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

Non-zero-sum games are games where the total gains and losses of all players do not add up to zero.

In game theory, a zero-sum game is one where the gains of one player are exactly balanced by the losses of the other player(s). In contrast, a non-zero-sum game is one where the total gains and losses of all players do not add up to zero. This means that it is possible for all players to benefit or all players to lose in a non-zero-sum game.

One example of a non-zero-sum game is the prisoner's dilemma. In this game, two suspects are arrested and held in separate cells. Each is given the opportunity to confess or remain silent. If both remain silent, they each receive a light sentence. If one confesses and the other remains silent, the confessor goes free and the other receives a heavy sentence. If both confess, they both receive a moderate sentence. This game is non-zero-sum because the total gains and losses of the two players do not add up to zero.

Another example of a non-zero-sum game is the game of chicken. In this game, two drivers are driving towards each other and must decide whether to swerve or continue driving straight. If both swerve, they both avoid a collision. If one swerves and the other continues driving straight, the one who continues driving straight "wins" and the other "loses". If both continue driving straight, they both "lose" in a collision. This game is also non-zero-sum because the total gains and losses of the two players do not add up to zero.

In non-zero-sum games, players must consider the potential outcomes for all players involved, rather than just their own individual gains and losses. This can lead to more complex strategies and outcomes than in zero-sum games.