resigned because I thought that all in all he was better than me. — And did he agree? — At table we assessed the pros and cons, and he decided that in the end he would win. — Have you ever happened to play so-called Fischer’s chess with him, with the pieces placed (almost) randomly at the start? — No, but we talked about it. It seems a very good idea to me, like shuffling a deck of cards: beginning from starting random arrays, creativity and talent get the upper hand over memorisation of the openings. It would also be a very good school of thought for economists.