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In game theory, an extensive-form game is a specification of a game allowing (as the name suggests) for the explicit representation of a number of key aspects, like the sequencing of players' possible moves, their choices at every decision point, the (possibly imperfect) information each player has about the other player's moves when they make a decision, and their payoffs for all possible ...
Figure 1: A game tree which depicts each player's possible information set by showing the options at each vertex (A and B for player's 1 and 2 respectively) Information sets are used in extensive form games and are often depicted in game trees. Game trees show the path from the start of a game and the subsequent paths that can be made depending ...
Game theory experienced a flurry of activity in the 1950s, during which the concepts of the core, the extensive form game, fictitious play, repeated games, and the Shapley value were developed. The 1950s also saw the first applications of game theory to philosophy and political science.
A Simple game is a simplified form of a cooperative game, where the possible gain is assumed to be either '0' or '1'. A simple game is couple (N, W), where W is the list of "winning" coalitions, capable of gaining the loot ('1'), and N is the set of players.
An extensive form representation of a signaling game. In game theory, a signaling game is a type of a dynamic Bayesian game. [1] The essence of a signaling game is that one player takes action, the signal, to convey information to another player. Sending the signal is more costly if the information is false.
In game theory, the centipede game, first introduced by Robert Rosenthal in 1981, is an extensive form game in which two players take turns choosing either to take a slightly larger share of an increasing pot, or to pass the pot to the other player. The payoffs are arranged so that if one passes the pot to one's opponent and the opponent takes ...
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.
In a normal extensive form, each player knows exactly where they are at in the game and what moves have been previously made. The extensive form can be used to visualize the concept of complete information. By definition, players know where they are as depicted by the nodes, and the final outcomes as illustrated by the utility payoffs.