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Topic: Perfect Bayesian equilibrium

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	Bayesian game - Wikipedia, the free encyclopedia
		In a Bayesian game (where players are modelled as risk-neutral), rational players are seeking to maximize their expected payoff, given their beliefs about the other players (in the general case, where players may be risk averse or risk-loving, the assumption is that players are expected utility-maximizing).
		PBE is in the spirit of subgame perfection in that it demands that subsequent play be optimal.
		PBE affords this means: players place beliefs on nodes occurring in their information sets, which means that the information set can be generated by nature (in the case of incomplete information) or by other players (in the case of imperfect information).
	en.wikipedia.org /wiki/Perfect_Bayesian_equilibrium (2112 words)

	PSC 796, Formal Theories of Choice
		Perfect Bayesian equilibrium is a stronger equilibrium concept requiring rational behavior at every information set (similar to subgame perfection) and beliefs derived from Bayes's rule wherever possible.
		Perfect Bayesian equilibrium is not fully satisfactory as an equilibrium concept: it does not completely pin down beliefs off the equilibrium path, and it does not always rule out unreasonable equilibria.
		Sequential equilibrium is not invariant to the addition of irrelevant actions to the game tree, and therefore it depends crucially on the way in which the game tree is constructed (the latter, though, could be said of most aspects of game theory).
	www.maxwell.syr.edu /maxpages/faculty/sherman/psc796.html (4422 words)

	SFB 504 glossary: (Strategic) Equilibrium
		As a strategic equilibrium is a profile of strategies that is unilaterally unimprovable given that all (other) players conform to their equilibrium strategies, the concept is weak and very general, but on the other hand most games possess several strategic equilibria.
		Nash equilibrium is the pure form of the basic concept of strategic equilibrium; as such, it is useful mainly in normal form games with complete information.
		Subgame perfect equilibrium: In extensive-form games with complete information, many strategy profiles that form best responses to one another imply incredible threats or promises that a player actually does not want to carry out anymore once he must face an (unexpected) off-equilibrium move of an opponent.
	www.sfb504.uni-mannheim.de /glossary/strateq.htm (1206 words)

	Trembling hand perfect equilibrium - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-08)
		Trembling hand perfect equilibrium is a refinement of Nash Equilibrium due to Reinhard Selten.
		A trembling hand perfect equilibrium is an equilibrium that takes the possibility of off-the-equilibrium play into account by assuming that the players, through a "slip of the hand" or tremble, may choose unintended strategies, albeit with negligible probability.
		In fact, a normal-form trembling hand perfect equilibrium does not even have to be subgame perfect.
	www.flyproxy.com /index.php?q=aHR0cDovL2VuLndpa2lwZWRpYS5vcmcvd2lraS9UcmVtYmxpbmdfaGFuZF9wZXJmZWN0X2VxdWlsaWJyaXVt (945 words)

	[No title]
		The general idea of the equilibrium is that the soft incumbent will choose Fight if there are enough periods left, so as to pretend to be tough and thereby deter entry.
		In the plausible perfect bayesian equilibrium, the entrant Stays Out for the first K repetitions, because the incumbent would choose to Fight entry if it occurred.
		This is an equilibrium because the tough incumbent wants to deter entry in the second period, which he can do only by choosing Accommodate in the first period, and he values deterring entry more than he values responding to entry with Fight instead of Accommodate.
	www.rasmusen.org /w/04.03.04a.htm (1116 words)

	6.2: Perfect Bayesian Equilibria of Sender-Receiver (Signalling) Games
		A Bayesian equilibrium of the Sender-Receiver game is (a) a strategy for each type of Sender, (b) a strategy for the Receiver, and (c) a conditional posterior belief system describing the Receiver's updated beliefs about the Sender's type as a function of the observed message, which satisfies two optimality conditions and a Bayes-consistency condition.
		And the Receiver's conditional posterior belief system must be consistent with Bayes' Rule whenever possible (i.e., on the equilibrium path).
		Perfect Bayesian equilibrium strengthens the Receiver-optimality condition to apply to off-the-path messages as well.
	www.virtualperfection.com /gametheory/Section6.2.html (498 words)

	Sequential equilibrium - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-08)
		Sequential equilibrium is a refinement of Nash Equilibrium for extensive form games due to David M. Kreps and Robert Wilson.
		Sequential equilibrium is a further refinement of subgame perfect equilibrium and even perfect Bayesian equilibrium.
		A refinement of sequential equilibrium that guarantees admissibility is quasi-perfect equilibrium.
	www.flyproxy.com /index.php?q=aHR0cDovL2VuLndpa2lwZWRpYS5vcmcvd2lraS9TZXF1ZW50aWFsX2VxdWlsaWJyaXVt (431 words)

	Signaling games - Wikipedia, the free encyclopedia
		Perfect Bayesian equilibrium is a refinement of Bayesian Nash equilibrium, which is an extension of Nash equilibrium to games of incomplete information.
		The perfect Bayesian equilibria in such a game can be divided in two different categories, pooling equilibria and separating equilibria.
		A pooling equilibrium is an equilibrium where senders with different types all choose the same message.
	en.wikipedia.org /wiki/Signaling_games (1338 words)

	College Catalog - Reed College
		Considerable attention is devoted to understanding the economic concept of efficiency and demonstrating the efficiency of competitive equilibrium in a general equilibrium framework.
		Numerous refinements of the Nash equilibrium concept, including sub-game perfect Nash equilibrium, Bayesian Nash equilibrium, and perfect Bayesian equilibrium, are also considered.
		The theory of international trade and the effects of trade policy tools are developed in both perfect and imperfect competition, with reference to the empirical evidence.
	web.reed.edu /catalog_2005_06/courses/econ/index.html (2099 words)

	Nash equilibrium - Wikipedia, the free encyclopedia
		In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally.
		If a game has a unique Nash equilibrium and is played among players with certain characteristics, then it is true (by definition of these characteristics) that the NE strategy set will be adopted.
		Pong has an equilibrium which can be played perfectly by a computer, but to make human vs. computer games interesting the programmers add small errors in execution, violating the second condition.
	en.wikipedia.org /wiki/Nash_equilibrium (2242 words)

	2005-05 - Abstract (Site not responding. Last check: 2007-10-08)
		This paper presents a modification of the inspection game: The "Bayesian Monitoring" model rests on the assumption that judges are interested in enforcing compliant behavior and making correct decisions.
		The Bayesian Monitoring model, just as the inspection game, has different implications than enforcement models in the tradition of Becker (1968).
		Total deterrence of bad behavior is impossible, and the equilibrium probability of good behavior is independent of the suspect's own payoff parameters.
	www.uni-saarland.de /fak1/fr12/csle/publications/2005-06.htm (269 words)

	Chronology of Game Theory
		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.
		With their paper The Bayesian Foundations of Solution Concepts of Games Tan and Werlang are among the first to formally discuss the assumptions about a player's knowledge that lie behind the concepts of Nash equilibria and rationalizability.
		An early published discussion of the idea of a Perfect Bayesian Equilibrium is the paper by D. Fudenberg and J. Tirole, Perfect Bayesian Equilibrium and Sequential Equilibrium.
	www.econ.canterbury.ac.nz /personal_pages/paul_walker/gt/hist.htm (6341 words)

	[No title]
		Incomplete information about partner’s type, Bayesian equilibrium: trespassers and inspectors, educational signalling game, advertising game.
		Perfect Bayesian equilibrium: a thief and a policeman, Caribean crises.
		Regime as equilibrium of institutions and their performance.
	www.ceu.hu /crc/Syllabi/alumni/economics/kokovin.html (1201 words)

	Game Theory
		A " Nash Equilibrium" will be reached when each agent's actions begets a reaction by all the other agents which, in turn, begets the same initial action.
		In 1950, John Nash introduced the concept of a "Nash Equilibrium" (NE), which became the organizing concept under Game Theory -- even though the concept actually stretched as far back as Cournot (1838).
		industrial organization, general equilibrium, monetary theory, etc.), and, in the process, went on to invent several solution concepts for coalitional games (e.g.
	cepa.newschool.edu /het/schools/game.htm (1057 words)

	Paul Resnick's Occasional Musings
		Equilibrium prices means that each consumer satisfies all their demand from their neighbor with lowest price-- price has to be higher if that seller wouldn't have enough to meet your demand.
		In Arrow-Debreu general equilibrium models, suppose that only local exchanges are possible, and define a new form of equilibrium that requires all the local markets to be in equilibrium.
		Through Bayesian updating, you can infer something about other people's information from their observed choices, and thus update your own priors about which is the better choice to make.
	presnick.livejournal.com (15877 words)

	SSRN-Signaling, Globality, and the Intuitive Criterion by Christian Ewerhart, Philipp Wichardt
		The paper considers an economically relevant class of signaling games that possess more than one Perfect Bayesian equilibrium.
		For this class of games, it is shown that a Perfect Bayesian equilibrium is unaffected by a small perturbation of the information structure if and only if it is consistent with a criterion suggested by Cho and Kreps (1987).
		Moreover, the equilibrium in the global signaling game is essentially unique.
	papers.ssrn.com /sol3/papers.cfm?abstract_id=555688 (274 words)

	Game Theory Forum
		Although they are similar and sometimes identical in some simple games, sequential equilibrium differs from PBE in imposing more restrictions on the way players update their beliefs (From a graduate textbook by Fudenberg and Tirole, "Game Theory"(1991, MIT Press), p.321).
		Sequential equilibrium requires 'sequential rationality' and 'consistency' conditions on an assessment (a pair of a strategy profile and a system of belief.) For more information, see any graduate text on game theory, for example, Fudenberg and Tirole(1991).
		Also see a paper "Perfect Bayesian Equilibrium and Sequential Equilibrium" by Fudenberg and Tirole (1991, Journal of Economic Theory 53:236-260.) if you need more rigorous treatments.
	levine.sscnet.ucla.edu /bin/workshops-php/discuss/discuss.php3?showID=396467000000000208 (138 words)

	Andrew G. Gilpin
		Computing an equilibrium of an extensive form game of imperfect information is a fundamental problem in computational game theory, but current techniques do not scale to large games.
		Our research advances in equilibrium computation have enabled us to solve for the optimal (equilibrium) strategies for this game.
		In more general TLAs, the buyers' optimal strategies are more intricate, and we derive the perfect Bayesian equilibrium for the game.
	www.cs.cmu.edu /~gilpin (1340 words)

	EC943-G-AU:course catalogue
		Game theoretic methodology is widely used in economics, and in some areas of the discipline provides the basic tool of analysis.
		This course seeks to familiarise students with the main game theoretic concepts applied in modern economics, and in particular the various so-called solution concepts - Nash equilibrium, subgame perfect equilibrium, Bayesian equilibrium and (weak) perfect Bayesian equilibrium.
		These concepts will be illustrated via a variety of economic models from areas such as industrial organisation, public goods, bargaining, and labor markets.
	www2.essex.ac.uk /courses/result.asp?coursecode=EC943&level=G&period=AU&yearofcourse=04 (274 words)

	European Union's Generalized System of Preferences and Tropical Deforestation: the Perfect Bayesian Equilibrium in a ... (Site not responding. Last check: 2007-10-08)
		European Union's Generalized System of Preferences and Tropical Deforestation: the Perfect Bayesian Equilibrium in a Signaling
		European Union's Generalized System of Preferences and Tropical Deforestation: the Perfect Bayesian Equilibrium in a Signaling Game
		This paper examines the recent proposal by the European Union to provide additional tariff reduction on wood-processed goods to tropical forest countries that meet certain sustainable forest management criteria.
	www.sp.uconn.edu /~boa96001/signaling.htm (138 words)

	EBSLG: The Information Limit to Honest Managerial Behavior
		This paper argues that in an economy hosting publicly traded companies where investors have only imperfect information about a firm’s type and where a honest financial report may be wrong, at least some bad firms managers will provide false statements.
		Furthermore, in equilibrium some good firm managers may also resort to corrupt auditors which will issue a favorable report without carrying out any investigation.
		The frequency of dishonest managers is analysed in keeping with the precision of the report and the total number of firms.
	ebslgwp.hhs.se /essewp/abs/essewpDR-04008.htm (218 words)

	6.3: Perfect Bayesian Equilibria of Extensive-Form Games (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-10-08)
		We have seen that Nash equilibria of extensive-form games can be undesirable because they can rely on incredible threats at off-the-equilibrium-path subgames.
		We were sometimes able to refine away such undesirable equilibria by strengthening our solution concept--demanding subgame perfection, which requires that the restriction of a strategy profile to any subgame be a Nash equilibrium of that subgame.
		I offer an example extensive-form game to demonstrate that subgame perfection will not eliminate all undesirable equilibria of extensive-form games.
	virtualperfection.com.cob-web.org:8888 /gametheory/Section6.3.html (204 words)

	Game Theory Forum
		So apparently men in the field of economics (and presumably other fields as well) have decided that as long as they refer to agents in problems and models as "she", then gender disparity in the field has been taken care of.
		One kind of Asymmetric equilibrium is as following: for one donor: contribute nothing regardless of his own value; the other donor: D(v)=0, if v
		It might be good to read "Perfect equilibrium in a bargaining model", Econometrica 50/1, 97-109, by Ariel Rubinstein.
	levine.sscnet.ucla.edu /bin/workshops-php/discuss/discuss.php3?... (934 words)

	Course Descriptions
		It covers the theory of consumer and producer behavior, decision-making under uncertainty, and provides an introduction to game theory focusing on static and dynamic games of complete information.
		This course provides an introduction to the techniques of modern macroeconomic analysis that are needed by all graduate students in economics.
		Dynamic programming will be emphasized as a method for formulating and solving decision problems with these features.
	www.georgetown.edu /departments/economics/graduate/descriptions.html (1753 words)

	Equilibrium Vengeance
		This paper introduces two ideas, emotional state dependent utility components (ESDUCs), and evolutionary perfect Bayesian equilibrium (EPBE).
		Incorporating behavioral noise and observational noise leads to a range of (short run) Perfect Bayesian equilibria (PBE) involving both vengeful and non-vengeful types.
		We then derive two (long run) EPBE, one where both types survive and reap mutual gains, and a second where only the non-vengeful type survives and there are no mutual gains.
	ideas.repec.org /p/ces/ceswps/_766.html (312 words)

	Game Theory Forum (Site not responding. Last check: 2007-10-08)
		I am a research student and currently doing research into both decision thoery and game theory.
		Attached is a word document regarding the problem i face and the game tree which i am not so sure about.
		1) Must a perfect bayesian equlibrium game tree always start with a chance node to determine the type of the first player?
	levine.sscnet.ucla.edu /bin/workshops-php/discuss/discuss.php3?showID=713719000000000120 (91 words)

	Advanced Game Theory
		Nash equilibrium and iterated dominance in strategic games with perfect information [O-R 2.1-2.4, 3.1-3.2] [F-T 1, 12.1]; plus:
		Subgame perfection, backward induction and iterated weak dominance in extensive games with perfect information [O-R 6] [F-T 3]; in particular:
		Sequential equilibrium, perfect Bayesian equilibrium and trembling-hand perfection in extensive games with imperfect information [O-R 11-12] [F-T 8, 11.1, 11.3]
	www.vwl.uni-muenchen.de /ls_rady/AdvancedGameTheory.html (281 words)

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