Question

Define Saddle point and explain.

Answer 1

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In this context, an equilibrium of a two-person zero-sum game where the payoff of one player is simultaneously maximized with respect to his own strategy choice and minimized with respect to the strategy choice of the other player.

Coming from one direction it looks like we've hit a maximum, but from another direction is looks like we've hit a minimum.

Here are 3 graphs:

y=x4 has a minimum at x=0

graph{y = x^4 [-12.35, 12.96, -6.58, 6.08]}

✔

y=−x2 has a maximum at x=0

graph{-x^2 [-12.35, 12.96, -6.58, 6.08]}

✔

y=x3 has a saddle point at x=0

graph{x^3 [-12.35, 12.96, -6.58, 6.08]}

Coming from the left it looks like a maximum, but coming from the right it looks like a minimum.

Here's one more for comparison:

y=−x5

graph{-x^5 [-10.94, 11.56, -5.335, 5.92]}

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