Zero-Sum Games and the Minimax Theorem: Classical Strictly-Competitive Theory
A rational competitor can guarantee a specific number - not a hope, not a range, an exact number - before a single card is dealt, a single kick is taken, or a single shot is fired. That is the promise of the minimax theorem, and this book teaches you to actually use it.
Zero-Sum Games and the Minimax Theorem is a working manual for the branch of game theory where one side's gain is always the other's exact loss. Inside, you'll learn to solve real payoff matrices by hand: spotting saddle points, eliminating dominated strategies, calculating optimal mixed strategies with a formula you can memorize, and reading the graphical and linear-programming methods that scale the same logic up to problems of any size.
Then the theory goes to work. Matching pennies and the ancient hand game morra reveal why unpredictability itself has a calculable price. A simplified poker model shows that bluffing isn't a psychological trick - it's a precise probability. Decades of professional soccer penalty-kick data confirm that elite athletes, without ever doing the math, converge on exactly the mixed strategy the theorem predicts. And the 1943 Battle of the Bismarck Sea shows the same logic driving a real wartime decision with real historical consequences.
The book closes with an extended, deliberately pointed warning: zero-sum thinking, powerful where it genuinely applies, is one of the most commonly misapplied ideas in economics and public debate. A separate chapter draws the line clearly - showing exactly where this framework stops being useful, in markets, trade, and negotiation, and why.
The second volume in a ten-book series tracing game theory from its founding proofs to its modern applications, written for readers of economics, history, and strategy - no advanced mathematics required.
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