Introduction to Lattices and Order

Davey, Brian A.; Priestley, H. A.

doi:10.1017/cbo9780511809088

Cited by 2,652 publications

(1,331 citation statements)

References 0 publications

Supporting

Mentioning

1,308

Contrasting

Unclassified

Order By: Relevance

“…Assumption 4 is not satis…ed for general concave production in private inputs (with no externalities). Further, in the case of production externalities as in Romer [50] we could have F (k; 1; K; 1) = k K for < 0; 2 (0; 1); and j j > , which also violates Assumption 4: 16 There are no shocks.…”

Section: The Economiesmentioning

confidence: 97%

See 1 more Smart Citation

Which recursive equilibrium?

Mirman

Morand²,

Reffett

2010

Proceedings of the Behavioral and Quantitative Game Theory: Conference on Future Directions

View full text Add to dashboard Cite

For simple versions of the Cass-Diamond growth model where the fundamental welfare theorems of economics fail, we prove the set of minimal state space recursive equilibrium (RE) is large, with multiple RE existing in multiple subclasses of functions. This situation remains the true even when uniqueness results are known, for both OLG and in…nity-lived agent versions of the model. This implies the set of Generalized Markov equilibrium (GME) is also large. We also provide explicit iterative procedures from computing particular RE in each subclass, with some procedures globally stable from a topological persective for particular RE when their domains are restricted. All iterative methods are order stable relative to perturbations of deep parameters. Finally, we construct an simple economy where existing correspondence-based methods for computing GME fails, and propose a new method that computes the set of GME as minimal state spaceWe thank Subir Chakrabarti, Ramu Gopolan, Takashi Kamihigashi, Rajnesh Mehra, Adrian Peralta-Alva, Ed Prescott, Manuel Santos, Yiannis Vailakis, × ukasz Woźny, and especially, Robert Becker for helpful discussions, as well as seminar participants at IU-PUI, ASU, and EWGET-2012 at Exeter for their helpful comments. Manjira Datta and Kevin Re¤ett thank the Center d'Economie de la Sorbonne (CES) and the Paris School of Economics for graciously arranging their visits during the Spring terms of both 2011 and 2012.y Manjira Datta, Department of Economics, Arizona State University; Leonard J. Mirman, Department of Economics, University of Virginia; Olivier F. Morand, Department of Economics, University of Connecticut; Kevin Re¤ett, Department of Economics, Arizona State University. We are in the process of rewriting this paper, so do not recirculate, as errors, types, etc. may remain; rather write the corresponding author at Kevin.Re¤ett@asu.edu for the most recent version. 1 RE using …xed points of the expanded set of state variables. Our results point to the complicated nature of the RE approximation problem even in simple macro models.

show abstract

Section: The Economiesmentioning

confidence: 97%

“…Thus g^is an greatest lower bound of B. Since m is the top element of H u m , it is a complete lattice (e.g., Davey and Priestley [16], Theorem 2.31). Dually, for A H l m ; de…ne g _ (k) = sup h2A h(k).…”

Section: Re In Olg Modelsmentioning

confidence: 99%

Which recursive equilibrium?

Mirman

Morand²,

Reffett

2010

Proceedings of the Behavioral and Quantitative Game Theory: Conference on Future Directions

View full text Add to dashboard Cite

show abstract

“…We employ basic notions from partial order theory [12]. A partial order is a set P with a partial order relation "≤" and it is denoted by (P, ≤).…”

Section: Basic Notions and Definitionsmentioning

confidence: 99%

Safety Control of Hidden Mode Hybrid Systems

Verma

Vecchio

2012

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

Abstract-In this paper, we consider the safety control problem for Hidden Mode Hybrid Systems (HMHSs), which are a special class of hybrid automata in which the mode is not available for control. For these systems, safety control is a problem with imperfect state information. We tackle this problem by introducing the notion of non-deterministic discrete information state and by translating the problem to one with perfect state information. The perfect state information control problem is obtained by constructing a new hybrid automaton, whose discrete state is an estimate of the HMHS mode and is, as such, available for control. This problem is solved by computing the capture set and the least restrictive control map for the new hybrid automaton. Sufficient conditions for the termination of the algorithm that computes the capture set are provided. Finally, we show that the solved perfect state information control problem is equivalent to the original problem with imperfect state information under suitable assumptions. We illustrate the application of the proposed technique to a collision avoidance problem between an autonomous vehicle and a human driven vehicle at a traffic intersection.Index Terms-Mode estimation, dynamic feedback, multiagent systems.

show abstract

“…The proposition s, which gures as a disjunct in a's account, is eliminated from the node bc onwards. 3 Formulae computed using The Logics Workbench, http://www.lwb.unibe.ch/.…”

Section: Theoremmentioning

confidence: 99%

Trustworthiness by Default

Klüwer

Waaler

2006

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. We present a framework for reasoning about trustworthiness, with application to con ict resolution and belief formation at various degrees of reliability. On the basis of an assignment of relative trustworthiness to sets of information sources, a lattice of degrees of trustworthiness is constructed; from this, a priority structure is derived and applied to the problem of forming the right opinion in the presence of possibly conicting information. Consolidated with an unquestioned knowledge base, this provides an unambiguous account of what an agent should believe, conditionally on which information sources are trusted. Applications in multi-agent doxastic logic are sketched.

show abstract

Introduction to Lattices and Order

Cited by 2,652 publications

References 0 publications

Which recursive equilibrium?

Which recursive equilibrium?

Safety Control of Hidden Mode Hybrid Systems

Trustworthiness by Default

Contact Info

Product

Resources

About