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Non-cooperative Game Theory
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 (e.g. through credible threats). However, 'cooperative' and 'non-cooperative' are only technical terms to describe the theory used to model a game, so it is possible to use cooperative game theory to model competition and using non-cooperative game theory to model cooperation. The key distinguishing feature is the absence of external authority to establish rules enforcing cooperative behavior. In the absence of external authority (such as contract law), players cannot group into ''coalitions'' and must compete independently. Negative-sum games and zero-sum games are both types of non-cooperative games. Non-cooperative game theory in academic literature A mention of non-cooperative game theory was made in John Nash's 1951 article in the journal ''Annals of Mathematics''. Nash Equilibrium, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strategy Game
A strategy game or strategic game is a game (e.g. a board game) in which the players' uncoerced, and often autonomous, decision-making skills have a high significance in determining the outcome. Almost all strategy games require internal decision tree-style thinking, and typically very high situational awareness. Strategy games are also seen as a descendant of war games, and define strategy in terms of the context of war, but this is more partial. A strategy game is a game that relies primarily on strategy, and when it comes to defining what strategy is, two factors need to be taken into account: its complexity and game-scale actions, such as each placement in a Total War series. The definition of a strategy game in its cultural context should be any game that belongs to a tradition that goes back to war games, contains more strategy than the average video game, contains certain gameplay conventions, and is represented by a particular community. Although war is dominant in strat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
War Of Attrition (game)
In game theory, the ''war of attrition'' is a dynamic timing game in which players choose a time to stop, and fundamentally trade off the strategic gains from outlasting other players and the real costs expended with the passage of time. Its precise opposite is the ''pre-emption game'', in which players elect a time to stop, and fundamentally trade off the strategic costs from outlasting other players and the real gains occasioned by the passage of time. The model was originally formulated by John Maynard Smith; a mixed evolutionarily stable strategy (ESS) was determined by Bishop & Cannings. An example is a second price ''all-pay'' auction, in which the prize goes to the player with the highest bid and each player pays the loser's low bid (making it an all-pay sealed-bid second-price auction). Examining the game To see how a war of attrition works, consider the all pay auction: Assume that each player makes a bid on an item, and the one who bids the highest wins a resource of v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trigger Strategy
In game theory, a trigger strategy is any of a class of strategies employed in a repeated non-cooperative game. A player using a trigger strategy initially cooperates but punishes the opponent if a certain level of defection (i.e., the trigger) is observed. The level of ''punishment'' and the sensitivity of the trigger vary with different trigger strategies. Trigger strategies *Grim trigger (the punishment continues indefinitely after the other player defects just once) *Tit for tat (the punishment continues as long as the other player defects) * Tit for two tats (a more forgiving variant of tit for tat) References ;Textbooks and general reference texts * Vives, X. (1999) ''Oligopoly pricing'', MIT Press, Cambridge MA (readable; suitable for advanced undergraduates.) * Tirole, J. (1988) ''The Theory of Industrial Organization'', MIT Press, Cambridge MA (An organized introduction to industrial organization) ;Classical paper on this subject * Friedman, J. (1971). A non-coope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trembling Hand Perfect Equilibrium
A tremor is an involuntary, somewhat rhythmic, muscle contraction and relaxation involving oscillations or twitching movements of one or more body parts. It is the most common of all involuntary movements and can affect the hands, arms, eyes, face, head, vocal folds, trunk, and legs. Most tremors occur in the hands. In some people, a tremor is a symptom of another neurological disorder. A very common tremor is the teeth chattering, usually induced by cold temperatures or by fear. Types Tremor is most commonly classified by clinical features and cause or origin. Some of the better-known forms of tremor, with their symptoms, include the following: * Cerebellar tremor (also known as intention tremor) is a slow, broad tremor of the extremities that occurs at the end of a purposeful movement, such as trying to press a button or touching a finger to the tip of one's nose. Cerebellar tremor is caused by lesions in or damage to the cerebellum resulting from stroke, tumor, or disease su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tit For Tat
Tit for tat is an English saying meaning "equivalent retaliation". It developed from "tip for tap", first recorded in 1558. It is also a highly effective strategy in game theory. An intelligent agent, agent using this strategy will first cooperate, then subsequently replicate an opponent's previous action. If the opponent previously was cooperative, the agent is cooperative. If not, the agent is not. Game theory Tit-for-tat has been very successfully used as a strategy for the iterated prisoner's dilemma. The strategy was first introduced by Anatol Rapoport in Robert Axelrod's two tournaments, held around 1980. Notably, it was (on both occasions) both the simplest strategy and the most successful in direct competition. An agent using this strategy will first cooperate, then subsequently replicate an opponent's previous action. If the opponent previously was cooperative, the agent is cooperative. If not, the agent is not. This is similar to reciprocal altruism in biology. Hist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proper Equilibrium
Proper equilibrium is a refinement of Nash Equilibrium due to Roger B. Myerson. Proper equilibrium further refines Reinhard Selten's notion of a trembling hand perfect equilibrium by assuming that more costly trembles are made with significantly smaller probability than less costly ones. Definition Given a normal form game and a parameter \epsilon > 0, a totally mixed strategy profile \sigma is defined to be \epsilon-proper if, whenever a player has two pure strategies s and s' such that the expected payoff of playing s is smaller than the expected payoff of playing s' (that is u(s,\sigma_) Example The game to the right is a var ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intra-household Bargaining
Intra-household bargaining refers to negotiations that occur between members of a household in order to arrive at decisions regarding the household unit, like whether to spend or save, whether to study or work. Bargaining is traditionally defined in economic terms of negotiating conditions of a purchase or contract and is sometimes used in place of direct monetary exchange. Bargaining process within a family is one of the important aspects of family economics. Bargaining also plays a role in the functioning and decision making of households, where agreements and decisions do not often have direct monetary values and affect various members of the household. Household dynamics The household is traditionally described as a single economic unit that "works as a group for its own good", meaning all members of the household contribute in an altruistic manner towards the benefit and functioning of the entire household. The household is "the basic residential unit in which economic produ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grim Trigger
In game theory, grim trigger (also called the grim strategy or just grim) is a trigger strategy for a repeated game. Initially, a player using grim trigger will cooperate, but as soon as the opponent defects (thus satisfying the trigger condition), the player using grim trigger will defect for the remainder of the iterated game. Since a single defect by the opponent triggers defection forever, grim trigger is the most strictly unforgiving of strategies in an iterated game. In Robert Axelrod's book '' The Evolution of Cooperation'', grim trigger is called "Friedman", for a 1971 paper by James Friedman, which uses the concept. The infinitely repeated prisoners' dilemma The infinitely repeated prisoners’ dilemma is a well-known example for the grim trigger strategy. The normal game for two prisoners is as follows: In the prisoners' dilemma, each player has two choices in each stage: # Cooperate # Defect for an immediate gain If a player defects, he will be punished for the rem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assured Destruction
Mutual assured destruction (MAD) is a doctrine of military strategy and national security policy which posits that a full-scale use of nuclear weapons by an attacker on a nuclear-armed defender with second-strike capabilities would cause the complete annihilation of both the attacker and the defender. It is based on the theory of rational deterrence, which holds that the threat of using strong weapons against the enemy prevents the enemy's use of those same weapons. The strategy is a form of Nash equilibrium in which, once armed, neither side has any incentive to initiate a conflict or to disarm. The term "mutual assured destruction", commonly abbreviated "MAD", was coined by Donald Brennan, a strategist working in Herman Kahn's Hudson Institute in 1962. However, Brennan came up with this acronym ironically, spelling out the English word " mad" to argue that holding weapons capable of destroying society was irrational. Theory Under MAD, each side has enough nuclear weapon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prisoner's Dilemma
The Prisoner's Dilemma is an example of a game analyzed in game theory. It is also a thought experiment that challenges two completely rational agents to a dilemma: cooperate with their partner for mutual reward, or betray their partner ("defect") for individual reward. This dilemma was originally framed by Merrill Flood and Melvin Dresher while working at RAND in 1950. Albert W. Tucker appropriated the game and formalized it by structuring the rewards in terms of prison sentences and named it "prisoner's dilemma". William Poundstone in his 1993 book ''Prisoner's Dilemma'' writes the following version:Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don't have enough evidence to convict the pair on the principal charge. They plan to sentence both to two years in prison on a lesser charge. Simultaneously, the police offer each prison ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
