26-07-2012, 02:22 PM
GAME THEORY
GAME THEORY.docx (Size: 155.56 KB / Downloads: 32)
INTRODUCTION TO GAME THEORY
Definition of Game Theory
Thestudyof mathematical models of conflict and cooperation between intelligent rational decision-makers.
Game theory is a method of studying strategic decision making. More formally, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." An alternative term suggested "as a more descriptive name for the discipline" is interactive decision theory. Game theory is mainly used in economics, political science, and psychology, as well as logic and biology. The subject first addressed zero-sum games, such that one person's gains exactly equal net losses of the other participant(s). Today, however, game theory applies to a wide range of class relations, and has developed into an umbrella term for the logical side of science, to include both human and non-humans, like computers. Classic uses include a sense of balance in numerous games, where each person has found or developed a tactic that cannot successfully better his results, given the other approach.
History
The Danish mathematician Zeuthen proved that a mathematical model has a winning strategy by using Brouwer's fixed point theorem. In his 1938 bookApplications aux Jeux de Hasard and earlier notes, ÉmileBorel proved a minimax theorem for two-person zero-sum matrix games only when the pay-off matrix was symmetric. Borel conjectured that non-existence of a mixed-strategy equilibria in two-person zero-sum games would occur, a conjecture that was proved false.
Game theory did not really exist as a unique field until John von Neumann published a paper in 1928. His paper was followed by his 1944 book Theory of Games and Economic Behavior, with Oskar Morgenstern, which considered cooperative games of several players. Von Neumann's work in game theory culminated in the 1944 book Theory of Games and Economic Behavior by von Neumann andOskar Morgenstern. This foundational work contains the method for finding mutually consistent solutions for two-person zero-sum games. During this time period, work on game theory was primarily focused on cooperative game theory, which analyses optimal strategies for groups of individuals, presuming that they can enforce agreements between them about proper strategies.
TYPES OF GAMES
Cooperative or non-cooperative
A game is cooperative if the players are able to form binding commitments. For instance the legal system requires them to adhere to their promises. In non-cooperative games this is not possible.Often it is assumed that communication among players is allowed in cooperative games, but not in non-cooperative ones. However, this classification on two binary criteria has been questioned, and sometimes rejected (Harsanyi 1974).
Of the two types of games, non-cooperative games are able to model situations to the finest details, producing accurate results. Cooperative games focus on the game at large. Considerable efforts have been made to link the two approaches. The so-called Nash-programmehas already established many of the cooperative solutions as non-cooperativeequilibria.Hybrid games contain cooperative and non-cooperative elements. For instance, coalitions of players are formed in a cooperative game, but these play in a non-cooperative fashion.
GAME THEORY.docx (Size: 155.56 KB / Downloads: 32)
INTRODUCTION TO GAME THEORY
Definition of Game Theory
Thestudyof mathematical models of conflict and cooperation between intelligent rational decision-makers.
Game theory is a method of studying strategic decision making. More formally, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." An alternative term suggested "as a more descriptive name for the discipline" is interactive decision theory. Game theory is mainly used in economics, political science, and psychology, as well as logic and biology. The subject first addressed zero-sum games, such that one person's gains exactly equal net losses of the other participant(s). Today, however, game theory applies to a wide range of class relations, and has developed into an umbrella term for the logical side of science, to include both human and non-humans, like computers. Classic uses include a sense of balance in numerous games, where each person has found or developed a tactic that cannot successfully better his results, given the other approach.
History
The Danish mathematician Zeuthen proved that a mathematical model has a winning strategy by using Brouwer's fixed point theorem. In his 1938 bookApplications aux Jeux de Hasard and earlier notes, ÉmileBorel proved a minimax theorem for two-person zero-sum matrix games only when the pay-off matrix was symmetric. Borel conjectured that non-existence of a mixed-strategy equilibria in two-person zero-sum games would occur, a conjecture that was proved false.
Game theory did not really exist as a unique field until John von Neumann published a paper in 1928. His paper was followed by his 1944 book Theory of Games and Economic Behavior, with Oskar Morgenstern, which considered cooperative games of several players. Von Neumann's work in game theory culminated in the 1944 book Theory of Games and Economic Behavior by von Neumann andOskar Morgenstern. This foundational work contains the method for finding mutually consistent solutions for two-person zero-sum games. During this time period, work on game theory was primarily focused on cooperative game theory, which analyses optimal strategies for groups of individuals, presuming that they can enforce agreements between them about proper strategies.
TYPES OF GAMES
Cooperative or non-cooperative
A game is cooperative if the players are able to form binding commitments. For instance the legal system requires them to adhere to their promises. In non-cooperative games this is not possible.Often it is assumed that communication among players is allowed in cooperative games, but not in non-cooperative ones. However, this classification on two binary criteria has been questioned, and sometimes rejected (Harsanyi 1974).
Of the two types of games, non-cooperative games are able to model situations to the finest details, producing accurate results. Cooperative games focus on the game at large. Considerable efforts have been made to link the two approaches. The so-called Nash-programmehas already established many of the cooperative solutions as non-cooperativeequilibria.Hybrid games contain cooperative and non-cooperative elements. For instance, coalitions of players are formed in a cooperative game, but these play in a non-cooperative fashion.