What is saddle point in game theory

Let the optimal strategy be s a for player a and s b for player b.A saddle point is a concept that comes up in optimization generally, independently of game theory.The concept is illustrated with the help of following example.Saddle point ,in mathematics, is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local.Saddle point in game theory a point ( x ∗, y ∗) ∈ x × y of a function f defined on the cartesian product x × y of two sets x and y such that (*) f ( x ∗, y ∗) = max x ∈ x f ( x, y ∗) = min y ∈ y f ( x ∗, y).

Not only can we assist events of the past as they actually happened, but can interact with people in the past.(its name derives from its being the minimum of a row that is also the maximum of a column in a payoff matrix—to be illustrated shortly—which corresponds to the shape of… read more structure of nuclear matterLet q 1 and q 2 be the probability for player b.Given the count of the high body of the show, it would not be surprising if a number of important characters ends dead (or not dead), and as george r.If a i j is positive, row player pays the column, and vice versa.

The following proof seems redundant and too simple to be convincing, would.The element in a payoff matrix that is the smallest in a particular row while, at the same time, the largest in its column.Mixed strategy means a situation where a saddle point does not exist, the maximin (minimax) principle for solving a game problem breaks down.A point on a smooth surface such that the surface near the point lies on different sides of the tangent plane.