15,294 research outputs found
A Nested Family of -total Effective Rewards for Positional Games
We consider Gillette's two-person zero-sum stochastic games with perfect
information. For each k \in \ZZ_+ we introduce an effective reward function,
called -total. For and this function is known as {\it mean
payoff} and {\it total reward}, respectively. We restrict our attention to the
deterministic case. For all , we prove the existence of a saddle point which
can be realized by uniformly optimal pure stationary strategies. We also
demonstrate that -total reward games can be embedded into -total
reward games
Solving Stochastic B\"uchi Games on Infinite Arenas with a Finite Attractor
We consider games played on an infinite probabilistic arena where the first
player aims at satisfying generalized B\"uchi objectives almost surely, i.e.,
with probability one. We provide a fixpoint characterization of the winning
sets and associated winning strategies in the case where the arena satisfies
the finite-attractor property. From this we directly deduce the decidability of
these games on probabilistic lossy channel systems.Comment: In Proceedings QAPL 2013, arXiv:1306.241
A survey of random processes with reinforcement
The models surveyed include generalized P\'{o}lya urns, reinforced random
walks, interacting urn models, and continuous reinforced processes. Emphasis is
on methods and results, with sketches provided of some proofs. Applications are
discussed in statistics, biology, economics and a number of other areas.Comment: Published at http://dx.doi.org/10.1214/07-PS094 in the Probability
Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Stochastic evolutionary game dynamics
In this review, we summarize recent developments in stochastic evolutionary
game dynamics of finite populations.Comment: To appear in "Reviews of Nonlinear Dynamics and Complexity" Vol. II,
Wiley-VCH, 2009, edited by H.-G. Schuste
Multigame Effect in Finite Populations Induces Strategy Linkage Between Two Games
Evolutionary game dynamics with two 2-strategy games in a finite population
has been investigated in this study. Traditionally, frequency-dependent
evolutionary dynamics are modeled by deterministic replicator dynamics under
the assumption that the population size is infinite. However, in reality,
population sizes are finite. Recently, stochastic processes in finite
populations have been introduced into evolutionary games in order to study
finite size effects in evolutionary game dynamics. However, most of these
studies focus on populations playing only single games. In this study, we
investigate a finite population with two games and show that a finite
population playing two games tends to evolve toward a specific direction to
form particular linkages between the strategies of the two games
Liveness of Randomised Parameterised Systems under Arbitrary Schedulers (Technical Report)
We consider the problem of verifying liveness for systems with a finite, but
unbounded, number of processes, commonly known as parameterised systems.
Typical examples of such systems include distributed protocols (e.g. for the
dining philosopher problem). Unlike the case of verifying safety, proving
liveness is still considered extremely challenging, especially in the presence
of randomness in the system. In this paper we consider liveness under arbitrary
(including unfair) schedulers, which is often considered a desirable property
in the literature of self-stabilising systems. We introduce an automatic method
of proving liveness for randomised parameterised systems under arbitrary
schedulers. Viewing liveness as a two-player reachability game (between
Scheduler and Process), our method is a CEGAR approach that synthesises a
progress relation for Process that can be symbolically represented as a
finite-state automaton. The method is incremental and exploits both
Angluin-style L*-learning and SAT-solvers. Our experiments show that our
algorithm is able to prove liveness automatically for well-known randomised
distributed protocols, including Lehmann-Rabin Randomised Dining Philosopher
Protocol and randomised self-stabilising protocols (such as the Israeli-Jalfon
Protocol). To the best of our knowledge, this is the first fully-automatic
method that can prove liveness for randomised protocols.Comment: Full version of CAV'16 pape
Nonlinear Markov Processes in Big Networks
Big networks express various large-scale networks in many practical areas
such as computer networks, internet of things, cloud computation, manufacturing
systems, transportation networks, and healthcare systems. This paper analyzes
such big networks, and applies the mean-field theory and the nonlinear Markov
processes to set up a broad class of nonlinear continuous-time block-structured
Markov processes, which can be applied to deal with many practical stochastic
systems. Firstly, a nonlinear Markov process is derived from a large number of
interacting big networks with symmetric interactions, each of which is
described as a continuous-time block-structured Markov process. Secondly, some
effective algorithms are given for computing the fixed points of the nonlinear
Markov process by means of the UL-type RG-factorization. Finally, the Birkhoff
center, the Lyapunov functions and the relative entropy are used to analyze
stability or metastability of the big network, and several interesting open
problems are proposed with detailed interpretation. We believe that the results
given in this paper can be useful and effective in the study of big networks.Comment: 28 pages in Special Matrices; 201
- …