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Topic: Bayesian game

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	Bayesian game - Wikipedia, the free encyclopedia
		Harsanyi's approach to modelling a Bayesian game in such a way allows game of incomplete information to become games of imperfect information (in which the history of the game is not available to all players).
		The employer starts the game with an initial belief about the applicant's type (unskilled with 90% chance), but during the course of the game this belief may be updated (depending on the payoffs of the different types of applicants) to 0% unskilled if he observes a university education or 100% unskilled if he does not.
		A Bayesian Nash equilibrium is defined as a strategy profile and beliefs specified for each player about the types of the other players that maximises the expected payoff for each player given their beliefs about the other players' types and given the strategies played by the other players.
	en.wikipedia.org /wiki/Bayesian_game (2112 words)

	EconPort - Handbook - Game Theory - Bayesian Games
		A Bayesian game is one where the players have incomplete information about the game.
		The common equilibrium notion for such games is Bayesian Nash Equilibrium (BNE).
		Bayesian matrix games can be implemented as extensive-form games with the Extensive Form Game software at Carnegie Mellon University.
	www.econport.org:8080 /econport/request?page=man_gametheory_bayesgames (193 words)

	Solution concept - Wikipedia, the free encyclopedia
		In game theory and economic modelling, a solution concept is a process via which equilibria of a game are identified.
		For example, consider a dynamic game in which the players are an incumbent firm in an industry and a potential entrant to that industry.
		Since the game is dynamic, any claim by the incumbent that it will fight is an incredible threat because by the time the decision node is reached where it can decide to fight (i.e.
	en.wikipedia.org /wiki/Solution_concept (1410 words)

	History of Game Theory (Site not responding. Last check: 2007-10-13)
		Lloyd Shapley's paper Stochastic Games showed that for the strictly competitive case, with future payoff discounted at a fixed rate, such games are determined and that they have optimal strategies that depend only on the game being played, not on the history or even on the date, ie: the strategies are stationary.
		For a Bayesian game the question arises as to whether or not it is possible to construct a situation for which there is no sets of types large enough to contain all the private information that players are supposed to have.
		Game Theory and the Law by Douglas G. Baird, Robert H. Gertner and Randal C. Picker is one of the first books in law and economics to take an explicitly game theoretic approach to the subject.
	william-king.www.drexel.edu /top/class/histf.html (5889 words)

	Game Theory
		The main purpose of game theory is to consider situations where instead of agents making decisions as reactions to exogenous prices ("dead variables"), their decisions are strategic reactions to other agents actions ("live variables").
		John von Neumann and Oskar Morgenstern (1944) introduced the strategic normal game, strategic extensive game, the concept of pure/mixed strategies, coalitional games as well as the axiomatization of expected utility theory, which was so useful for economics under uncertainty.
		In game theory's first theorem, Zermelo (1913) argued that a game of chess with rational players could be solved trivially by an algorithm.
	cepa.newschool.edu /het/schools/game.htm (1057 words)

	march 24 (Site not responding. Last check: 2007-10-13)
		A game of incomplete information can be transformed into a game with imperfect information by introducing another player "nature", which decides the type of player.
		Bayesian equilibrium (defined on page 433): a player maximizes his expected payoff given knowledge about himself and the probability weighted payoffs from the optimal strategies of the different types of opponents that he could face.
		Bayesian updating: a player's action in one time period may reveal some information about his type, which helps the next player choose what to do.
	www.udel.edu /Economics/mulligaj/spring_1998/ec861/mar24.htm (1235 words)

	COOPERATIVE EXTENSIONS OF THE BAYESIAN GAME
		This is the very first comprehensive monograph in a burgeoning, new research area — the theory of cooperative game with incomplete information with emphasis on the solution concept of Bayesian incentive compatible strong equilibrium that encompasses the concept of the Bayesian incentive compatible core.
		Cooperative Extensions of the Bayesian Game is an essential reference in strategic cooperative game theory, and serves as an informative textbook for PhD courses in advanced economic theory, mathematical economics, game theory, and industrial organization.
		Readership: Researchers in economics, game theory and political science, and post-graduate students in economics and game theory.
	www.worldscibooks.com /economics/5845.html (366 words)

	Bayesian equilibrium (Site not responding. Last check: 2007-10-13)
		Bayesian equilibrium in double auctions populated by biased heuristic traders...
		Games in extensive form IV Sequential equilibrium (OR 12.1-2)...
		Game Theory and Related Topics - Pescara October 2-4 2003...
	www.scienceoxygen.com /math/572.html (110 words)

	SFB 504 glossary: (Strategic) Equilibrium
		Profile of plans leading to an outcome of a game that is stable in the sense that given the other players adhere to the equilibrium prescription, no single player wants to deviate from the prescription.
		One of the major achievements of game theory accordingly has been the refinement of the concept of strategic equilibrium to allow for sharper predictions.
		Perfect Bayesian Nash equilibrium: Parallel to the extension of Nash equilibrium to subgame perfect equilibrium in games of complete information, the concept of Bayesian Nash equilibrium loses much of its bite in extensive form games and is accordingly refined to 'Perfect Bayesian' equilibrium.
	www.sfb504.uni-mannheim.de /glossary/strateq.htm (1206 words)

	6.1: Static Games of Incomplete Information
		We can think of the game which follows as a strategic-form game being played by a single type of each player, where at least one player doesn't know which type of some other player she is facing.
		A strategy for a player in the incomplete-information game is a strategy for each of that player's types for the appropriate strategic-form game.
		A Bayesian equilibrium of a static game of incomplete information is a strategy profile such that every type of every player is maximizing her expected utility given the type-contingent strategies of her opponents and the probability distribution over types of each player.
	www.virtualperfection.com /gametheory/Section6.1.html (439 words)

	Directory of Academic Statisticians 2005
		Bayesian modelling and inference in particular in image analysis, mixture modelling and genetics.
		Bayesian inference and modelling, Bayesian statistics in health economics, inference for computer models, fractional Bayes factors, elicitation, outliers, uncertainty analysis, environmental statistics.
		Bayesian model criticism and comparison, hierarchical models, dynamic models for infectious disease transmission, animal population dynamics.
	www.swan.ac.uk /statistics/das/dirint5.htm (5250 words)

	GISAI: Glossary (Site not responding. Last check: 2007-10-13)
		In discussions of meta-rationality, the Bayesian Probability Theorem is used to estimate the strength of the binding between your beliefs and reality - i.e., the extent to which the fact that you believe X licenses you to conclude that X is true.
		The ontology of a Life game consists of dead cells, live cells, and the cellular-automaton rules.
		The computational representation of the game - in a classical AI - would look like a tree; a single node representing the start of the game, with nine branches leading to nine first-move nodes; each first-move node would have eight branches leading to a total of seventy-two possible second-move nodes, and so on.
	www.singinst.org /GISAI/meta/glossary.html (7238 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		The most pervasive example of such a problem is whether to undertake a public project and, if undertaken, how the costs of the project are to be distributed among the members of the group.
		The third part extends Bayesian game theory by allowing communication prior to the play of the game.
		This is important because Bayesian game models are used in nearly every part of economics to model problems in which agents may have different information and the preliminary results by the investigator show that pre-play communication can have a very significant effect on the outcome of the Bayesian game.
	www.cs.utexas.edu /users/yguan/NSFAbstracts/Abstracts/SBE/SBR.SBE.a8912072.txt (378 words)

	Product Contributions
		Bayesian analysis enables the True Skill ranking systems to identify player skill with great speed, to the extent that a new player joining a league consisting of a million players can be ranked accurately in fewer than 20 games.
		Drivatars, a new form of artificial intelligence for Xbox's Forza Motorsport game, have enhanced racing gaming by giving gamers humanlike competition that greatly enhances the realism and the challenge of the racing experience.
		Microsoft Research technology has analyzed a number of games and has provided improved code optimization and code layout on the disk for faster gaming.
	www.research.microsoft.com /aboutmsr/pastpresentfuture/contributions.aspx (3304 words)

	On Purification of Equilibrium in Bayesian Games and Ex-Post Nash Equilibrium
		On Purification of Equilibrium in Bayesian Games and Ex-Post Nash Equilibrium
		Kalai (2002) demonstrates that in semi anonymous Bayesian games with sufficiently many players any Bayesian equilibrium is approximately ex-post Nash.
		In this paper we demonstrate that the existence of an approximate expost Nash property implies a purification result of the standard sort for the original Bayesian game.
	ideas.repec.org /p/van/wpaper/0512.html (433 words)

	Robustness of Bayesian Equilibria
		The standard model of a Bayesian game used in most applications assumes that players' beliefs are derived from a common knowledge prior on preference parameters.
		I then perturb the embedded set using the notion of common p-belief (Monderer and Samet, 1989) by considering all types for which it is common p-belief that all players derive their beliefs about preference parameters from similar priors.
		For types in the perturbed set, I define an $\varepsilon$-equilibrium in which every player's strategy is an equilibrium strategy for the game where his individual prior is a common knowledge prior.
	ideas.repec.org /p/ecm/nasm04/199.html (386 words)

	Glossary of research economics
		Bayesian analysis: "In Bayesian analysis all quantities, including the parameters, are random variables.
		Contexts: game theory; IO Beveridge curve: The graph of the inverse relation of unemployment to job vacancies.
		cooperative game: A game structure in which the players have the option of planning as a group in advance of choosing their actions.
	www.econterms.com /econtent.html (14590 words)

	Experiments with a Bayesian game player (ResearchIndex)
		In [7] we proposed a Bayesian algorithm for game playing that we will call BP.
		BP maintains a probabilistic model of its uncertainty and uses it to grow its search tree in the most relevant directions, and to value the tree's nodes.
		Here we describe the first implementations of this algorithm and report on experiments comparing it with the standard (alpha-beta, or AB) approach, and the "probability product" (PP) approach, in several popular games.
	citeseer.ist.psu.edu /12409.html (716 words)

	Test: Spam in the wild
		The company is adding Bayesian filtering to Version 9 of its product, to be released later this year, which should improve overall performance.
		One product submitted for this test, Gordano Messaging Server, was dropped because it not only uses the same poor algorithm as MailEssentials and Praetor, but it also comes with an empty rule set, and the vendor doesn't even provide an initial guess at a word list.
		If per-user controls and quarantines are not as important as other policy-based and content-based mail filtering, Tumbleweed's MMS appliance did an excellent job of filtering spam and gave very flexible control over mail flows.
	www.networkworld.com /reviews/2003/0915spam.html (4583 words)

	Resource Links on Self-Organisation, Complexity and Artificial Life
		Games of Life in Colour - by Gunnar Johnsson
		Game of Life Varients - by David Ingalls Bell
		Bayesian Methods for Neural Nets - FAQ by David MacKay
	www.calresco.org /links.htm (1190 words)

	APA Pacific Division - 2005 Pacfic Division Program
		Topic: Revising Beliefs about Game Theory: Strategies for Rational Choice
		"Update and Revision in the Course of a Game".
		"Foolish Games: Hobbes and the Safer Strategy of Trustworthiness"
	apa-pacific.org /archive/2005p.php (4910 words)

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