n-person game

N-person games are a branch of game theory that involve more than two players. These games can be classified in various ways, including the number of players, the extent of information available to players, and whether players can communicate and make binding agreements.

In cooperative N-person games, players can form coalitions and make binding agreements. The von Neumann–Morgenstern theory analyzes these games by assigning values to coalitions and seeking stable outcomes, known as solutions, where no player has an incentive to deviate.

Noncooperative N-person games, on the other hand, do not allow for binding agreements. In these scenarios, the focus is on finding Nash equilibria, which are stable outcomes where no single player can improve their situation by unilaterally changing their strategy.1

A specific application of N-person games is in voting systems, where concepts like the Banzhaf value are used to measure a player's voting power based on their ability to influence outcomes.2