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A GENERAL NOTION OF UNIFORM STRATEGIES

BASTIEN MAUBERT, SOPHIE PINCHINAT
2014 International Game Theory Review  
We consider two-player turn-based game arenas for which we investigate uniformity properties of strategies.  ...  We exhibit a generic solution for the synthesis problem provided the binary relation that defines the sets of related plays is recognizable by a finite state transducer.  ...  A General Notion of Uniform Strategies 17 3.6.  ... 
doi:10.1142/s0219198914400040 fatcat:kk3x7nbd6rfora4igkpclhx73a

The Complexity of Synthesizing Uniform Strategies

Bastien Maubert, Sophie Pinchinat, Laura Bozzelli
2013 Electronic Proceedings in Theoretical Computer Science  
We investigate uniformity properties of strategies. These properties involve sets of plays in order to express useful constraints on strategies that are not \mu-calculus definable.  ...  Typically, we can state that a strategy is observation-based.  ...  We introduce the generic notion of uniformity properties and associated so-called uniform strategies (those satisfying uniformity properties).  ... 
doi:10.4204/eptcs.112.17 fatcat:ivlu6ajcgbdi5ggpmsrozmtfd4

Ordinal Bayesian incentive compatibility in random assignment model [article]

Sulagna Dasgupta, Debasis Mishra
2021 arXiv   pre-print
We explore the consequences of weakening the notion of incentive compatibility from strategy-proofness to ordinal Bayesian incentive compatibility (OBIC) in the random assignment model.  ...  If the common prior of the agents is a uniform prior, then a large class of random mechanisms are OBIC with respect to this prior -- this includes the probabilistic serial mechanism.  ...  Our notion of locally robust OBIC is incomparable to OBIC with respect to generic priors used in these papers.  ... 
arXiv:2009.13104v2 fatcat:fa7lts64dvctngtqjv7siwxy3m

Bounding Rationality by Discounting Time [article]

Lance Fortnow, Rahul Santhanam
2009 arXiv   pre-print
We use this notion to give a direct correspondence between the existence of equilibria where Alice has a winning strategy and the hardness of factoring.  ...  We define a new notion of bounded rationality, where the payoffs of players are discounted by the computation time they take to produce their actions.  ...  In general, uniform equilibrium is a strong notion of equilibrium, since there should be no gain in deviating irrespective of how ǫ, δ → 0.  ... 
arXiv:0911.3162v1 fatcat:2kywohnrpre4fkq3o5yn7ew5fq

Uniform Strategies [article]

Bastien Maubert
2012 arXiv   pre-print
We exhibit a generic solution for the synthesis problem provided the bundles of plays rely on any binary relation definable by a finite state transducer.  ...  We consider turn-based game arenas for which we investigate uniformity properties of strategies. These properties involve bundles of plays, that arise from some semantical motive.  ...  We introduce the generic notion of uniformity properties and associated so-called uniform strategies (those satisfying uniformity properties).  ... 
arXiv:1212.0526v1 fatcat:ce4kpjay7jcjllsosqlugwj2te

Uniform Unfolding and Analytic Measurability [article]

Benedikt Loewe
1996 arXiv   pre-print
To show this we develop the notion of strategic fusion and give a proof of a uniform unfolding theorem which allows us to reduce the proof of analytic measurability to the definition of a certain function  ...  We regard Forcing Notions P adding real numbers and the algebras of P-measurable sets.  ...  For the general context of uniform unfolding we need two fundamental notions: Definition 3.4 Let P be an arboreal forcing and τ i : i ∈ ω a sequence of strategies for one fixed player in the game G P .  ... 
arXiv:math/9606208v1 fatcat:s2sbeurtknfmrgls7kh5vj7vtu

A STIT-Extension of ATL [chapter]

Jan Broersen, Andreas Herzig, Nicolas Troquard
2006 Lecture Notes in Computer Science  
As a demonstration of the applicability of the formalism, we show how it sheds new light on the problem of modelling 'uniform strategies' in epistemic versions of ATL.  ...  Here we present an extension of ATL, introducing ideas from STIT-theory, that can express that a group of agents A perform a certain strategy.  ...  Actually it is not completely clear to us what in the context of ATSs, should be understood by a 'uniform strategy'. The notion of 'uniform strategy' comes from game theory [15] .  ... 
doi:10.1007/11853886_8 fatcat:wxm2domdoffxxacdltawhdiwxq

Probabilistic Rewrite Strategies. Applications to ELAN [chapter]

Olivier Bournez, Claude Kirchner
2002 Lecture Notes in Computer Science  
We propose an extension of the ELAN strategy language to deal with randomized systems.  ...  This leads us to interesting new problems, and we address the generalization of the usual concepts in abstract reduction systems to randomized systems.  ...  We will then say that a PARS is locally confluent (LC) (respectively confluent (C) , normalizing (N) , terminating (T) , unique normal form property (UN) , inductive (Ind) , increasing (Inc) , finitely  ... 
doi:10.1007/3-540-45610-4_18 fatcat:jnf4m7qw45dfplstqy4uui75pi

Page 408 of Mathematical Reviews Vol. 37, Issue 2 [page]

1969 Mathematical Reviews  
A uniform space is called procomplete if there exists a winning strategy for «. Con- ditions for a uniform space to be procomplete are given.  ...  If u is a uniformity on X and U is a surrounding from u, then U’={(A, B) € $(X)x $(X): BC U(A), AC U(B)} is a surrounding on $(X) and the 2175 GENERAL TOPOLOGY system of these U’ generates a uniformity  ... 

General complementarities on complete partial orders

Kerim Keskin, H Sağlam, Agah Turan
2014 Fixed Point Theory and Applications  
This paper proves the existence of a Nash equilibrium for extended (semi-) uniform g-modular games, i.e., non-cooperative games where the strategy space is a complete partially ordered set, and the best  ...  A notion of quasilattices has also been introduced by Calciano [] , and this notion has been linked to that of lattices by means of specific theorems, contrary to the notion of d'Orey [] .  ...  On the other hand, among those very few attempts to extend the set of strategy sets, d'Orey [] has employed quasilattices while requiring even a stronger notion of increasingness than that of Veinott  ... 
doi:10.1186/1687-1812-2014-101 fatcat:dqjaala4cnbnjm5mmduusvgc44

On fairness of completion-based theorem proving strategies [chapter]

Maria Paola Bonacina, Jieh Hsiang
1991 Lecture Notes in Computer Science  
Intuitively, fairness of a search plan guarantees the generation of a successful derivation if the inference mechanism of the strategy indicates that there is one.  ...  In a theorem proving strategy, on the other hand, one is usually only interested in proving a specific theorem. Therefore the notion of fairness should be defined accordingly.  ...  Since uniform fairness is defined in terms of redundancy and our notion of redundancy is more general than those in [13] and [4] , we give a new proof of this result: Theorem 5.1 (Kounalis and Rusinowitch  ... 
doi:10.1007/3-540-53904-2_109 fatcat:bshblf4yy5bxhd7z7k5zidmt5m

Uniform strategies, rational relations and jumping automata

Laura Bozzelli, Bastien Maubert, Sophie Pinchinat
2015 Information and Computation  
A general concept of uniform strategies has recently been proposed as a relevant notion in game theory for computer science, which subsumes various notions from the literature.  ...  Regarding the full semantics, relying on information set automata we establish that the existence of a uniform strategy is decidable for rational relations and we provide a nonelementary synthesis procedure  ...  We show that the standard notion of "uniform strategy" or "observation-based strategy" in these games, and hence the essence of imperfect information, is a quite simple instance of our general notion of  ... 
doi:10.1016/j.ic.2015.03.012 fatcat:pyadktusjvcpro3vehpcapfx7e

Does Nash Envy Immunity [article]

Ching-Hua Yu
2017 arXiv   pre-print
Hence a strategy profile can be more robust if it is resilient against certain irrational behaviors. In this paper, we propose a stability notion that is resilient against envy.  ...  Together with Nash equilibrium and another stability notion called immunity, we show how these separate notions are related to each other, whether they exist in games, and whether and when a strategy profile  ...  [19] is based on exhaustively searching all possible k-uniform -Nash equilibria, where "k-uniform" means that each strategy is a uniform distribution over a multiset of size k.  ... 
arXiv:1703.03262v1 fatcat:ynyeszfi6fcnbmhntspkjgqgyu

Random Strategies are Nearly Optimal for Generalized van der Waerden Games

C. Kusch, J. Rué, C. Spiegel, T. Szabó
2017 Electronic Notes in Discrete Mathematics  
Based on the ideas of Bednarska and Luczak [1], who studied biased H-games, we prove general winning criteria for Maker and Breaker and a hypergraph generalization of their result.  ...  As in the result of [1], the random strategy for Maker is again the best known strategy.  ...  These criteria will also allow us to generalize the results of [1] to uniform hypergraphs.  ... 
doi:10.1016/j.endm.2017.07.037 fatcat:am4qd6jpavddbnynkvpgzrsywi

Uniform Lazy Narrowing

M. Alpuente
2003 Journal of Logic and Computation  
Since actual implementations of functional logic languages are based on the transformation of the original program into a uniform one-which is then executed using a lazy narrowing strategy-our results  ...  We also introduce a complete refinement of lazy narrowing, called uniform lazy narrowing, which is still equivalent to needed narrowing over the aforementioned class.  ...  After recalling in Section 2 some basic notions about functional logic programming and (lazy) narrowing strategies, we characterize in Section 3 the class of uniform programs as a subclass of the inductively  ... 
doi:10.1093/logcom/13.2.287 fatcat:ui3pkqxg5rfffp2i2lapladeou
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