Information set (game theory)

The information set is the basis for decision making in a game, which includes the actions available to both sides and the benefits of each action.The information set is an important concept in non-perfect games. In game theory, an information set is the set of all possible actions in the game for a given player, built on their observations and a set for a particular player that, given what that player has observed, shows the decision vertices available to the player which are undistinguishable to them at the current point in the game. For a better idea on decision vertices, refer to Figure 1. If the game has perfect information(The total knowledge possessed by a market participant of the state of an economic environment), every information set contains only one member, namely the point actually reached at that stage of the game, since each player knows the exact mix of chance moves and player strategies up to the current point in the game. Otherwise, it is the case that some players cannot be sure exactly what has taken place so far in the game and what their position is(what should they do). 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 on each player's next move. For non-perfect information game problems, there is hidden information. That is, each player does not have complete knowledge of the opponent's information, such as cards that do not appear in a poker game. Therefore, when constructing a game tree, it is difficult to determine precisely where a node is located based on known information alone, as we do not know certain information about our opponent. We can only be sure that we are at one of a range of possible nodes. This inability to distinguish the set of nodes in a particular player's game tree is known as the 'information set'.

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Information set (game theory)

Bayesian game

In game theory, a Bayesian game is a strategic decision-making model which assumes players have incomplete information. Players hold private information relevant to the game, meaning that the payoffs are not common knowledge. Bayesian games model the outcome of player interactions using aspects of Bayesian probability. They are notable because they allowed, for the first time in game theory, for the specification of the solutions to games with incomplete information. Hungarian economist John C.

Nash equilibrium

In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs.

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