Game Theory:

A game is a formal description of a strategic situation.

Game theory is the formal study of decision-making where several players must make choices that potentially affect the interests of the other players.

Mixed strategy

A mixed strategy is an active randomization, with given a probability that determines the player’s decision. As a special case, mixed strategy can be the deterministic choice of one of the given pure strategies.

Strategic equilibrium

A Strategic equilibrium, also called Nash equilibrium, is a list of strategies, one for each player, which has the property that no player can unilaterally change his strategy and get a better payoff.

Payoff

A payoff is a number, also called utility that reflects the desirability of an outcome to a player, for whatever reason. When the outcome is random, payoffs are usually weighted with their probabilities. The expected payoff incorporates the player’s attitude towards risk. The object of study in game theory is the game, which is a formal model of an interactive situation. It typically involves several players; a game with only one player is usually called a decision problem. The formal definition lays out the players, their preferences, their information, the strategic actions available to them, and how these influence the outcome.

Levels of games:

A coalitional (or cooperative) game is a high-level description, specifying only what payoffs each potential group, or coalition, can obtain by the cooperation of its members. What is not made explicit is the process by which the coalition forms.

As an example, the players may be several parties in parliament. Each party has a different strength, based upon the number of seats occupied by party members.

The game describes which coalitions of parties can form a majority, but does not explain, for example, the negotiation process through which an agreement to vote en bloc is achieved.

Non-cooperative game theory is concerned with the analysis of strategic choices. The paradigm of non-cooperative game theory is that the details of the ordering and timing of players’ choices are crucial to determining the outcome of a game.

The term “non-cooperative” means this branch of game theory explicitly models the process of 6 players making choices out of their own interest.

Branches of game theory:

A central assumption in many variants of game theory is that the players are rational. A rational player is one who always chooses an action which gives the outcome he most prefers, given what he expects his opponents to do.