scholarly journals Quasi-Perfect Stackelberg Equilibrium

2019 ◽  
Vol 33 ◽  
pp. 2117-2124 ◽  
Author(s):  
Alberto Marchesi ◽  
Gabriele Farina ◽  
Christian Kroer ◽  
Nicola Gatti ◽  
Tuomas Sandholm
Keyword(s):  
Broad Class ◽  
Stackelberg Equilibrium ◽  
Correlated Equilibrium ◽  
Equilibrium Concept ◽  
Extensive Form ◽  
Tree Form ◽  
Axiomatic Definition ◽  
Security Games ◽  
Definition Of ◽  
Perfect Equilibria

Equilibrium refinements are important in extensive-form (i.e., tree-form) games, where they amend weaknesses of the Nash equilibrium concept by requiring sequential rationality and other beneficial properties. One of the most attractive refinement concepts is quasi-perfect equilibrium. While quasiperfection has been studied in extensive-form games, it is poorly understood in Stackelberg settings—that is, settings where a leader can commit to a strategy—which are important for modeling, for example, security games. In this paper, we introduce the axiomatic definition of quasi-perfect Stackelberg equilibrium. We develop a broad class of game perturbation schemes that lead to them in the limit. Our class of perturbation schemes strictly generalizes prior perturbation schemes introduced for the computation of (non-Stackelberg) quasi-perfect equilibria. Based on our perturbation schemes, we develop a branch-and-bound algorithm for computing a quasi-perfect Stackelberg equilibrium. It leverages a perturbed variant of the linear program for computing a Stackelberg extensive-form correlated equilibrium. Experiments show that our algorithm can be used to find an approximate quasi-perfect Stackelberg equilibrium in games with thousands of nodes.

Insensitive average residence times in generalized semi-Markov processes

1981 ◽  
Vol 13 (04) ◽  
pp. 720-735 ◽  
Author(s):  
A. D. Barbour ◽  
R. Schassberger
Keyword(s):  
Steady State ◽  
Markov Processes ◽  
Broad Class ◽  
Residence Times ◽  
Steady State Distribution ◽  
State Distribution ◽  
Lifetime Distributions ◽  
Definition Of ◽  
Semi Markov Processes ◽  
Networks Of Queues

For a broad class of stochastic processes, the generalized semi-Markov processes, conditions are known which imply that the steady state distribution of the process, when it exists, depends only on the means, and not the exact shapes, of certain lifetime distributions entering the definition of the process. It is shown in the present paper that this insensitivity extends to certain average and conditional average residence times. Particularly interesting applications can be found in the field of networks of queues.

scholarly journals Theory of existence and uniqueness for the nonlinear Maxwell-Boltzmann equation I

1977 ◽  
Vol 16 (3) ◽  
pp. 379-414 ◽  
Author(s):  
Aleksander Glikson
Keyword(s):  
Boltzmann Equation ◽  
Existence And Uniqueness ◽  
Broad Class ◽  
Physical Space ◽  
Uniqueness Result ◽  
Cauchy Problems ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Boltzmann Gas ◽  
Definition Of

A review of the development of the theory of existence and uniqueness of solutions to initial-value problems for mostly reduced versions of the nonlinear Maxwell-Boltzmann equation with a cut-off of intermolecular interaction, precedes the formulation and discussion of a somewhat generalized initial-value problem for the full nonlinear Maxwell-Boltzmann equation, with or without a cut-off. This is followed by a derivation of a new existence-uniqueness result for a particular Cauchy problem for the full nonlinear Maxwell-Boltzmann equation with a cut-off, under the assumption that the monatomic Boltzmann gas in the unbounded physical space X is acted upon by a member of a broad class of external conservative forces with sufficiently well-behaved potentials, defined on X and bounded from below. The result represents a significant improvement of an earlier theorem by this author which was until now the strongest obtained for Cauchy problems for the full Maxwell-Boltzmann equation. The improvement is basically due to the introduction of equivalent norms in a Banach space, the definition of which is connected with an exponential function of the total energy of a free-streaming molecule.

scholarly journals DEFORMATION CONDITIONS FOR PSEUDOREPRESENTATIONS

2019 ◽  
Vol 7 ◽  
Author(s):  
PRESTON WAKE ◽  
CARL WANG-ERICKSON
Keyword(s):  
Stability Condition ◽  
Deformation Theory ◽  
Axiomatic Definition ◽  
Galois Deformation ◽  
Definition Of

Given a property of representations satisfying a basic stability condition, Ramakrishna developed a variant of Mazur’s Galois deformation theory for representations with that property. We introduce an axiomatic definition of pseudorepresentations with such a property. Among other things, we show that pseudorepresentations with a property enjoy a good deformation theory, generalizing Ramakrishna’s theory to pseudorepresentations.

Extensions of the Lewis system S5

1951 ◽  
Vol 16 (2) ◽  
pp. 112-120 ◽  
Author(s):  
Schiller Joe Scroggs
Keyword(s):  
Broad Class ◽  
Characteristic Matrix ◽  
Normal Extension ◽  
Strict Implication ◽  
Finite Characteristic ◽  
Material Implication ◽  
Sentential Calculus ◽  
The Third ◽  
Simple Class ◽  
Definition Of

Dugundji has proved that none of the Lewis systems of modal logic, S1 through S5, has a finite characteristic matrix. The question arises whether there exist proper extensions of S5 which have no finite characteristic matrix. By an extension of a sentential calculus S, we usually refer to any system S′ such that every formula provable in S is provable in S′. An extension S′ of S is called proper if it is not identical with S. The answer to the question is trivially affirmative in case we make no additional restrictions on the class of extensions. Thus the extension of S5 obtained by adding to the provable formulas the additional formula p has no finite characteristic matrix (indeed, it has no characteristic matrix at all), but this extension is not closed under substitution—the formula q is not provable in it. McKinsey and Tarski have defined normal extensions of S4* by imposing three conditions. Normal extensions must be closed under substitution, must preserve the rule of detachment under material implication, and must also preserve the rule that if α is provable then ~◊~α is provable. McKinsey and Tarski also gave an example of an extension of S4 which satisfies the first two of these conditions but not the third. One of the results of this paper is that every extension of S5 which satisfies the first two of these conditions also satisfies the third, and hence the above definition of normal extension is redundant for S5. We shall therefore limit the extensions discussed in this paper to those which are closed under substitution and which preserve the rule of detachment under material implication. These extensions we shall call quasi-normal. The class of quasi-normal extensions of S5 is a very broad class and actually includes all extensions which are likely to prove interesting. It is easily shown that quasi-normal extensions of S5 preserve the rules of replacement, adjunction, and detachment under strict implication. It is the purpose of this paper to prove that every proper quasi-normal extension of S5 has a finite characteristic matrix and that every quasi-normal extension of S5 is a normal extension of S5 and to describe a simple class of characteristic matrices for S5.

Some remarks on axiomatic definition of entropy measure

2017 ◽  
Vol 33 (3) ◽  
pp. 1945-1952 ◽  
Author(s):  
Krzysztof Piasecki
Keyword(s):  
Entropy Measure ◽  
Axiomatic Definition ◽  
Definition Of

An axiomatic definition of the leximin

1986 ◽  
Vol 2 (4) ◽  
pp. 455-463 ◽  
Author(s):  
Eduardas Vilkas
Keyword(s):  
Axiomatic Definition ◽  
Definition Of

scholarly journals The Köthe Dual of an Abstract Banach Lattice

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
E. Jiménez Fernández ◽  
M. A. Juan ◽  
E. A. Sánchez-Pérez
Keyword(s):  
Integral Representation ◽  
Banach Lattice ◽  
Broad Class ◽  
Banach Lattices ◽  
Vector Measures ◽  
Integrable Functions ◽  
Suitable Definition ◽  
Integral Structures ◽  
Definition Of ◽  
Köthe Dual

We analyze a suitable definition of Köthe dual for spaces of integrable functions with respect to vector measures defined onδ-rings. This family represents a broad class of Banach lattices, and nowadays it seems to be the biggest class of spaces supported by integral structures, that is, the largest class in which an integral representation of some elements of the dual makes sense. In order to check the appropriateness of our definition, we analyze how far the coincidence of the Köthe dual with the topological dual is preserved.

scholarly journals Cladistic hypotheses as degree of equivalence relational structures: implications for three-item statements

2021 ◽  
Author(s):  
Valentin Rineau ◽  
Stéphane Prin
Keyword(s):  
Phylogenetic Trees ◽  
Phylogenetic Reconstruction ◽  
Equivalence Relations ◽  
Strong Connection ◽  
Relational Structures ◽  
Degree Of Equivalence ◽  
Axiomatic Definition ◽  
Finite Set ◽  
Definition Of ◽  
Supertree Methods

AbstractThree-item statements, as minimal informative rooted binary phylogenetic trees on three items, are the minimal units of cladistic information. Their importance for phylogenetic reconstruction, consensus and supertree methods relies on both (i) the fact that any cladistic tree can always be decomposed into a set of three-item statements, and (ii) the possibility, at least under some conditions, to build a new cladistic tree by combining all or part of the three-item statements deduced from several prior cladistic trees. In order to formalise such procedures, several k-adic rules of inference, i.e., rules that allow us to deduce at least one new three-item statement from exactly k other ones, have been identified. However, no axiomatic background has been proposed, and it remains unknown if a particular k-adic rule of inference can be reduced to more basic rules. In order to solve this problem, we propose here to define three-item statements in terms of degree of equivalence relations. Given both the axiomatic definition of the latter and their strong connection to hierarchical classifications, we establish a list of the most basic properties for three-item statements. With such an approach, we show that it is possible to combine five three-item statements from basic rules although they are not combinable only from dyadic rules. Such a result suggests that all higher k-adic rules are well reducible to a finite set of simpler rules.

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