Saturday, 7 March 2009

Rationality & Game Theory - The Centipede Game & Chess Players



"Game theory is a branch of applied mathematics that is used in the social sciences (most notably economics), biology, engineering, political science, international relations, computer science (mainly for artificial intelligence), and philosophy." (Wikipedia),

The centipede game (introduced by Rosenthal, 1981) is one mathematical game which tests the conflicts between self-interest and mutual benefit in human interactions. The traditional centipede game had a limit of 100 rounds (hence the name). (see Wikipedia)

Ignacio Palacios-Huerta and Oscar Volij have recently published a study looking at the behaviour of skilled chess players playing the centipede game. (pdf link here)
The centipede game is perhaps the best example of what is known as “paradoxes of backward induction.”These paradoxes involve sequential games all of whose correlated equilibria, and a fortiori all its Nash equilibria, imply a very counterintuitive play.

A particular instance of the centipede game can be described as follows. A pile of $4 and a pile of $1 are lying on a table. Player I has two options, either to “stop” or to “continue.”If he stops, the game ends and he gets $4 while Player II gets the remaining dollar. If he continues, the two piles are doubled to $8 and $2, and Player II is faced with a similar decision: either to take the larger pile ($8), thus ending the game and leaving the smaller pile ($2) for Player I, or to let the piles double again and let Player I decide. The game continues for at most six rounds. If by then neither of the players have stopped, Player I gets $256 and Player II gets $64. Figure 1 depicts
this situation.

Palacios-Huerta and Volij found that the chess players were far more likely to play optimally than non-chess playing students. Amongst chess players, grandmasters always played optimally and took the $4. This increased rationality (hyper-rationality) amongst chess players has the disadvantage that they are less likely to share a larger reward through cooperation (suboptimal game strategy). I find this study very interesting. One interpretation of the results is that chess grandmasters may be more sociopathic or selfish than the average person (see chart above), i.e. by being more rational and less morally empathic to others.


CHESS PLAYERS PROPORTION OF OBSERVATIONS AT EACH TERMINAL NODE
BY TYPE OF PLAYER I IN THE PAIR

Chess Players - Economists



Below is a list of chess playing Economists:
  • Anderson, Benjamin (American economist, skilled chess player & friend of Capablanca) - Wikipedia
  • Bondarevsky, Igor (Economist by profession, coached Boris Spassky) - Wikipedia
  • Dell, Edmund (UK politician, historian, businessman & author of The Politics of Economic Interdependence 1987) - Obituary
  • Forintos, Gyozo (Hungarian Economist) - Wikipedia
  • Franklin, Benjamin (Polymath, statesman, economist, philosopher, inventor, scientist, musician and avid chess player) - Wikipedia
  • Friedman, Milton (Nobel prize winner, one of the most influential economists of the 20C) - Link
  • Gipslis, Aivars (Graduated from Latvian University as an Economist) - Link & Wikipedia
  • Karpov, Anatoly (degree from Leningrad State University) - ALCHEssMIST Chess Players & Wikipedia
  • Mundell, Robert Alexander (Professor of Economics, Columbia University & Nobel Prize winner 1999, "father of the Euro") - Chessbase Link
  • Novotelnov, Nikolai (Economist, chess journalist, Champion of the RSFSR in 1947) - Link
  • Rogoff, Ken (Professor of Economics, Harvard University) - Homepage
Any other suggestions welcome.

Chess Quote - Anatoly Karpov on Chess



Chess is everything: art, science, and sport.
-- Anatoly Karpov

Anatoly Yevgenyevich Karpov (born 1951) was undisputed World Chess Champion from 1975 to 1985. He was an academically gifted schoolboy who initially went on to study Mathematics at Moscow State University before transferring to Leningrad State University to graduate in Economics. Anatoly Karpov had a great rivalry with Garry Kasparov, contesting 5 World Championships, with Karpov having 19 wins, 21 losses, and 104 draws in 144 games. [see Wikipedia]

Chess Quote - Child Prodigies - Chess - Mathematics - Music


Chess, like mathematics and music, is a nursery for child prodigies.

-- Jamie Murphy (Time Magazine Monday April 21st 1986)

From article about the Polgar sisters (Susan 16 years old / Sophia 11 years old / Judit 9 years old) describing their exceptional performance at New York Open Chess Tournament in 1986.
(Time article link - Don't Play Around with the Polgars)


Caricature of child prodigy composer Erich Wolfgang Korngold, at the piano, surrounded by (from left) Siegfried Wagner, Max Reger, Artur Nikisch, Richard Strauss & Eugen d'Albert.

Chess In Literature - Geoffrey Chaucer - The Canterbury Tales



The Canterbury Tales is actually a collection of stories written between 1387 and 1400 by Geoffrey Chaucer. It is the story of a group of 30 pilgrims travelling to Canterbury (England). The pilgrims, who come from all levels of society, tell stories to each other, as they travel to Canterbury. Chaucer never actually finished this ambitious project and we are still uncertain about the order of the tales in the work. The printing press had not even been invented when Chaucer was writing The Canterbury Tales. As a result the manuscript was only available in several handwritten copies.

The game of chess is mentioned on one occasion in The Canterbury Tales. It occurs in "The Franklin's Tale":
Her friends saw that it was no alleviation, but grief for her, to roam by the sea, and planned to disport themselves somewhere else. They led her by rivers and springs and eke in other delectable places; they danced and they played at tables and chess.