What is the saddle point of a matrix?
Given a matrix of n x n size, the task is to find saddle point of the matrix. A saddle point is an element of the matrix such that it is the minimum element in its row and maximum in its column.
A necessary and sufficient condition for a saddle point to exist is the presence of a payoff matrix element which is both a minimum of its row and a maximum of its column. A game may have more than one saddle point, but all must have the same value. SEE ALSO: Game, Payoff Matrix, Value.
- In game theory, strategic dominance (commonly called simply dominance) occurs when one strategy is better than another strategy for one player, no matter how that player's opponents may play.
- Zero-sum is a situation in game theory in which one person's gain is equivalent to another's loss, so the net change in wealth or benefit is zero. A zero-sum game may have as few as two players, or millions of participants. Zero-sum games are found in game theory, but are less common than non-zero sum games.
- Fair Game. A game which is not biased toward any player. A game in which a given player can always win by playing correctly is therefore called an unfair game. SEE ALSO: Futile Game, Game, Martingale, Unfair Game.
If a critical point is not stable then it is unstable. In the figure above we see that a center is stable but not asymptotically stable, that a saddle point is unstable, that a node is either asymptotically stable (sink) or unstable (source) and that a spiral either is asymptotically stable or unstable.
- These economic variables remain unchanged from their equilibrium values in the absence of external influences. Economic equilibrium may also be defined as the point at which supply equals demand for a product, with the equilibrium price existing where the hypothetical supply and demand curves intersect.
- (Mech.) the kind of equilibrium of a body so placed that when moved slighty it neither tends to return to its former position not depart more widely from it, as a perfect sphere or cylinder on a horizontal plane. See also: Neutral.
- The direction field is defined as the collection of small line segments passing through various points having a slope that will satisfy the given differential equation (see Graph) at that point. These lines can then be sketched in lightly to aid in constructing the direction field (see Graph).
Game Saddle Point. A necessary and sufficient condition for a saddle point to exist is the presence of a payoff matrix element which is both a minimum of its row and a maximum of its column. A game may have more than one saddle point, but all must have the same value.
- Game theory is the process of modeling the strategic interaction between two or more players in a situation containing set rules and outcomes. While used in a number of disciplines, game theory is most notably used as a tool within the study of economics.
- John von Neumann
- Lloyd S. Shapley, 92, Nobel Laureate and a Father of Game Theory, Is DeadLloyd S. Shapley, 92, Nobel Laureate and a Father of Game Theory, Is Dead.
Updated: 21st September 2018