Game theory is the study of mathematical models of strategic interaction among rational decision-makers. It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed zero-sum games, in which each participant's gains or losses are exactly balanced by those of the other participants. In the 21st century, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.
The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher while working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence rewards and named it "prisoner's dilemma", presenting it as follows:
Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:
GNS theory is an informal field of study developed by Ron Edwards which attempts to create a unified theory of how role-playing games work. Focused on player behavior, in GNS theory participants in role-playing games organize their interactions around three categories of engagement: gamism, narrativism and simulation.
The game of chicken, also known as the hawk–dove game or snowdrift game, is a model of conflict for two players in game theory. The principle of the game is that while the outcome is ideal for one player to yield, but the individuals try to avoid it out of pride for not wanting to look like a 'chicken'. So each player taunts the other to increase the risk of shame in yielding. However, when one player yields, the conflict is avoided, and the game is for the most part over.
In international relations, the security dilemma, also referred to as the spiral model, is a situation where one party heightening security measures can lead to an escalation or conflict with one or more other parties, producing an outcome which no party truly desires. Under the international relations theory of anarchy, actions by a state intended to heighten its security, such as increasing its military strength, committing to use weapons or making alliances, can lead other states to respond with similar measures, producing increased tensions that create conflict.
The foundations of negotiation theory are decision analysis, behavioral decision making, game theory, and negotiation analysis. Another classification of theories distinguishes between Structural Analysis, Strategic Analysis, Process Analysis, Integrative Analysis and behavioral analysis of negotiations.
In game theory, a non-cooperative game is a game with competition between individual players, as opposed to cooperative games, and in which alliances can only operate if self-enforcing.
In game theory, grim trigger is a trigger strategy for a repeated game.
In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most commonly used solution concepts are equilibrium concepts, most famously Nash equilibrium.
Metagame, Hypergame, or game about the game, is an approach to a game that transcends or operates outside of the prescribed rules of the game, uses external factors to affect the game, or goes beyond the supposed limits or environment set by the game.
In game theory, strategic dominance occurs when one strategy is better than another strategy for one player, no matter how that player's opponents may play. Many simple games can be solved using dominance. The opposite, intransitivity, occurs in games where one strategy may be better or worse than another strategy for one player, depending on how the player's opponents may play.
In game theory, a focal point is a solution that people tend to choose by default in the absence of communication. The concept was introduced by the American economist Thomas Schelling in his book The Strategy of Conflict (1960). Schelling states that "(p)eople can often concert their intentions or expectations with others if each knows that the other is trying to do the same" in a cooperative situation, so their action would converge on a focal point which has some kind of prominence compared with the environment. However, the conspicuousness of the focal point depends on time, place and people themselves. It may not be a definite solution.
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games. The original Folk Theorem concerned the payoffs of all the Nash equilibria of an infinitely repeated game. This result was called the Folk Theorem because it was widely known among game theorists in the 1950s, even though no one had published it. Friedman's (1971) Theorem concerns the payoffs of certain subgame-perfect Nash equilibria (SPE) of an infinitely repeated game, and so strengthens the original Folk Theorem by using a stronger equilibrium concept: subgame-perfect Nash equilibria rather than Nash equilibria.
A collective action problem or social dilemma is a situation in which all individuals would be better off cooperating but fail to do so because of conflicting interests between individuals that discourage joint action. The collective action problem has been addressed in political philosophy for centuries, but was most clearly established in 1965 in Mancur Olson's The Logic of Collective Action.
Risk dominance and payoff dominance are two related refinements of the Nash equilibrium (NE) solution concept in game theory, defined by John Harsanyi and Reinhard Selten. A Nash equilibrium is considered payoff dominant if it is Pareto superior to all other Nash equilibria in the game. When faced with a choice among equilibria, all players would agree on the payoff dominant equilibrium since it offers to each player at least as much payoff as the other Nash equilibria. Conversely, a Nash equilibrium is considered risk dominant if it has the largest basin of attraction. This implies that the more uncertainty players have about the actions of the other player(s), the more likely they will choose the strategy corresponding to it.
In game theory, the traveler's dilemma is a non-zero-sum game in which each player proposes a payoff. The lower of the two proposals wins; the lowball player receives the lowball payoff plus a small bonus, and the highball player receives the same lowball payoff, minus a small penalty. Surprisingly, the Nash equilibrium is for both players to aggressively lowball. The traveler's dilemma is notable in that naive play appears to outperform the Nash equilibrium; this apparent paradox also appears in the centipede game and the finitely-iterated prisoner's dilemma.
Metagame analysis involves framing a problem situation as a strategic game in which participants try to realise their objectives by means of the options available to them. The subsequent meta-analysis of this game gives insight in possible strategies and their outcome.
Cooperative bargaining is a process in which two people decide how to share a surplus that they can jointly generate. In many cases, the surplus created by the two players can be shared in many ways, forcing the players to negotiate which division of payoffs to choose. Such surplus-sharing problems are faced by management and labor in the division of a firm's profit, by trade partners in the specification of the terms of trade, and more.
Confrontation analysis is an operational analysis technique used to structure, understand and think through multi-party interactions such as negotiations. It is the underpinning mathematical basis of drama theory.
In the philosophy of mind, collective intentionality characterizes the intentionality that occurs when two or more individuals undertake a task together. Examples include two individuals carrying a heavy table up a flight of stairs or dancing a tango.
