Published online by Cambridge University Press: 05 June 2012
A strategic interaction wherein outcomes are systematically determined by the combination of players' actions is called a game. By this definition, poker and baseball are games, but so are wars and arms rivalries. Because outcomes in games are jointly determined, players' well-being depends not only on their own decisions but also on the decisions of others. This interdependence can greatly complicate any attempted rational choice by the players. It also makes game theory, the formal study of such strategic interaction, both challenging and fascinating.
Elements of a Game
Games consist of certain elements, the specifics of which distinguish the different games. The players may be individuals or groups, including nations. Explicit and/or implicit rules control the feasible actions, order of play, available information, and determination of outcomes. Preferences over outcomes in turn determine players' payoffs or utilities. In basic game theory, players are assumed to have common knowledge of the rationality of all players and of the elements of the game, including payoffs. When these assumptions hold, the game is said to be one of complete information.
To illustrate these elements, consider a simple game that we will refer to as the aggression game. The game involves two players called, generically, A and B. Player A moves first and can either Aggress against player B or Refrain. If B is aggressed against, then B can either Retaliate or Appease.