Strategic Game Theory -- Glossary

This is a glossary of introductory game-theory terms, roughly in the order in which they were used first in class.

So strategic games are distinguished from individual decision making by the presence of significant interactions among the players. Games can be classified according to a variety of categories, including the timing of the play, the common or conflicting interests of the players, the number of times an interaction occurs, the amount of information available to the players, the type of rules, and the feasibility of coordinated action.

Players have strategies that lead to different outcomes with different associated payoffs. Payoffs incorporate everything that is important to a player about a game, and are calculated using probabilistic averages or expected values if outcomes are random or involve some risk. Rationality, or consistent, behaviour is assumed of all players, who must also be aware of all of the relevant rules of conduct. Equilibrium arises when all players use strategies that are best responses to others' strategies; some classes of games allow learning from experience and the study of dynamic movements towards equilibrium.

Actions taken by players to fix the rules of later play are known as strategic moves. These first moves must be observable and irreversible to be true first moves, and they must be credible if they are to have their desired effect in altering the equilibrium outcome of the game. Commitment is an unconditional first move used to seize a first-mover advantage when one exists. Such a move usually entails committing to a strategy that would not have been one's equilibrium strategy in the original version of the game, so there may exist an incentive to renege later.

Conditional first moves such as threats and promises are response rules designed either to deter rivals' actions and preserve the status quo, or to compel rivals' actions and alter the status quo. Threats carry the possibility of mutual harm but cost nothing if they work; threats that create only the risk of a bad outcome are known as acts of brinkmanship. Promises are costly only to the maker and only if they are successful. Threats can be arbitrarily large, although excessive size compromises credibility, but promises are usually kept just large enough to be effective.

Credibility must be established for any strategic move. There are a number of general principles to consider in making moves credible, and a number of specific devices that can be used to acquire credibility. These generally work either by reducing one's own future freedom to choose or by altering one's own payoffs from future actions. Specific devices of this kind include establishing a reputation, using teamwork, demonstrating apparent irrationality, burning bridges, and making contracts, although the acquiring of credibility is often context-specific. Similar devices exist for countering strategic moves made by rival players.

The Prisoner's Dilemma is probably the most famous game of strategy; each play has a dominant strategy (to Defect), but the equilibrium is worse for all players than when each users her dominated strategy (to Cooperate). The most well known solution to the dilemma is repetition of play. In a finite game of known length, the present value of cooperation is eventually zero and backwards induction yields an equilibrium with no cooperative behaviour (end-game behaviour). With infinite play (or an unknown end date), cooperation can be achieved using an appropriate contingent strategy such as tit-for-tat (TFT) or the grim trigger strategy; in either case, cooperation is possible if the present value of cooperation exceeds the present value of defecting. More generally, the prospect of "no tomorrow" or of short-term relationships leads to increased competition among players.

Experimental evidence suggests that players often cooperate longer than theory might predict.

Tit-for-tat has been observed to be a simple, nice, provocable, and forgiving strategy that performs very well on the average in repeated Prisoner's Dilemmas.

Prisoner's Dilemmas arise in a variety of contexts: policy setting, labour arbitration, evolutionary biology, product pricing, and environmental decision-making are some in which the Prisoner's Dilemma can help explain actual behaviour.

Last Updated 26 April 2000
Robert Marks,