What is the concept of zero-sum games in game theory?

In game theory, zero-sum games refer to a type of game where the total utility or payoff gained by one player is exactly equal to the total utility or payoff lost by the other player(s). In other words, the gains and losses of the players involved in a zero-sum game always sum up to zero, hence the term "zero-sum."

In such games, the interests of the players are completely opposed to each other, meaning that any gain for one player directly corresponds to an equal loss for the other player(s). This implies that the total utility or payoff in the game remains constant throughout, regardless of the strategies employed by the players.

Zero-sum games are often represented in the form of a matrix, known as a payoff matrix, which outlines the possible strategies and corresponding payoffs for each player. Common examples of zero-sum games include poker, chess, and most competitive sports.

It is important to note that not all games fall under the category of zero-sum games. In non-zero-sum games, the total utility or payoff can vary, allowing for the possibility of win-win or lose-lose outcomes, where the interests of the players may align or diverge to different degrees.