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Determined game (or Strictly determined game) In game theory, a strictly determined game is a two-player zero-sum game that has at least one Nash equilibrium with both players using pure strategies. [2] [3] Dictator A player is a strong dictator if he can guarantee any outcome regardless of the other players.
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]
Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two competing entities, where the result is an advantage for one side and an equivalent loss for the other. [1]
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 the mathematical theory of games, in particular the study of zero-sum continuous games, not every game has a minimax value. This is the expected value to one of the players when both play a perfect strategy (which is to choose from a particular PDF). This article gives an example of a zero-sum game that has no value. It is due to Sion and ...
The game of Go is one of the most popular games in the world. As a result of its elegant and simple rules, the game has long been an inspiration for mathematical research. Shen Kuo , an 11th century Chinese scholar, estimated in his Dream Pool Essays that the number of possible board positions is around 10 172 .
The first theorem in this sense is von Neumann's minimax theorem about two-player zero-sum games published in 1928, [2] which is considered the starting point of game theory. Von Neumann is quoted as saying "As far as I can see, there could be no theory of games
In game theory, a game is said to be a potential game if the incentive of all players to change their strategy can be expressed using a single global function called the potential function. The concept originated in a 1996 paper by Dov Monderer and Lloyd Shapley. [1] The properties of several types of potential games have since been studied.