Economics: the formal definition of a game

I gave a brief history of game theory in my introductory post. Game theory is about making actions based on what you think others might do, taking into account that other people are acting based on what you might do. The circularity is what makes game theory interesting.

For completeness, here is a formal definition of a game. A game involves three components:

1. A list of players
2. Moves each player can make (strategies)
3. A listing of payoffs, or benefits, for each player on each eventual outcome (a utility function for outcomes)

Game theory assumes that each player only cares about maximizing personal payoff. Sounds like a reasonable enough assumption for a business environment.