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Beautiful Game TheoryHow Soccer Can Help Economics$
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Ignacio Palacios-Huerta

Print publication date: 2014

Print ISBN-13: 9780691144023

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691144023.001.0001

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Pelé Meets John Von Neumann in the Penalty Area

Pelé Meets John Von Neumann in the Penalty Area

(p.9) 1 Pelé Meets John Von Neumann in the Penalty Area
Beautiful Game Theory

Ignacio Palacios-Huerta

Princeton University Press

The movie A Beautiful Mind (2001) portrays the life and work of John F. Nash Jr., who received the Nobel Prize in Economics in 1994. A class of his theories deals with how people should behave in strategic situations that involve what are known as “mixed strategies,” that is, choosing among various possible strategies when no single one is always the best when you face a rational opponent. This chapter uses data from a specific play in soccer (a penalty kick) with professional players to provide the first complete test of a fundamental theorem in game theory: the minimax theorem. The minimax theorem can be regarded as a special case of the more general theory of Nash. It applies only to two-person, zero-sum or constant-sum games, whereas the Nash equilibrium concept can be used with any number of players and any mixture of conflict and common interest in the game.

Keywords:   soccer, penalty kick, game theory, minimax theorem, John F. Nash Jr., mixed strategies, equilibrium concept

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