Popularized by movies such as "A Beautiful Mind," game theory is the mathematical modeling of strategic interaction among rational (and irrational) agents. Beyond what we call `games' in common language, such as chess, poker, soccer, etc., it includes the modeling of conflict among nations, political campaigns, competition among firms, and trading behavior in markets such as the NYSE. How could you begin to model keyword auctions, and peer to peer file-sharing networks, without accounting for the incentives of the people using them? The course will provide the basics: representing games and strategies, the extensive form (which computer scientists call game trees), Bayesian games (modeling things like auctions), repeated and stochastic games, and more. We'll include a variety of examples including classic games and a few applications.
Although backward induction is a cornerstone of game theory, most laboratory experiments have found that agents are not able to successfully backward induct. Much of this evidence, however, is generated using the Centipede game, which is ill-suited for testing the theory. In this study, we analyze the play of world class chess players both in the centipede game and in another class of games - Race to 100 games - that are pure tests of backward induction. We find that world class chess players behave like student subjects in the centipede game, virtually never playing the backward induction equilibrium In the race to 100 games, in contrast, we find that many chess players properly backward induct. Consistent with our claim that the Centipede game is not a useful test of backward induction, we find no systematic within-subject relationship between choices in the centipede game and performance in pure backward induction games.
chess game theory pdf download
Chess is a board game between two players. It is sometimes called international chess or Western chess to distinguish it from related games, such as xiangqi (Chinese chess) and shogi (Japanese chess). The current form of the game emerged in Spain and the rest of Southern Europe during the second half of the 15th century after evolving from chaturanga, a similar but much older game of Indian origin. Today, chess is one of the world's most popular games, played by millions of people worldwide.
Chess is an abstract strategy game and involves no hidden information. It is played on a chessboard with 64 squares arranged in an eight-by-eight grid. At the start, each player controls sixteen pieces: one king, one queen, two rooks, two bishops, two knights, and eight pawns. The player controlling the white pieces moves first, followed by the player controlling the black pieces. The object of the game is to checkmate the opponent's king, whereby the king is under immediate attack (in "check") and there is no way for it to escape. There are also several ways a game can end in a draw.
Organized chess arose in the 19th century. Chess competition today is governed internationally by FIDE (the International Chess Federation). The first universally recognized World Chess Champion, Wilhelm Steinitz, claimed his title in 1886; Magnus Carlsen is the current World Champion. A huge body of chess theory has developed since the game's inception. Aspects of art are found in chess composition, and chess in its turn influenced Western culture and art, and has connections with other fields such as mathematics, computer science, and psychology.
One of the goals of early computer scientists was to create a chess-playing machine. In 1997, Deep Blue became the first computer to beat the reigning World Champion in a match when it defeated Garry Kasparov. Today's chess engines are significantly stronger than the best human players and have deeply influenced the development of chess theory.
The game is played on a square board of eight rows (called ranks) and eight columns (called files). By convention, the 64 squares alternate in color and are referred to as light and dark squares; common colors for chessboards are white and brown, or white and dark green.
The object of the game is to checkmate the opponent; this occurs when the opponent's king is in check, and there is no legal way to get it out of check. It is never legal for a player to make a move that puts or leaves the player's own king in check. In casual games, it is common to announce "check" when putting the opponent's king in check, but this is not required by the rules of chess and is not usually done in tournaments.[2]
In competition, chess games are played with a time control. If a player's time runs out before the game is completed, the game is automatically lost (provided the opponent has enough pieces left to deliver checkmate).[1] The duration of a game ranges from long (or "classical") games, which can take up to seven hours (even longer if adjournments are permitted), to bullet chess (under 3 minutes per player for the entire game). Intermediate between these are rapid chess games, lasting between one and two hours per game, a popular time control in amateur weekend tournaments.
Portable Game Notation (PGN) is a text-based file format for recording chess games, based on short form English algebraic notation with a small amount of markup. PGN files (suffix .pgn) can be processed by most chess software, as well as being easily readable by humans.
Until about 1980, the majority of English language chess publications used descriptive notation, in which files are identified by the initial letter of the piece that occupies the first rank at the beginning of the game. In descriptive notation, the common opening move 1.e4 is rendered as "1.P-K4" ("pawn to king four"). Another system is ICCF numeric notation, recognized by the International Correspondence Chess Federation though its use is in decline.
Chess theory usually divides the game of chess into three phases with different sets of strategies: the opening, typically the first 10 to 20 moves, when players move their pieces to useful positions for the coming battle; the middlegame; and last the endgame, when most of the pieces are gone, kings typically take a more active part in the struggle, and pawn promotion is often decisive.
Opening theory is concerned with finding the best moves in the initial phase of the game. There are dozens of different openings, and hundreds of variants. The Oxford Companion to Chess lists 1,327 named openings and variants.[22]
Endgame theory is concerned with positions where there are only a few pieces left. Theoretics categorize these positions according to the pieces, for example "King and pawn endings" or "Rook versus a minor piece".
A chess opening is the group of initial moves of a game (the "opening moves"). Recognized sequences of opening moves are referred to as openings and have been given names such as the Ruy Lopez or Sicilian Defense. They are catalogued in reference works such as the Encyclopaedia of Chess Openings. There are dozens of different openings, varying widely in character from quiet positional play (for example, the Réti Opening) to very aggressive (the Latvian Gambit). In some opening lines, the exact sequence considered best for both sides has been worked out to more than 30 moves.[23] Professional players spend years studying openings and continue doing so throughout their careers, as opening theory continues to evolve.
The game of chess was then played and known in all European countries. A famous 13th-century Spanish manuscript covering chess, backgammon, and dice is known as the Libro de los juegos, which is the earliest European treatise on chess as well as being the oldest document on European tables games. The rules were fundamentally similar to those of the Arabic shatranj. The differences were mostly in the use of a checkered board instead of a plain monochrome board used by Arabs and the habit of allowing some or all pawns to make an initial double step. In some regions, the Queen, which had replaced the Wazir, and/or the King could also make an initial two-square leap under some conditions.[63]
Writings about chess theory began to appear in the late 15th century. An anonymous treatise on chess of 1490 with the first part containing some openings and the second 30 endgames is deposited in the library of the University of Göttingen.[71] The book El Libro dels jochs partitis dels schachs en nombre de 100 was written by Francesc Vicent in Segorbe in 1495, but no copy of this work has survived.[71] The Repetición de Amores y Arte de Ajedrez (Repetition of Love and the Art of Playing Chess) by Spanish churchman Luis Ramírez de Lucena was published in Salamanca in 1497.[68] Lucena and later masters like Portuguese Pedro Damiano, Italians Giovanni Leonardo Di Bona, Giulio Cesare Polerio and Gioachino Greco, and Spanish bishop Ruy López de Segura developed elements of opening theory and started to analyze simple endgames.
At the same time, the intellectual movement of romanticism had had a far-reaching impact on chess, with aesthetics and tactical beauty being held in higher regard than objective soundness and strategic planning. As a result, virtually all games began with the Open Game, and it was considered unsportsmanlike to decline gambits that invited tactical play such as the King's Gambit and the Evans Gambit.[75] This chess philosophy is known as Romantic chess, and a sharp, tactical style consistent with the principles of chess romanticism was predominant until the late 19th century.[76]
As the 19th century progressed, chess organization developed quickly. Many chess clubs, chess books, and chess journals appeared. There were correspondence matches between cities; for example, the London Chess Club played against the Edinburgh Chess Club in 1824.[79] Chess problems became a regular part of 19th-century newspapers; Bernhard Horwitz, Josef Kling, and Samuel Loyd composed some of the most influential problems. In 1843, von der Lasa published his and Bilguer's Handbuch des Schachspiels (Handbook of Chess), the first comprehensive manual of chess theory. 2ff7e9595c
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