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Cooperative game theory is a branch of game theory that deals with the study of games where players can form coalitions, cooperate with one another, and make binding agreements. The theory offers mathematical methods for analysing scenarios in which two or more players are required to make choices that will affect other players wellbeing. [5]
In cooperative game theory, the Kalai-Smorodinsky solution reopened the study of bargaining by showing that the long unchallenged Nash solution is not unique. He later axiomatized the Egalitarian solution to bargaining problems and, with Dov Samet, formulated its extension to general (NTU) cooperative games, unifying it with the Shapley (TU) Value.
Constant sum: A game is a constant sum game if the sum of the payoffs to every player are the same for every single set of strategies. In these games, one player gains if and only if another player loses. A constant sum game can be converted into a zero sum game by subtracting a fixed value from all payoffs, leaving their relative order unchanged.
The game was introduced in 1957 by R. Duncan Luce and Howard Raiffa in their classic book, Games and Decisions. [1] Some authors prefer to avoid assigning sexes to the players and instead use Players 1 and 2, and some refer to the game as Bach or Stravinsky, using two concerts as the two events. [2]
In cooperative game theory, the Shapley value is a method (solution concept) for fairly distributing the total gains or costs among a group of players who have collaborated. For example, in a team project where each member contributed differently, the Shapley value provides a way to determine how much credit or blame each member deserves.
Game theory is the study of mathematical models of strategic interactions. [1] It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. [2]
Behavioral game theory seeks to examine how people's strategic decision-making behavior is shaped by social preferences, social utility and other psychological factors. [1] Behavioral game theory analyzes interactive strategic decisions and behavior using the methods of game theory, [2] experimental economics, and experimental psychology.
Consider a transferable utility cooperative game (,) where denotes the set of players and is the characteristic function.An imputation is dominated by another imputation if there exists a coalition , such that each player in weakly-prefers (for all ) and there exists that strictly-prefers (<), and can enforce by threatening to leave the grand coalition to form (()).