Introduction to Game Theory pp 35-63 | Cite as

# Two-Person Zero-Sum Games

Chapter

## Abstract

Let \(
\vec \pi
\) be a game in normal form with strategy sets for every choice of

*X*_{1},...,*X*_{ N }We say that this game is*zero-sum*if$$
\sum\limits_{i = 1}^N {{\pi _i}\,({x_1},\,.\,.\,.\,,\,{x_N})\, = \,0,}
$$

*x*_{ i }∈*X*_{ i }, 1 ≤*i*≤*N*. The corresponding definition for a game in extensive form states that the sum of the components of \( \vec p(v) \) is zero for each terminal vertex*v*. This condition is certainly true for ordinary recreational games. It says that one player cannot win an amount unless the other players jointly lose the same amount. Nonrecreational games, however, tend not to be zero-sum. Competitive situations in economics and international politics are often of the type where the players can jointly do better by playing appropriately, and jointly do worse by playing stupidly. The phrase “zero-sum game” has entered the language of politics and business.### Keywords

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## Copyright information

© Springer-Verlag New York, Inc. 1994