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Beautiful Game Theory

How Soccer Can Help Economics

By Ignacio Palacios-Huerta
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  • Contains 8 key ideas
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Beautiful Game Theory by Ignacio Palacios-Huerta
Synopsis

Beautiful Game Theory (2014) shows us how applicable economics is to our daily lives by looking at the fascinating world of professional soccer. By examining compelling statistics and studies on shoot-outs, referee calls, and ticket sales, Beautiful Game Theory offers some interesting insights into the psychology of behavioral economics.

Key idea 1 of 8

The minimax theorem explains and predicts how players act and what strategies they use.

To appreciate how soccer helps us understand economics, we first have to understand John Neumann’s minimax theorem. His game theory theorem concerns two-player zero-sum games, games in which the positive payoff for one player always means negative payoff for the other.

Minimax assumes that players choose strategies that aim to minimize their opponents’ maximum possible payoff – hence “minimax.” And since we’re talking about zero-sum games, this also means that each player also attempts to minimize his own maximum loss.

For example, in a game of Rock Paper Scissors, only one player can win, and the other will lose. Each player’s strategy is therefore to minimize the payoff (the win) for the other.

There are two such strategies: pure and mixed. Pure strategies are strategies whereby a player always chooses the same move (like playing Rock every time), whereas mixed strategies employ variations of Rock, Paper and Scissors.

An important hypothesis of minimax theory is that if it’s disadvantageous for the other player to know your choice in advance, then you will benefit from choosing random strategies.

For example, imagine that you are playing Rock Paper Scissors against a long-time friend. If you tend to play Paper most often, then your friend can easily exploit this by pursuing a pure strategy – that is, by always playing Scissors.

However, if one person plays pure and the other plays mixed, the mixed strategy will win two-thirds of the time. On the other hand, if both players play mixed strategies, then both will have equal chances to win.

Thus, if two players randomly play Rock, Paper or Scissors, they should each win 50 percent of the games.

Ideally, then, both players should mix moves, because every pure strategy would only have a 33 percent chance of winning.

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