Operations research
Explainer
Saddle Points: When a Game Has a Sure Answer
Two mining firms bid for one contract, and neither can outsmart the other
Quick check · tap an answer to continue
Lesson notes
Key points
- In a two-person zero-sum game, whatever one player wins, the other player loses exactly.
- The row player looks at each row's worst payoff and picks the best of those, called the maximin.
- The column player finds each column's largest payoff and picks the smallest, called the minimax.
- Guess what happens when maximin equals minimax: that cell is a saddle point, and both play pure strategies.
Definitions
- Zero-sum game
- A game where one player's gain equals the other player's loss, so payoffs always sum to zero.
Takeaway: Maximin equals minimax means a saddle point and pure strategies.
Quick check: What must be true for a payoff matrix to have a saddle point?
- Maximin equals minimax
- All payoffs are positive
- The matrix is square
A saddle point exists only when the maximin and minimax values coincide.
Zero-sum gameMaximinMinimaxSaddle point
Lessons like this, for your syllabus.
Short narrated study videos written for your course, level and exam. Free to start.
Get lessons for your own syllabus