Explain the concept of zero-sum games in game theory.

Zero-sum games are games in which one player's gain is equal to another player's loss.

In game theory, a zero-sum game is a type of game in which the total payoff for all players involved is zero. This means that any gain made by one player is exactly offset by a loss made by another player. In other words, the sum of the payoffs for all players is always zero, hence the name "zero-sum game".

Examples of zero-sum games include poker, chess, and rock-paper-scissors. In poker, for example, the total amount of money in the pot is fixed, and any gain made by one player is at the expense of another player's loss. Similarly, in chess, any gain made by one player in terms of capturing an opponent's piece is offset by the loss of that piece for the opponent.

Zero-sum games are often used in economics to model situations where resources are limited and one person's gain comes at the expense of another person's loss. They are also used in political science to model situations where one country's gain comes at the expense of another country's loss.

In order to analyse zero-sum games, game theorists use a variety of mathematical tools, including matrix algebra and the minimax theorem. The minimax theorem states that in any zero-sum game, there exists a strategy for each player that guarantees the best possible outcome, regardless of the other player's strategy. This is known as the minimax strategy, and it is a key concept in game theory.