The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Debraj Ray - One of the best experts on this subject based on the ideXlab platform.
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Maximality in the farsighted stable set
Econometrica, 2019Co-Authors: Debraj Ray, Rajiv VohraAbstract:Harsanyi (1974) and Ray and Vohra (2015) extended the stable set of von Neumann and Morgenstern to impose farsighted credibility on coalitional deviations. But the resulting farsighted stable set suffers from a conceptual drawback: while coalitional moves improve on existing outcomes, coalitions might do even better by moving elsewhere. Or other coalitions might intervene to impose their favored moves. We show that every farsighted stable set satisfying some reasonable and easily verifiable properties is unaffected by the imposition of these stringent Maximality constraints. The properties we describe are satisfied by many, but not all farsighted stable sets.
Navin Kashyap - One of the best experts on this subject based on the ideXlab platform.
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the communication complexity of achieving sk capacity in a class of pin models
International Symposium on Information Theory, 2015Co-Authors: Manuj Mukherjee, Navin KashyapAbstract:The communication complexity of achieving secret key (SK) capacity in the multiterminal source model of Csiszar and Narayan is the minimum rate of public communication required to generate a maximal-rate SK. It is well known that the minimum rate of communication for omniscience, denoted by R CO , is an upper bound on the communication complexity, denoted by R SK . A source model for which this upper bound is tight is called R SK -maximal. In this paper, we establish a sufficient condition for R SK -Maximality within the class of pairwise independent network (PIN) models defined on hypergraphs. This allows us to compute R SK exactly within the class of PIN models satisfying this condition. On the other hand, we also provide a counterexample that shows that our condition does not in general guarantee R SK -Maximality for sources beyond PIN models.
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the communication complexity of achieving sk capacity in a class of pin models
arXiv: Information Theory, 2015Co-Authors: Manuj Mukherjee, Navin KashyapAbstract:The communication complexity of achieving secret key (SK) capacity in the multiterminal source model of Csisz$\'a$r and Narayan is the minimum rate of public communication required to generate a maximal-rate SK. It is well known that the minimum rate of communication for omniscience, denoted by $R_{\text{CO}}$, is an upper bound on the communication complexity, denoted by $R_{\text{SK}}$. A source model for which this upper bound is tight is called $R_{\text{SK}}$-maximal. In this paper, we establish a sufficient condition for $R_{\text{SK}}$-Maximality within the class of pairwise independent network (PIN) models defined on hypergraphs. This allows us to compute $R_{\text{SK}}$ exactly within the class of PIN models satisfying this condition. On the other hand, we also provide a counterexample that shows that our condition does not in general guarantee $R_{\text{SK}}$-Maximality for sources beyond PIN models.
Rajiv Vohra - One of the best experts on this subject based on the ideXlab platform.
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Maximality in the farsighted stable set
Econometrica, 2019Co-Authors: Debraj Ray, Rajiv VohraAbstract:Harsanyi (1974) and Ray and Vohra (2015) extended the stable set of von Neumann and Morgenstern to impose farsighted credibility on coalitional deviations. But the resulting farsighted stable set suffers from a conceptual drawback: while coalitional moves improve on existing outcomes, coalitions might do even better by moving elsewhere. Or other coalitions might intervene to impose their favored moves. We show that every farsighted stable set satisfying some reasonable and easily verifiable properties is unaffected by the imposition of these stringent Maximality constraints. The properties we describe are satisfied by many, but not all farsighted stable sets.
Joel David Hamkins - One of the best experts on this subject based on the ideXlab platform.
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the necessary Maximality principle for c c c forcing is equiconsistent with a weakly compact cardinal
Mathematical Logic Quarterly, 2005Co-Authors: Joel David Hamkins, Hugh W WoodinAbstract:The Necessary Maximality Principle for c.c.c. forcing with real parameters is equiconsistent with the existence of a weakly compact cardinal. The Necessary Maximality Principle for c.c.c. forcing, denoted 2mpccc(R), asserts that any statement about a real in a c.c.c. extension that could be- come true in a further c.c.c. extension and remain true in all subsequent c.c.c. extensions, is already true in the minimal extension containing the real. We show that this principle is equiconsistent with the existence of a weakly compact cardinal. The principle is one of a family of principles considered in (Ham03) (build- ing on ideas of (Cha00) and overlapping with independent work in (SV01)). MSC: 03E55, 03E40. Keywords: forcing axiom, ccc forcing, weakly compact cardinal. The first author is affiliated with the College of Staten Islandof CUNY and The CUNY Graduate Center, and his research has been supported by grants from the Research Foun- dation of CUNY and the National Science Foundation DMS-9970993. The research of the second author has been partially supported by National Science Foundation grant DMS-9970255.
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the necessary Maximality principle for c c c forcing is equiconsistent with a weakly compact cardinal
arXiv: Logic, 2004Co-Authors: Joel David Hamkins, Hugh W WoodinAbstract:The Necessary Maximality Principle for c.c.c. forcing asserts that any statement about a real in a c.c.c. extension that could become true in a further c.c.c. extension and remain true in all subsequent c.c.c. extensions, is already true in the minimal extension containing the real. We show that this principle is equiconsistent with the existence of a weakly compact cardinal.
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a simple Maximality principle
Journal of Symbolic Logic, 2003Co-Authors: Joel David HamkinsAbstract:In this paper, following an idea of Christophe Chalons, I propose a new kind of forcing axiom, the Maximality Principle, which asserts that any sentence φ holding in some forcing extension Vℙ and all subsequent extensions Vℙ*ℚ holds already in V. It follows, in fact, that such sentences must also hold in all forcing extensions of V. In modal terms, therefore, the Maximality Principle is expressed by the scheme (◊ □ φ) ⇒ □ φ, and is equivalent to the modal theory S5. In this article, I prove that the Maximality Principle is relatively consistent with ZFC. A boldface version of the Maximality Principle, obtained by allowing real parameters to appear in φ, is equiconsistent with the scheme asserting that Vδ ≺ V for an inaccessible cardinal δ, which in turn is equiconsistent with the scheme asserting that ORD is Mahlo. The strongest principle along these lines is □ , which asserts that holds in V and all forcing extensions. From this, it follows that 0# exists, that x# exists for every set x, that projective truth is invariant by forcing, that Woodin cardinals are consistent and much more. Many open questions remain.
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a simple Maximality principle
arXiv: Logic, 2000Co-Authors: Joel David HamkinsAbstract:In this paper, following an idea of Christophe Chalons, I propose a new kind of forcing axiom, the Maximality Principle, which asserts that any sentence phi holding in some forcing extension V^P and all subsequent extensions V^P*Q holds already in V. It follows, in fact, that such sentences must also hold in all forcing extensions of V. In modal terms, therefore, the Maximality Principle is expressed by the scheme (diamond box phi) implies (box phi), and is equivalent to the modal theory S5. In this article, I prove that the Maximality Principle is relatively consistent with ZFC. A boldface version of the Maximality Principle, obtained by allowing real parameters to appear in phi, is equiconsistent with the scheme asserting that V_delta is an elementary substructure of V for an inaccessible cardinal delta, which in turn is equiconsistent with the scheme asserting that ORD is Mahlo. The strongest principle along these lines is the Necessary Maximality Principle, which asserts that the boldface MP holds in V and all forcing extensions. From this, it follows that 0# exists, that x# exists for every set x, that projective truth is invariant by forcing, that Woodin cardinals are consistent and much more. Many open questions remain.
Manuj Mukherjee - One of the best experts on this subject based on the ideXlab platform.
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the communication complexity of achieving sk capacity in a class of pin models
International Symposium on Information Theory, 2015Co-Authors: Manuj Mukherjee, Navin KashyapAbstract:The communication complexity of achieving secret key (SK) capacity in the multiterminal source model of Csiszar and Narayan is the minimum rate of public communication required to generate a maximal-rate SK. It is well known that the minimum rate of communication for omniscience, denoted by R CO , is an upper bound on the communication complexity, denoted by R SK . A source model for which this upper bound is tight is called R SK -maximal. In this paper, we establish a sufficient condition for R SK -Maximality within the class of pairwise independent network (PIN) models defined on hypergraphs. This allows us to compute R SK exactly within the class of PIN models satisfying this condition. On the other hand, we also provide a counterexample that shows that our condition does not in general guarantee R SK -Maximality for sources beyond PIN models.
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the communication complexity of achieving sk capacity in a class of pin models
arXiv: Information Theory, 2015Co-Authors: Manuj Mukherjee, Navin KashyapAbstract:The communication complexity of achieving secret key (SK) capacity in the multiterminal source model of Csisz$\'a$r and Narayan is the minimum rate of public communication required to generate a maximal-rate SK. It is well known that the minimum rate of communication for omniscience, denoted by $R_{\text{CO}}$, is an upper bound on the communication complexity, denoted by $R_{\text{SK}}$. A source model for which this upper bound is tight is called $R_{\text{SK}}$-maximal. In this paper, we establish a sufficient condition for $R_{\text{SK}}$-Maximality within the class of pairwise independent network (PIN) models defined on hypergraphs. This allows us to compute $R_{\text{SK}}$ exactly within the class of PIN models satisfying this condition. On the other hand, we also provide a counterexample that shows that our condition does not in general guarantee $R_{\text{SK}}$-Maximality for sources beyond PIN models.
