Game Theory - Nonzero-sum Games

Most conflict situations are not zero-sum games or limited to two players. A nonzero-sum game is one in which the amount won by the victor is not equal to the amount lost by the loser. The Minimax Theorem does not apply to either of these types of games, but various weaker forms of a solution have been proposed including noncooperative and cooperative solutions.

When more than two people are involved in a conflict, oftentimes players agree to form a coalition. These players act together, behaving as a single player in the game. There are two extremes of coalition formation; no formation and complete formation. When no coalitions are formed, games are said to be non-cooperative. In these games, each player is solely interested in her own payoff. A proposed solution to these types of conflicts is known as a non-cooperative equilibrium. This solution suggests that there is a point at which no player can gain an advantage by changing strategy. In a game when complete coalitions are formed, games are described as cooperative. Here, players join together to maximize the total payoff for the group. Various solutions have also been suggested for these cooperative games.