Game Theory Part I Vocab

Asymmetric Information

Information is said to be asymmetric in a game if some aspects of it—rules about what actions are permitted and the order of moves if any, payoffs as functions of the players strategies, outcomes of random choices by "nature," and of previous actions by the actual players in the game—are known to some of the players but are not common knowledge among all players.

Constant-Sum Game

A game in which the sum of all players' payoffs is a constant, the same for all their strategy combinations. Thus, there is a strict conflict of interests among the players—a higher payoff to one must mean a lower payoff to the collectivity of all the other players. If the payoff scales can be adjusted to make this constant equal to zero, then we have a zero-sum game.

Cooperative Game

A game in which the players decide and implement their strategy choices jointly, or where joint-action agreements are directly and collectively enforced.

Equilibrium

A configuration of strategies where each player's strategy is his best response to the strategies of all the other players.

Evolutionary Game

A situation where the strategy of each player in a population is fixed genetically, and strategies that yield higher payoffs in random matches with others from the same population reproduce faster than those with lower payoffs.

Expected Payoff

The probability-weighted average (statistical mean or expectation) of the payoffs of one player in a game, corresponding to all possible realizations of a random choice of nature or mixed strategies of the players.

External Uncertainty

A player's uncertainty about external circumstances such as the weather or product quality.

Game (Game of Strategy)

An action situation where there are two or more mutually aware players, and the outcome for each depends on the actions of all.

Imperfect Information

A game is said to have perfect information if each player, at each point where it is his turn to act, knows the full history of the game up to that point, including the results of any random actions taken by nature or previous actions of other players in the game, including pure actions as well as the actual outcomes of any mixed strategies they may play. Otherwise, the game is said to have imperfect information.

Noncooperative Game

A game where each player chooses and implements his action individually, without any joint-action agreements directly enforced by other players.

Payoff

The objective, usually numerical, that a player in a game aims to maximize.

Perfect Information

A game is said to have perfect information if players face neither strategic nor external uncertainty.

Rational Behavior

Perfectly calculating pursuit of a complete and internally consistent objective (payoff) function.

Screening

Strategy of a less-informed player to elicit information credibly from a more-informed player.

Screening Devices

Methods used for screening.

Sequential Moves

The moves in a game are sequential if the rules of the game specify a strict order such that at each action node only one player takes an action, with knowledge of the actions taken (by others or himself) at previous nodes.

Signals

Devices used for signaling.

Signaling

Strategy of a more-informed player to convey his "good" information credibly to a less-informed player.

Simultaneous Moves

The moves in a game are simultaneous if each player must take his action without knowledge of the choices of others.

Strategic Uncertainty

A player's uncertainty about an opponent's moves made in the past or made at the same time as her own.

Strategy

A complete plan of action for a player in a game, specifying the action he would take at all nodes where it is his turn to act according to the rules of the game (whether these nodes are on or off the equilibrium path of play). If two or more nodes are grouped into one information set, then the specified action must be the same at all these nodes.

Zero-Sum Game

A game where the sum of the payoffs of all players equals zero for every configuration of their strategy choices. (This is a special case of a constant-sum game, but in practice no different because adding a constant to all the payoff numbers of any one player makes no difference to his choices.)