Game theory is the branch of mathematics in which games are studied: that is, models describing human behaviour. This is a glossary of some terms of the subject.

Definitions of a game

Notational conventions

\sigma\ _i is an element of \Sigma\ ^i. an element of, is a tuple of strategies for all players other than i.

Normal form game

A game in normal form is a function: Given the tuple of strategies chosen by the players, one is given an allocation of payments (given as real numbers). A further generalization can be achieved by splitting the game into a composition of two functions: the outcome function of the game (some authors call this function "the game form"), and: the allocation of payoffs (or preferences) to players, for each outcome of the game.

Extensive form game

This is given by a tree, where at each vertex of the tree a different player has the choice of choosing an edge. The outcome set of an extensive form game is usually the set of tree leaves.

Cooperative game

A game in which players are allowed to form coalitions (and to enforce coalitionary discipline). A cooperative game is given by stating a value for every coalition: It is always assumed that the empty coalition gains nil. Solution concepts for cooperative games usually assume that the players are forming the grand coalition N, whose value \nu(N) is then divided among the players to give an allocation.

Simple game

A Simple game is a simplified form of a cooperative game, where the possible gain is assumed to be either '0' or '1'. A simple game is couple (N, W), where W is the list of "winning" coalitions, capable of gaining the loot ('1'), and N is the set of players.

Glossary