Strategy (game theory)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.
Extensive-form gameIn game theory, an extensive-form game is a specification of a game allowing 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 game outcomes.
Symmetric gameIn game theory, a symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. If one can change the identities of the players without changing the payoff to the strategies, then a game is symmetric. Symmetry can come in different varieties. Ordinally symmetric games are games that are symmetric with respect to the ordinal structure of the payoffs.
Complete informationIn economics and game theory, complete information is an economic situation or game in which knowledge about other market participants or players is available to all participants. The utility functions (including risk aversion), payoffs, strategies and "types" of players are thus common knowledge. Complete information is the concept that each player in the game is aware of the sequence, strategies, and payoffs throughout gameplay.
Game theoryMathematical models of strategic interactionsGame theory is the field of applied mathematics that models interactions between multiple agents as "games" of strategy between "players". It is a scientific method of describing, predicting, evaluating, and selecting choices (or "actions"), often with the view of maximising utility outcomes (or "payoffs") for one or more players.
Perfect informationPerfect information is a concept in game theory and economics that describes a situation where all players in a game or all participants in a market have knowledge of all relevant information in the system. This is different than complete information, which implies common knowledge of each agent's utility functions, payoffs, strategies and "types". A system with perfect information may or may not have complete information.
Matrix (mathematics)Array of numbersAn m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts.
Nash equilibriumSolution concept of a non-cooperative gameIn game theory, a Nash equilibrium is a situation where no player could gain more by changing their own strategy (holding all other players' strategies fixed) in a game. A Nash equilibrium is the most commonly used solution concept for non-cooperative games.
Graph (discrete mathematics)In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line).
Cardinal utilityIn economics, a cardinal utility expresses not only which of two outcomes is preferred, but also the intensity of preferences, i.e. how much better or worse one outcome is compared to another. In consumer choice theory, economists originally attempted to replace cardinal utility with the apparently weaker concept of ordinal utility.
Strategic dominanceIn game theory, a strategy Adominates another strategy B if A will always produce a better result than B, regardless of how any other player plays. Some very simple games (called straightforward games) can be solved using dominance. TerminologyA player can compare two strategies, A and B, to determine which one is better.
Ordinal utilityIn economics, an ordinal utility function is a function representing the preferences of an agent on an ordinal scale. Ordinal utility theory claims that it is only meaningful to ask which option is better than the other, but it is meaningless to ask how much better it is or how good it is. All of the theory of consumer decision-making under conditions of certainty can be, and typically is, expressed in terms of ordinal utility.*As an Amazon Associate I earn from qualifying purchases.