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Admissible Strategies in Infinite Games over Graphs
[chapter]

2009
*
Lecture Notes in Computer Science
*

As the main result, we provide a characterization of the goals admitting positional

doi:10.1007/978-3-642-03816-7_27
fatcat:inziggqosfbcfb6ws4stcjztxq
*admissible*strategies. ... We consider*games*played on finite graphs, whose objective is to obtain a trace belonging to a given set of accepting traces. We focus on the states from which Player 1 cannot force a win. ... The*game*consists*in*the two players taking turns at picking a successor state, eventually giving rise to an*infinite*path*in*the*game*graph. ...##
###
Admissibility in Infinite Games
[chapter]

*
STACS 2007
*

*In*a multi-player non-zero-sum setting, we show that for

*infinite*extensive

*games*of perfect information with only two possible payoffs (win or lose), the concept of iterated

*admissibility*is sound and ... We analyse the notion of iterated

*admissibility*, i.e., avoidance of weakly dominated strategies, as a solution concept for extensive

*games*of

*infinite*horizon. ... As illustrated

*in*the introduction, there is no hope that

*admissibility*yields a meaningful solution for arbitrary

*infinite*

*games*. ...

##
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ON EQUILIBRIUM REFINEMENT FOR DISCONTINUOUS GAMES

2011
*
International Game Theory Review
*

For instance, perfect equilibria

doi:10.1142/s021919891100299x
fatcat:c25u5itbnfacfcd3tb6o3r523m
*in*compact, continuous*games*need not be*admissible*. ...*In*moving from finite-action to*infinite*-action*games*, standard refinements of the Nash equilibrium concept cease to satisfy certain "natural" properties. ...*In*an attempt to better understand the failure of*admissibility**in**infinite**games*, this paper highlights additional properties of perfectness and stability for*infinite*normal-form*games*. ...##
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Infinite Coordination Games
[chapter]

2010
*
Lecture Notes in Computer Science
*

We investigate the prescriptive power of sequential iterated

doi:10.1007/978-3-642-15164-4_1
fatcat:zd7es75s5bfq3i5cumfoimv4ha
*admissibility**in*coordination*games*of the Gale-Stewart style, i.e., perfectinformation*games*of*infinite*duration with only two payoffs. ... We show that, on this kind of*games*, the procedure of eliminating weakly dominated strategies is independent of the elimination order and that, under maximal simultaneous elimination, the procedure converges ... As*games*with more than two payoffs fail to satisfy this property, we cannot rely on our previous results about*admissibility**in**infinite*non-zero sum*games*. ...##
###
Certain infinite zero-sum two-person games

1956
*
Canadian Journal of Mathematics - Journal Canadien de Mathematiques
*

It is a simple matter to construct

doi:10.4153/cjm-1956-047-x
fatcat:jl2bv3lucfhedk6f7kxp44euba
*admissible**games*and*in*fact determinate*games**in*which, for some £ and rj, K(%, rj) does not exist. ... The theorem of von Neumann, that every finite, zero-sum two-person*game*has a value, has been extended*in*various ways to*infinite**games*. ...##
###
Best-Effort Strategies for Losing States
[article]

2008
*
arXiv
*
pre-print

We consider

arXiv:0811.1664v1
fatcat:2dikjzfnfnd5zlqicb2lwbsicy
*games*played on finite graphs, whose goal is to obtain a trace belonging to a given set of winning traces. We focus on those states from which Player 1 cannot force a win. ... Along the way, we prove several results of theoretical and practical interest, such as a characterization of*admissible*strategies, which also provides a simple algorithm for computing such strategies ... The*game**in*Figure 1 , already presented*in*the introduction, settles this question*in*the negative. Suppose the goal is to visit*infinitely*often s 0 . ...##
###
Admissibility in Games with Imperfect Information (Invited Talk)

2017
*
International Conference on Concurrency Theory
*

While

doi:10.4230/lipics.concur.2017.2
dblp:conf/concur/BrenguierPRS17
fatcat:7hjalaiyxjc6fgtyozmbj2iidu
*admissibility*is a classical concept for*games**in*normal form, i.e. matrix*games*, it was first studied*in*this context of*infinite*duration*games*by Berwanger*in*[6] . ... Contributions*In*this paper, we study the notion of*admissible*strategies*in*the more general setting of*infinite*duration*games*with imperfect information. ... Player 2 perfectly informed As we mentioned following Theorem 20,*in*regular*games*the validity of the condition*in*the theorem depends only on the set of last vertices*in*the histories forming a monochromatic ...##
###
Infinite horizon noncooperative differential games with nonsmooth costs

2007
*
Journal of Mathematical Analysis and Applications
*

*In*the present paper, we consider a class of two players

*infinite*horizon differential

*games*, with piecewise smooth costs exponentially discounted

*in*time. ... We also provide examples of piecewise linear costs whose corresponding

*games*have either

*infinitely*many Nash equilibria or no solutions at all. ... On the other hand, any change

*in*the behavior of the costs will translate

*in*some sort of instability of the

*game*, leading either to

*infinitely*many

*admissible*solution, or to one unique

*admissible*solution ...

##
###
Kernels in directed graphs: a poison game

1993
*
Discrete Mathematics
*

Meyniel, Kernels

doi:10.1016/0012-365x(93)90496-g
fatcat:4mmlyrmh3zfa3knccp7zbscd2q
*in*directed graphs: a poison*game*, Discrete Mathematics 115 (1993) 273-276. ... We consider a two player*game*on a progressively and locally finite directed graph and we prove that the first player wins if and only if the graph has a local kernel. The result is sharp. ...*Admissible**games*are*games**in*which A applies an*admissible*strategy. ...##
###
Page 3507 of Mathematical Reviews Vol. , Issue 2001E
[page]

2001
*
Mathematical Reviews
*

Summary: “

*In*general, nonlinear output feedback dynamic*games*are*infinite*-dimensional. ... An information state approach is introduced to recast these*games*as*games*of full information*in**infinite*di- mensions. ...##
###
Carathéodory's method for a class of dynamic games

2002
*
Journal of Mathematical Analysis and Applications
*

differential

doi:10.1016/s0022-247x(02)00276-7
fatcat:ke7ggz2kbbgsrfcqot6enhtywe
*games*. ... Both the finite-horizon and*infinite*-horizon cases are considered. Examples are given to illustrate the presented results. 2002 Elsevier Science (USA). All rights reserved. ...*In*Section 4 we will introduce the notion of an overtaking Nash equilibrium for*infinite*horizon dynamic*games*and give our extension of Carathéodory's method to the*infinite*horizon case. ...##
###
Finite high-order games and an inductive approach towards Gowers's dichotomy

2001
*
Annals of Pure and Applied Logic
*

We derive 'quantitative' versions of the original Gowers Combinatorial Lemma and of Gowers's Dichotomy, which place them

doi:10.1016/s0168-0072(01)00034-3
fatcat:qx5hi3eucjg6td4kw7pwfa46qq
*in*the context of the recently introduced*infinite*dimensional asymptotic theory ... We present the notion of finite high-order Gowers*games*, and prove a statement parallel to Gowers's Combinatorial Lemma for these*games*. ... It is not true that every sequence which comes out of an α-*game*is α-*admissible*, or even (α + 1)-*admissible*; but the following lemma shows that player S has a winning strategy*in*the α-*game**in*X for Σ ...##
###
Value Without Absolute Convergence

2011
*
Social Science Research Network
*

Unlike the example

doi:10.2139/ssrn.1806897
fatcat:jrtvppyai5akxb3pzj62bbtzh4
*in*the introduction, the sum of the values*in*<1,1,-1,1,1,-1...>,*in*the given order, does not converge (have a finite limit), since that sum is*infinite*. ... We address the problem of how to extend this sum-principle when there are an*infinite*number of parts. Sometimes the sum of an*infinite*number of values is a well-defined finite number. ... All*admissible*covering sequences will assign an*infinite*value to this option, and hence its value is*infinite*. ...##
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Pursuit Game for an Infinite System of First-Order Differential Equations with Negative Coefficients
[article]

2020
*
arXiv
*
pre-print

*In*this paper we study a linear pursuit differential

*game*described by an

*infinite*system of first-order differential equations

*in*Hilbert space. ... Discussion and Conclusion We studied a linear pursuit differential

*game*described by an

*infinite*system of first-order differential equations

*in*Hilbert space l 2 . ... A dual approach which is still

*in*its infancy is the 'design-then-approximate' method, i.e. first an

*infinite*-dimensional controller or strategy for the

*infinite*-dimensional problem is designed, and then ...

##
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Optimal control of a stochastic system with an exponential-of-integral performance criterion

1994
*
Systems & control letters (Print)
*

Existence conditions for state-feedback

doi:10.1016/0167-6911(94)90089-2
fatcat:4g256f7canfs5o56xsfjn57byu
*admissible*controllers are formulated and optimality conditions are derived. ... Connections between the exponential-of-integral optimal control problem and stochastic differential*games*are discussed. ...*In*[12] , the relationship between the*infinite*-horizon exponential-of-integral control problem and a certain*infinite*-horizon stochastic differential*game*was rigorously established. ...
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