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UNIVERSALLY RATIONAL BELIEF HIERARCHIES

ELIAS TSAKAS
2014 International Game Theory Review  
In this paper, we define the universally rational belief hierarchies, as those that do not exhibit this property.  ...  Then, he constructed the corresponding Harsanyi type space model that represents the rational belief hierarchies.  ...  N-rational belief hierarchies and universally rational belief hierarchies In the previous section, we introduced the notion of N-rational probability measures.  ... 
doi:10.1142/s0219198914400039 fatcat:2tifsgc7w5f3vmwles7prrlgdy

Rational belief hierarchies

Elias Tsakas
2014 Journal of Mathematical Economics  
We call these Borel probability measures rational, and introduce the notion of a rational belief hierarchy, where the first order beliefs are described by a rational measure over the fundamental space  ...  Then, we derive the corresponding rational type space model, thus providing a Bayesian representation of rational belief hierarchies.  ...  Intuitively, rational belief hierarchies form a strict subset of all belief hierarchies.  ... 
doi:10.1016/j.jmateco.2013.10.005 fatcat:eusxr7cw4raz3o7qzvhjczcvw4

FROM CLASSICAL TO EPISTEMIC GAME THEORY

ANDRÉS PEREA
2014 International Game Theory Review  
To that purpose we will discuss how important notions such as reasoning about the opponents, belief hierarchies, common belief, and the concept of common belief in rationality arose, and gradually entered  ...  Afterwards we discuss how important epistemic notions such as belief hierarchies, common belief, and common belief in rationality, arose and how they slowly but surely provided an alternative to the classical  ...  That is, belief hierarchies come into play.  ... 
doi:10.1142/s0219198914400015 fatcat:css75sbz2vfijit3t33bxvbf7e

Rationality, some preliminary remarks

Etienne VERMEERSCH
1974 Philosophica  
As has been said in the beginning, k-rational people tend to universality 7 to a conviction that their belief should be shared by all men.  ...  In what follows, the adjective k-rationall will be used to refer to beliefs, knowledge etc. which have been reached by strictly scientific procedures.  ... 
doi:10.21825/philosophica.82719 fatcat:lnryhetgf5gx3egmjtdswkvv7m

Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games

Pierpaolo Battigalli, Marciano Siniscalchi
1999 Journal of Economic Theory  
Any (co herent) statement concerning the players' dispositions to hold in teractive beliefs has a representation in our "universal" space.  ...  other's conditional beliefs, etc.  ...  to a (beliefs-closed) subset of the space of (coherent) hierarchies of CPSs, which can thus be rightfully deemed universal.  ... 
doi:10.1006/jeth.1999.2555 fatcat:m4ob5lvxofgtla7cyutmgqv6xe

Every hierarchy of beliefs is a type [article]

Miklos Pinter
2012 arXiv   pre-print
When modeling game situations of incomplete information one usually considers the players' hierarchies of beliefs, a source of all sorts of complications.  ...  Hars\'anyi (1967-68)'s idea henceforth referred to as the "Hars\'anyi program" is that hierarchies of beliefs can be replaced by "types". The types constitute the "type space".  ...  Case 4: Complete universal type space that does not contain every hierarchy of beliefs.  ... 
arXiv:0805.4007v3 fatcat:iezs3rb5qbhbvods6yyao7dkau

Epistemic Game Theory: Beliefs and Types [chapter]

Marciano Siniscalchi
2008 The New Palgrave Dictionary of Economics  
However, the first con-structions of universal type spaces consisting of hierarchies of beliefs are due to Armbruster and Böge [2] , Böge and Eisele [9] and Mertens and Zamir [24] .  ...  How could an individual simultaneously hold (infinitely) many distinct first-order beliefs? Which of these should be used, say, to verify whether she is rational?  ... 
doi:10.1057/978-1-349-95121-5_2375-1 fatcat:wyspkeazxjaulkqmw2otmkhw3a

Epistemic Game Theory: Beliefs and Types [chapter]

Marciano Siniscalchi
2018 The New Palgrave Dictionary of Economics  
However, the first con-structions of universal type spaces consisting of hierarchies of beliefs are due to Armbruster and Böge [2] , Böge and Eisele [9] and Mertens and Zamir [24] .  ...  How could an individual simultaneously hold (infinitely) many distinct first-order beliefs? Which of these should be used, say, to verify whether she is rational?  ... 
doi:10.1057/978-1-349-95189-5_2375 fatcat:cqulbbmoinamndnmw7562klxmy

Book Reviews

Geir B. Asheim
2003 Journal of Economics  
In an extensive form game, a player must also form beliefs about what his opponents will do in parts of the game that will not be reached if the opponents play according to their rationally chosen strategies  ...  A behavioral conjecture specifies beliefs about how a player will act at each of his information sets.  ...  , and so on, this kind of non-equilibrium analysis requires that hierarchies of beliefs are explicitly modelled.  ... 
doi:10.1007/s007120300010 fatcat:aruxt7hvtnawjdeqmxixjbcxnm

Page 682 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
Therefore, the space C of coherent hierarchies over S properly contains the universal space T* of ‘all possible types’ over S.  ...  Thus, this hierarchy of beliefs cannot be the description of the beliefs of some type in some Harsanyi [J. C.  ... 

Mindreading and endogenous beliefs in games

Lauren Larrouy, Guilhem Lecouteux
2017 Journal of Economic Methodology  
Princeton, NJ: Princeton University Press. i 2 , the belief that P1 is likely to choose 1 -in her own mind.  ...  We assumed that players form their beliefs by simulating the reasoning of the other players, and showed that the belief hierarchy of Bayes rational players, when their rationality is common belief (by  ...  rationality of the others and her belief about their actions.  ... 
doi:10.1080/1350178x.2017.1335425 fatcat:ttnyo2udtbdujczlgbhoyglytu

Uncertain rationality, depth of reasoning and robustness in games with incomplete information

Fabrizio Germano, Jonathan Weinstein, Peio Zuazo-Garin
2020 Theoretical Economics  
This paper studies how a wide class of departures from common belief in rationality impact Weinstein and Yildiz's discontinuity.  ...  We weaken ICR to ICR λ , where λ is a sequence whose term λ n is the probability players attach to ( n − 1)th‐order belief in rationality.  ...  Belief hierarchies and universal type space We follow Brandenburger and Dekel's (1993) formulation of universal type space.  ... 
doi:10.3982/te2734 fatcat:dgnwnrzqnvbahmqcwjldtv4mvm

An Epistemic Characterization of Extensive Form Rationalizability

Pierpaolo Battigalli, Marciano Siniscalchi
1999 Social Science Research Network  
We use an extensive form, universal type space to provide the following epistemic characterization of extensive form rationalizability.  ...  Our main contribution is to show that a strategy profile s is extensive form rationalizable if and only if there is a state in which s is played and (0) everybody is rational, (  ...  A key feature of this epistemic model is that it is universal: every "conceivable" profile of hierarchies of conditional beliefs is included in the model.  ... 
doi:10.2139/ssrn.159152 fatcat:yidiaxeyp5a6hgtr6ssdz7i5jq

Page 6714 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
Mertens and Zamir provided a universal type space for the normal form environment; this paper extends considera- tion to conditional beliefs about beliefs leading to hierarchies of conditional belief systems  ...  In parallel, to model rational behavior agents must have beliefs at each contingency. Logical coherency of the model leads to consideration of hierarchies of beliefs (beliefs about beliefs...).  ... 

Page 3545 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews  
We reflect on ordinary reason- ing and systems of rational belief to motivate numerically based probabilistic semantics, which abandons truth-functionality.  ...  The notion of a universal inference operation, generalizing usual inference operations and introduced here as an expressive counterpart for belief change operations, allows a more adequate comparison between  ... 
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