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Admissible Strategies in Infinite Games over Graphs [chapter]

Marco Faella
2009 Lecture Notes in Computer Science  
As the main result, we provide a characterization of the goals admitting positional 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.  ... 
doi:10.1007/978-3-642-03816-7_27 fatcat:inziggqosfbcfb6ws4stcjztxq

Admissibility in Infinite Games [chapter]

Dietmar Berwanger
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.  ... 
doi:10.1007/978-3-540-70918-3_17 dblp:conf/stacs/Berwanger07 fatcat:e2zxrcnklnh4djblk2i357yp6a

ON EQUILIBRIUM REFINEMENT FOR DISCONTINUOUS GAMES

ORIOL CARBONELL-NICOLAU
2011 International Game Theory Review  
For instance, perfect equilibria 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.  ... 
doi:10.1142/s021919891100299x fatcat:c25u5itbnfacfcd3tb6o3r523m

Infinite Coordination Games [chapter]

Dietmar Berwanger
2010 Lecture Notes in Computer Science  
We investigate the prescriptive power of sequential iterated 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.  ... 
doi:10.1007/978-3-642-15164-4_1 fatcat:zd7es75s5bfq3i5cumfoimv4ha

Certain infinite zero-sum two-person games

A. L. Dulmage, J. E. L. Peck
1956 Canadian Journal of Mathematics - Journal Canadien de Mathematiques  
It is a simple matter to construct 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.  ... 
doi:10.4153/cjm-1956-047-x fatcat:jl2bv3lucfhedk6f7kxp44euba

Best-Effort Strategies for Losing States [article]

Marco Faella
2008 arXiv   pre-print
We consider 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 .  ... 
arXiv:0811.1664v1 fatcat:2dikjzfnfnd5zlqicb2lwbsicy

Admissibility in Games with Imperfect Information (Invited Talk)

Romain Brenguier, Arno Pauly, Jean-François Raskin, Ocan Sankur, Marc Herbstritt
2017 International Conference on Concurrency Theory  
While 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  ... 
doi:10.4230/lipics.concur.2017.2 dblp:conf/concur/BrenguierPRS17 fatcat:7hjalaiyxjc6fgtyozmbj2iidu

Infinite horizon noncooperative differential games with nonsmooth costs

Fabio S. Priuli
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  ... 
doi:10.1016/j.jmaa.2007.02.030 fatcat:hxbwmgyzwvfjla7o2it7rmko5e

Kernels in directed graphs: a poison game

P. Duchet, H. Meyniel
1993 Discrete Mathematics  
Meyniel, Kernels 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.  ... 
doi:10.1016/0012-365x(93)90496-g fatcat:4mmlyrmh3zfa3knccp7zbscd2q

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

Dean A. Carlson
2002 Journal of Mathematical Analysis and Applications  
differential 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.  ... 
doi:10.1016/s0022-247x(02)00276-7 fatcat:ke7ggz2kbbgsrfcqot6enhtywe

Finite high-order games and an inductive approach towards Gowers's dichotomy

Roy Wagner
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 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  ... 
doi:10.1016/s0168-0072(01)00034-3 fatcat:qx5hi3eucjg6td4kw7pwfa46qq

Value Without Absolute Convergence

Luc Lauwers, Peter Lloyd Vallentyne
2011 Social Science Research Network  
Unlike the example 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.  ... 
doi:10.2139/ssrn.1806897 fatcat:jrtvppyai5akxb3pzj62bbtzh4

Pursuit Game for an Infinite System of First-Order Differential Equations with Negative Coefficients [article]

Gafurjan Ibragimov, Massimiliano Ferrara, Idham Arif Alias, Mehdi Salimi
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  ... 
arXiv:2002.07416v1 fatcat:xuojlcz3srdwnjinvj2mq5cwde

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

Thordur Runolfsson
1994 Systems & control letters (Print)  
Existence conditions for state-feedback 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.  ... 
doi:10.1016/0167-6911(94)90089-2 fatcat:4g256f7canfs5o56xsfjn57byu
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