5,134 research outputs found
A survey of stochastic ω regular games
We summarize classical and recent results about two-player games played on graphs with ω-regular objectives. These games have applications in the verification and synthesis of reactive systems. Important distinctions are whether a graph game is turn-based or concurrent; deterministic or stochastic; zero-sum or not. We cluster known results and open problems according to these classifications
Zero-Sum Stochastic Games with Partial Information and Average Payoff
We consider discrete time partially observable zero-sum stochastic game with
average payoff criterion. We study the game using an equivalent completely
observable game. We show that the game has a value and also we come up with a
pair of optimal strategies for both the players.Comment: Journal of Optimization Theory and Applications, 201
A Random Walk Perspective on Hide-and-Seek Games
We investigate hide-and-seek games on complex networks using a random walk
framework. Specifically, we investigate the efficiency of various degree-biased
random walk search strategies to locate items that are randomly hidden on a
subset of vertices of a random graph. Vertices at which items are hidden in the
network are chosen at random as well, though with probabilities that may depend
on degree. We pitch various hide and seek strategies against each other, and
determine the efficiency of search strategies by computing the average number
of hidden items that a searcher will uncover in a random walk of steps. Our
analysis is based on the cavity method for finite single instances of the
problem, and generalises previous work of De Bacco et al. [1] so as to cover
degree-biased random walks. We also extend the analysis to deal with the
thermodynamic limit of infinite system size. We study a broad spectrum of
functional forms for the degree bias of both the hiding and the search strategy
and investigate the efficiency of families of search strategies for cases where
their functional form is either matched or unmatched to that of the hiding
strategy. Our results are in excellent agreement with those of numerical
simulations. We propose two simple approximations for predicting efficient
search strategies. One is based on an equilibrium analysis of the random walk
search strategy. While not exact, it produces correct orders of magnitude for
parameters characterising optimal search strategies. The second exploits the
existence of an effective drift in random walks on networks, and is expected to
be efficient in systems with low concentration of small degree nodes.Comment: 31 pages, 10 (multi-part) figure
A Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow
In this paper we present a Semi-Lagrangian scheme for a regularized version
of the Hughes model for pedestrian flow. Hughes originally proposed a coupled
nonlinear PDE system describing the evolution of a large pedestrian group
trying to exit a domain as fast as possible. The original model corresponds to
a system of a conservation law for the pedestrian density and an Eikonal
equation to determine the weighted distance to the exit. We consider this model
in presence of small diffusion and discuss the numerical analysis of the
proposed Semi-Lagrangian scheme. Furthermore we illustrate the effect of small
diffusion on the exit time with various numerical experiments
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