Game Theory by Brian Clegg

Author:Brian Clegg [Clegg, Brian]
Language: eng
Format: epub
ISBN: 0103448276
Publisher: Icon
Published: 2022-09-15T00:00:00+00:00

Nash equilibria

The most significant contribution Nash would make to game theory was to describe an outcome known as a Nash equilibrium. Imagine, for example, a game where each player can choose red or blue. Player 1 chooses red and player 2 chooses blue. This solution is a Nash equilibrium if things would not be better for player 1 by choosing blue, and things would not be better for player 2 by choosing red. In some games, such as the prisoner’s dilemma, there is a single Nash equilibrium (in that case, reneging on each other), but there can be more than one. As this demonstrates, unlike von Neumann’s minimax strategy, which only applies to zero-sum games, Nash equilibria are available for applications with more complex outcomes.

For example, consider a game where there is £5 available in a pot. Two players are given the choice of asking for £2 or £3. If they choose the same amount they get nothing, but if they choose different amounts they get what they ask for. Here, both outcomes where they win something is a Nash equilibrium, because in either case, each player is making the best decision given the choice of the other player.

Player 1 ↓ | Player 2 → £2 £3

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