Can there be more than one saddle point in a matrix?
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.
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.
- Payoff Matrix. An matrix which gives the possible outcome of a two-person zero-sum game when player A has possible moves and player B moves. The analysis of the matrix in order to determine optimal strategies is the aim of game theory.
- 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.
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.
- Whittow describes a saddle as "low point or col on a ridge between two summits", whilst the Oxford Dictionary of English implies that a col is the lowest point on the saddle. Monkhouse describes a saddle as a "broad, flat col in a ridge between two mountain summits."
- The saddle is a supportive structure for a rider or other load, fastened to an animal's back by a girth. The most common type is the equestrian saddle designed for a horse. However, specialized saddles have been created for camels and other creatures.
- The flex tree allows the saddle to flex from front to back and side to side. Dakota, Fabtron, Big Horn, and High Horse by Circle Y all use a Ralide flex tree. The one difference in the High Horse flex is that the ball of the bar (where the saddle meets your horse in the front) is made out of neoprene for extra comfort.
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.
- Definition of unstable equilibrium. : a state of equilibrium of a body (as a pendulum standing directly upward from its point of support) such that when the body is slightly displaced it departs further from the original position — compare stable equilibrium.
- 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.
- conditions. In equilibrium. …equilibrium is said to be stable if small, externally induced displacements from that state produce forces that tend to oppose the displacement and return the body or particle to the equilibrium state. Examples include a weight suspended by a spring or a brick lying on a level surface.
Updated: 2nd October 2019