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	Folk theorem (game theory) - Wikipedia, the free encyclopedia
		In game theory, folk theorems are a class of theorems which imply that in repeated games, any outcome is a feasible solution concept, if under that outcome the players' minimax conditions are satisfied.
		A repeated game is one in which there is not necessarily a final move, but rather, there is a sequence of rounds, during which the player may gather information and choose moves.
		In mathematics, the term folk theorem refers generally to a theorem which is believed and discussed, but has not been published.
	en.wikipedia.org /wiki/Folk_theorem_of_repeated_games (535 words)

	Jacob Crandall's Research -- Lessons Learned from the Folk Theorem
		Convex combinations of the various joint payoffs of the game form the games payoff space (its convex hull), which is depicted by the union of the shaded regions (light and dark) in the figure.
		The folk theorem shows that there are an infinite number of Nash equilibria in all games in which the joint payoff m = (m_1, m_2) is not pareto efficient (which constitutes a large portion of general-sum games).
		A polnomial-time nash equilibrium algorithm for repeated games.
	students.cs.byu.edu /~crandall/FolkTheorem.html (1178 words)

	5.3: A Folk Theorem Sampler
		The original motivation for developing a theory of repeated games was to show that cooperative behavior was an equilibrium.
		Each folk theorem considers a class of games and identifies a set of payoff vectors each of which can be supported by some equilibrium strategy profile.
		Some folk theorems identify sets of payoff vectors which can be supported by Nash equilibria; of course, of more interest are those folk theorems which identify payoffs supported by subgame-perfect equilibria.
	www.virtualperfection.com /gametheory/Section5.3.html (352 words)

	Repeated Games and Folk Theorems (Site not responding. Last check: 2007-10-20)
		AMCA: Patience and Collusion in Repeated Games by Andreas Krause...
		A polynomial-time nash equilibrium algorithm for repeated games...
		The Folk Theorem for All Games with Almost Perfect...
	www.scienceoxygen.com /math/562.html (167 words)

	List of games in game theory - Wikipedia, the free encyclopedia
		Game theory studies strategic interaction between individuals in situations called games.
		Classes of these games have been given names.
		This is a list of the most commonly studied games.
	en.wikipedia.org /wiki/List_of_games_in_game_theory (250 words)

	Unilateral Commitments and Finitely Repeated Games
		More precisely, we suppose that each player can restrict his original set of strategies in a preliminary round of the repeated game, in which players simultaneously and unilaterally commit themselves (in an enforceable way) to a subset of their strategies; these commitments are announced before the repeated game starts.
		This result, which is a kind of folk theorem, is formally stated and proved in section 3, after notations and settings are fixed in section 2.
		In this context, what our result adds to standard Nash equilibrium folk theorems for finitely repeated games is that when unilateral commitments are allowed, we only need that there exists a feasible payoff vector strictly greater than the minmax vector.
	www.dima.unige.it /~patrone/abstract/UC.htm (557 words)

	Microeconomic Theory 2 (Site not responding. Last check: 2007-10-20)
		The purpose of this course is to present some issues which are part of the core of modern microeconomics: theory of general equilibrium, externalities, public goods, game theory and topics in information economics.
		Elements of Game Theory a) Normal-Form Games and Nash Equilibrium: normal-form representation of the game, iterated elimination of strictly dominated strategies, motivation and definition of Nash equilibrium, Nash equilibrium in mixed strategies.
		Repeated Games and Folk Theorem: two-stage repeated games, infinitely repeated games, folk theorem.
	www.ceu.hu /econ/economic/micro2.htm (983 words)

	An `Anti-Folk Theorem' in Asynchronously Repeated Games (Site not responding. Last check: 2007-10-20)
		The standard model of repeated games assumes perfect synchronization in the timing of decisions between the players.
		The results complement a recent Folk Theorem result by Dutta (1995) for stochastic games which can be applied to asynchronously repeated games if a full dimensionality condition holds.
		However, because the minimax benchmark in an asynchronously repeated game may be different than for a standard repeated game, the form of multiplicity will in general be different for the two.
	www.e.u-tokyo.ac.jp /%7Eamatsui/anti7ab.html (281 words)

	vu02-w04 (Site not responding. Last check: 2007-10-20)
		This paper studies a class of dynamic games, called repeated games with asynchronous moves, where not all players may revise their actions in every period.
		We establish a folk theorem: when players are sufficiently patient, any feasible payoff vector where every player receives more than his effective minimax value can be approximated by a perfect equilibrium in the repeated game with asynchronous moves.
		This folk theorem integrates Fudenberg and Maskin's (1986) folk theorem for standard repeated games, Lagunoff and Matsui's (1997) anti-folk theorem for repeated pure coordination game with asynchronous moves, and Wen's (2002) folk theorem for repeated sequential games.
	www.vanderbilt.edu /Econ/wparchive/abstracts/vu02-w04.html (170 words)

	Encyclopedia: 1 (number)
		A numeral is a symbol or group of symbols that represents a number.
		The unary numeral system is the simplest numeral system to represent natural numbers: in order to represent a number N, an arbitrarily chosen symbol is repeated N times.
		In mathematics, factorization or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original.
	www.nationmaster.com /encyclopedia/1-(number) (1104 words)

	Prisoner's Dilemma
		We assume here that the game is symmetric, i.e., that the reward, punishment, temptation or sucker payoff is the same for each player, and payoffs have only ordinal significance, i.e., they indicate whether one payoff is better than another, but tell us nothing about how much better.
		The most obvious generalization from the two-player to the many-player game would pay each player R if all cooperate, P if all defect, and, if some cooperate and some defect, it would pay the cooperators S and the defectors T. But it is unlikely that we face many situations of this structure.
		No human agents can actually play an infinitely repeated game, of course, but the infinite IPD has been considered an appropriate way to model a series of interactions in which the participants never have reason to think the current interaction is their last.
	plato.stanford.edu /entries/prisoner-dilemma (14078 words)

	Folk Theorem
		A stage game is repeatedly played by successive generations of finitely-lived players with dynastic preferences.
		The result applies to any stage game for which the standard Folk Theorem yields a payoff set with a non-empty interior.
		We are also able to characterize entirely when a Sequential Equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a Subgame Perfect Equilibrium of the standard repeated game.
	www.georgetown.edu /faculty/la2/Folktheorem.htm (205 words)

	Infinite Games: 06/01/2004 - 06/30/2004 (Site not responding. Last check: 2007-10-20)
		Whether or not we attribute the Pythagorean theorem to Pythagoras, it seems fairly certain that he had the pioneering insight into the numerical ratios which determine the musical scale, since this plays a key role in many other areas of the Pythagorean tradition and since no evidence remains of earlier Greek or Egyptian musical theories.
		If games both fashion and reflect culture, it stands to reason that to a certain extent a whole civilization and, within that civilization, an entire era can be characterized by its games.
		This statement is significant because all the other theorems proposed by Fermat were settled, either by proofs he supplied, or by rigorous proofs found afterwards.
	infinitegames.blogspot.com /2004_06_01_infinitegames_archive.html (12816 words)

	The Folk Theorem in Dynastic Repeated Games
		"The Folk Theorem in Dynastic Repeated Games," Cowles Foundation Discussion Papers 1490, Cowles Foundation, Yale University.
		"The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol.
		"Repeated games with M-period bounded memory (pure strategies)," Journal of Mathematical Economics, Elsevier, vol.
	ideas.repec.org /p/cla/levrem/122247000000000577.html (810 words)

	summer in tel aviv (Site not responding. Last check: 2007-10-20)
		In repeated games with imperfect public monitoring, players can use public signals to perfectly coordinate their behavior.
		We then turn our attention to games with private monitoring where the monitoring technology is "almost public." We characterize the perfect public equilibria of games with public monitoring that induce equilibria in "close-by" games with private monitoring.
		We also show that If the game with private monitoring is close to a game with public monitoring that is itself almost perfect, then a folk theorem holds for the game with private monitoring.
	econ.tau.ac.il /calendar/sita99/abstract3.htm (214 words)

	Europe - Mathematics and the Liberal Arts
		Although this brief excerpt does not mention it, it is not uncommon for the construction to be repeated in the same tracery in a different scale---a kind of reaching to infinity that is reminiscent of fractals.
		Hargittal, István and Lengyel Györgi, The seventeen two-dimensional space-group symmetries in Hungarian folk needlework.
		The authors give some solutions and theorems on minimality, although they leave their discovery of a 16 move solution to the four-couples-with-an-island problem as "a nice exercise for the reader".
	math.truman.edu /~thammond/history/Europe.html (10638 words)

	Syllabus
		A game tree is defined, as well as information sets and pure, mixed and behavioral strategies.
		We then turn to the analysis of dynamic games, covering repeated games, finitely repeated games, the folk theorem for repeated games, subgame perfection, and punishment strategies.
		Next, games with incomplete information are studied, including direct revelation games, concepts of efficiency, and information transmission.
	www.cramton.umd.edu /Econ703/Syllabus.html (469 words)

	Credible Assignments and Coordination Failure in Laboratory Public Goods Games (Site not responding. Last check: 2007-10-20)
		We were able to discover one assignment that was credible in the last match of the evolutionary repeated game.
		A fundamental result from the theory of repeated games is that recurrent strategic situations can replace an incentive problem, like the free rider problem, with a strategy coordination problem.
		While it was not the most credible trigger, it was effective because of its influence on learning in the evolutionary repeated game.
	erl.tamu.edu /jvh_gtee/pg2.htm (1293 words)

	EC218 Game Theory
		Nash, J. "Equilibrium Points in n-Person Games," Proceedings of the National Academy of Sciences of the United States of America, Vol.
		Application 1: Repeated oligopoly (introduction to infinitely repeated games and the principle of optimality).
		Kandori, M. and Obara, I. "Efficiency in Repeated Games Revisited: the Role of Private Strategies," mimeo.
	www.econ.brown.edu /fac/Pedro_Dal_Bo/ec218 (829 words)

	PIER Working Paper 05-024 Abstract (Site not responding. Last check: 2007-10-20)
		For repeated games with noisy private monitoring and communication, we examine robustness of perfect public equilibrium/subgame perfect equilibrium when private monitoring is "close" to some public monitoring.
		When informational size is small relative to distributional variability (and private signals are sufficiently close to public monitoring), a uniformly strict equilibrium with public monitoring remains an equilibrium with private monitoring and communication.
		To demonstrate that uniform strictness is not overly restrictive, we prove a uniform folk theorem with public monitoring which, combined with our robustness result, yields a new folk theorem for repeated games with private monitoring and communication.
	www.econ.upenn.edu /Centers/pier/Archive/Abstracts/05-024A.htm (188 words)

	research
		For this game, we explicitly construct a symmetric sequential equilibrium using private
		For repeated games with noisy private monitoring and communication, we examine robustness of
		new folk theorem for repeated games with private monitoring and communication.
	www.econ.ucla.edu /iobara/research.html (1333 words)

	Abstract of "Repeated Games with Outside Offers" (Site not responding. Last check: 2007-10-20)
		Trigger-strategy equilibria, which generate all feasible and individually rational payoffs in ordinary repeated games, restrict the outcomes to payoffs near the Pareto frontier for a large class of outside offer distributions.
		The interpretation is that voluntary repeated relationships should be mutually beneficial.
		Our result includes the equilibrium set of long-run, one-shot player games and the perfect folk theorem as polar cases, and connects them with a characterization of intermediate cases.
	www.econ.keio.ac.jp /staff/takakofg/repabs.html (162 words)

	Private Monitoring, Likelihood Ratio Condition, and the Folk Theorem (ResearchIndex)
		Abstract: This paper investigates infinitely repeated prisoner-dilemma games where the discount factor is less than but close to 1.
		18 The Structure of Nash Equilibrium in Repeated Games with Fin..
		The Robustness of Repeated Game Equilibria to Incomplete Payoff..
	citeseer.ist.psu.edu /matsushima00private.html (458 words)

	The Folk Theorem in Repeated Games of Incomplete Information (ResearchIndex)
		For the case of equal discount factors, however, a result akin to the Folk...
		0.5: The Folk Theorems for Repeated Games: A Synthesis - Benoît, Krishna (1998)
		3 An Analog of the Minmax Theorem for Vector Payoffs (context) - Blackwell - 1956
	citeseer.ist.psu.edu /cripps97folk.html (418 words)

	Communication in Private Monitoring Games (Site not responding. Last check: 2007-10-20)
		Communication in Repeated Games with Imperfect Private Monitoring...
		IngentaConnect Communication in Repeated Games with Private Monitoring...
		Contracting with Repeated Moral Hazard and Private Evaluations...
	www.scienceoxygen.com /math/565.html (213 words)

	IngentaConnect A Folk Theorem for Repeated Sequential Games (Site not responding. Last check: 2007-10-20)
		We introduce the concept of effective minimax for sequential games and establish a Folk theorem for repeated sequential games.
		The Folk theorem asserts that any feasible payoff vector where every player receives more than his effective minimax value in a sequential stage game can be supported by a subgame perfect equilibrium in the corresponding repeated sequential game when players are sufficiently patient.
		The model of repeated sequential games and the concept of effective minimax provide an alternative view to the Anti–Folk theorem of Lagunoff and Matsui (1997) for asynchronously repeated pure coordination games.
	www.ingentaconnect.com /content/bpl/roes/2002/00000069/00000002/art00214 (191 words)

	Tit-for-Tat doesn't explain us but it does explain Homo Sovieticus \| Samizdata.net
		Economists are fond of using the Folk Theorem of repeated games and the Tit-for-Tat simulations to argue that human cooperation can be understood in terms of long-run, enlightened self-interest, but we will argue in chapter 11 that this view is profoundly incorrect.
		Indeed, some of the major predictive failures of game theory stem from not recognizing the positive and negative aspects of preference and welfare interdependence.
		So although game theory may not be very good at explaining the social harmonies and social complexities to be found in a successful and interesting place like Massachusetts, it is great at making sense of the old USSR.
	www.samizdata.net /blog/archives/002792.html (1055 words)

	The Folk Theorem in Dynastic Repeated Games ewp-game/0410001
		A canonical interpretation of an infinitely repeated game is that of a “dynastic” repeated game: a stage game repeatedly played by successive generations of finitely-lived players with dynastic preferences.
		In our model all players live one period and do not observe the history of play that takes place before their birth, but instead receive a private message from their immediate predecessors.
		Our results stem from the fact that, in equilibrium, a player may be unable to communicate effectively relevant information to his successor in the same dynasty.
	econwpa.wustl.edu /eprints/game/papers/0410/0410001.abs (346 words)

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