Mixed Strategy Equilibria in the context of "Game theory"

⭐ In the context of Game theory, Mixed Strategy Equilibria initially emerged as a solution concept within what specific type of game?

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⭐ Core Definition: Mixed Strategy Equilibria

In game theory, a move, action, or play is any one of the options which a player can choose in a setting where the optimal outcome depends not only on their own actions but also on the actions of others. The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players. Some examples of "games" include chess, bridge, poker, monopoly, diplomacy or battleship.

The term strategy is typically used to mean a complete algorithm for playing a game, telling a player what to do for every possible situation. A player's strategy determines the action the player will take at any stage of the game. However, the idea of a strategy is often confused or conflated with that of a move or action, because of the correspondence between moves and pure strategies in most games: for any move X, "always play move X" is an example of a valid strategy, and as a result every move can also be considered to be a strategy. Other authors treat strategies as being a different type of thing from actions, and therefore distinct.

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👉 Mixed Strategy Equilibria in the context of Game theory

Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of behavioral relations. It is now an umbrella term for the science of rational decision making in humans, animals, and computers.

Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by Theory of Games and Economic Behavior (1944), co-written with Oskar Morgenstern, which considered cooperative games of several players. The second edition provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.

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