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Prisoner's Dilemma
The prisoner's dilemma is a game theory thought experiment involving two rational agents, each of whom can either cooperate for mutual benefit or betray their partner ("defect") for individual gain. The dilemma arises from the fact that while defecting is rational for each agent, cooperation yields a higher payoff for each. The puzzle was designed by Merrill Flood and Melvin Dresher in 1950 during their work at the RAND Corporation. They invited economist Armen Alchian and mathematician John Williams to play a hundred rounds of the game, observing that Alchian and Williams often chose to cooperate. When asked about the results, John_Forbes_Nash_Jr., John Nash remarked that rational behavior in the Prisoner's dilemma#The_iterated_prisoner's_dilemma, iterated version of the game can differ from that in a single-round version. This insight anticipated a Folk_theorem_(game_theory), key result in game theory: cooperation can emerge in repeated interactions, even in situations where it i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of Human behavior, behavioral relations. It is now an umbrella term for the science of rational Decision-making, decision making in humans, animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games 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 mathematical economics. His paper was f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nash Equilibrium
In game theory, the Nash equilibrium is the most commonly used solution concept for non-cooperative games. A Nash equilibrium is a situation where no player could gain by changing their own strategy (holding all other players' strategies fixed). The idea of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to his model of competition in an oligopoly. If each player has chosen a strategy an action plan based on what has happened so far in the game and no one can increase one's own expected payoff by changing one's strategy while the other players keep theirs unchanged, then the current set of strategy choices constitutes a Nash equilibrium. If two players Alice and Bob choose strategies A and B, (A, B) is a Nash equilibrium if Alice has no other strategy available that does better than A at maximizing her payoff in response to Bob choosing B, and Bob has no other strategy available that does better than B at maximizing his payoff in response to Alice c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Altruism
Altruism is the concern for the well-being of others, independently of personal benefit or reciprocity. The word ''altruism'' was popularised (and possibly coined) by the French philosopher Auguste Comte in French, as , for an antonym of egoism. He derived it from the Italian , which in turn was derived from Latin , meaning "alterity, other people" or "somebody else". Altruism may be considered a synonym of selflessness, the opposite of self-centeredness. Altruism is an important moral value in many cultures and religions. It can Moral circle expansion, expand beyond care for humans to include other Sentience, sentient beings and future generations. Altruism, as observed in populations of organisms, is when an individual performs an action at a cost to itself (in terms of e.g. pleasure and quality of life, time, probability of survival or reproduction) that benefits, directly or indirectly, another individual, without the expectation of reciprocity or compensation for that ac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Axelrod (political Scientist)
Robert Marshall Axelrod (born May 27, 1943) is an American political scientist. He is Professor of Political Science and Public Policy at the University of Michigan where he has been since 1974. He is best known for his interdisciplinary work on the evolution of cooperation. His current research interests include complexity theory (especially agent-based modeling), international security, and cyber security. His research includes innovative approaches to explaining conflict of interest, the emergence of norms, how game theory is used to study cooperation, and cross-disciplinary studies on evolutionary processes. Biography Axelrod received his B.A. in mathematics from the University of Chicago in 1964. In 1969, he received his Ph.D. in political science from Yale University for a thesis entitled ''Conflict of interest: a theory of divergent goals with applications to politics''. He taught at the University of California, Berkeley, from 1968 until 1974. Among his honors and awa ... [...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 W. 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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tit For Tat
Tit for tat is an English saying meaning "equivalent retaliation". It is an alternation of '' tip for tap'' "blow for blow", first recorded in 1558. It is also a highly effective strategy in game theory. 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. 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. Few have extended the game theoretical approach to other applications such as finance. In that context the tit for tat strategy was shown to be associated to the trend following strategy. Implicatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Aumann
Robert John Aumann (Yisrael Aumann, ; born June 8, 1930) is an Israeli-American mathematician, and a member of the United States National Academy of Sciences. He is a professor at the Center for the Study of Rationality in the Hebrew University of Jerusalem. He also holds a visiting position at Stony Brook University, and is one of the founding members of the Stony Brook Center for Game Theory. Aumann received the Nobel Memorial Prize in Economic Sciences in 2005 for his work on conflict and cooperation through game theory analysis. He shared the prize with Thomas Schelling. Early life and education Aumann was born in Frankfurt am Main, Germany, and fled to the United States with his family in 1938, two weeks before the Kristallnacht pogrom. He attended the Rabbi Jacob Joseph School, a yeshiva high school in New York City. Aumann graduated from the City College of New York in 1950 with a B.S. in mathematics. He received his M.S. in 1952, and his Ph.D. in Mathematics in 1955, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cooperation
Cooperation (written as co-operation in British English and, with a varied usage along time, coöperation) takes place when a group of organisms works or acts together for a collective benefit to the group as opposed to working in competition for selfish individual benefit. In biology, many animal and plant species cooperate both with other members of their own species and with members of other species with whom they have (symbiotic or mutualism (biology), mutualistic) relationships. Among humans Humans cooperate for the same reasons as other animals: immediate benefit, genetic relatedness, and reciprocity, but also for particularly human reasons, such as honesty signaling (indirect reciprocity), cultural group selection, and for reasons having to do with cultural evolution. Language allows humans to cooperate on a very large scale. Certain studies have suggested that fairness affects human cooperation; individuals are willing to punish at their own cost (''altruistic punis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Induction
Mathematical induction is a method for mathematical proof, proving that a statement P(n) is true for every natural number n, that is, that the infinitely many cases P(0), P(1), P(2), P(3), \dots all hold. This is done by first proving a simple case, then also showing that if we assume the claim is true for a given case, then the next case is also true. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: A proof by induction consists of two cases. The first, the base case, proves the statement for n = 0 without assuming any knowledge of other cases. The second case, the induction step, proves that ''if'' the statement holds for any given case n = k, ''then'' it must also hold for the next case n = k + 1. These two steps establish that the statement holds for every natural number n. The base case does not necessarily begin with n = 0, but often with n = 1, and possibly with any fixed natural number n = N, establishing the trut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peace War Game
Peace war game is an iterated game originally played in academic groups and by computer simulation for years to study possible strategies of cooperation and aggression. As peace makers became richer over time it became clear that making war had greater costs than initially anticipated. The only strategy that acquired wealth more rapidly was a constant aggressor making war continually to gain resources. This led to the development of the "provokable nice guy" strategy, a peace-maker until attacked.N.R. Miller"Nice Strategies Finish First: A Review of ''The Evolution of Cooperation''" '' Politics and the Life Sciences'', Association for Politics and the Life Sciences, 1985. Multiple players continue to gain wealth cooperating with each other while bleeding the constant aggressor. The peace war game is a variation of the iterated prisoner's dilemma in which the decisions ( Cooperate, Defect) are replaced by (Peace, War). Strategies remain the same with reciprocal altruism, " Tit fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jonathan Pool
Jonathan Pool, born 1942 in Chicago, is a political scientist from the United States. He works on the political and economic consequences of linguistic circumstances and language policy. Pool studied political science in Harvard between 1960 and 1964. He then joined the Peace Corps and went to Turkey, where he taught English. After his return he studied in Chicago, where he graduated in 1968 and earned his PhD in 1971. Pool worked at the universities of Chicago, New York (Stony Brook), Washington (Seattle), Stanford as well as in Mannheim, Paderborn, and Bielefeld in Germany. After 1996 he worked as a chief strategist for Centerplex, an enterprise in Tukwila, Washington, near Seattle. He now is president of Utilika Foundation. Pool has always been impressed by the degree to which peoples' first language and linguistic knowledge influence their lives. When, as a nine-year-old, he had a friend whose parents had immigrated from Brazil, he decided to learn Portuguese while his f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
