181 research outputs found
Discounting in Games across Time Scales
We introduce two-level discounted games played by two players on a
perfect-information stochastic game graph. The upper level game is a discounted
game and the lower level game is an undiscounted reachability game. Two-level
games model hierarchical and sequential decision making under uncertainty
across different time scales. We show the existence of pure memoryless optimal
strategies for both players and an ordered field property for such games. We
show that if there is only one player (Markov decision processes), then the
values can be computed in polynomial time. It follows that whether the value of
a player is equal to a given rational constant in two-level discounted games
can be decided in NP intersected coNP. We also give an alternate strategy
improvement algorithm to compute the value
Minimum Partial-Matching and Hausdorff RMS-Distance under Translation: Combinatorics and Algorithms
We consider the RMS-distance (sum of squared distances between pairs of points) under translation between two point sets in the plane. In the Hausdorff setup, each point is paired to its nearest neighbor in the other set. We develop algorithms for finding a local minimum in near-linear time on the line, and in nearly quadratic time in the plane. These improve substantially the worst-case behavior of the popular ICP heuristics for solving this problem. In the partial-matching setup, each point in the smaller set is matched to a distinct point in the bigger set. Although the problem is not known to be polynomial, we establish several structural properties of the underlying subdivision of the plane and derive improved bounds on its complexity. In addition, we show how to compute a local minimum of the partial-matching RMS-distance under translation, in polynomial time
The Influence of Coalition Formation on Idea Selection in Dispersed Teams: A Game Theoretic Approach
Sie, R. L. L., Bitter-Rijpkema, M., & Sloep, P. B. (2009). The Influence of Coalition Formation on Idea Selection in Dispersed Teams: A Game Theoretic Approach. In U. Cress, V. Dimitrova & M. Specht (Eds.), Learning in the Synergy of Multiple Disciplines. Proceedings of the Fourth European Conference on Technology-Enhanced Learning (EC-TEL 2009) (pp. 732-737). September, 29 - October, 2, 2009, Nice, France. Lecture Notes in Computer Science Vol. 5794. Berlin: Springer-Verlag.In an open innovation environment, organizational learning takes place by means of dispersed teams which expand their knowledge through collaborative idea generation. Research is often focused on finding ways to extend the set of ideas, while the main problem in our opinion is not the number of ideas that is generated, but a non-optimal set of ideas accepted during idea selection. When selecting ideas, coalitions form and their composition may influence the resulting set of accepted ideas. We expect that computing coalitional strength during idea selection will help in forming the right teams to have a grand coalition, or having a better allocation of accepted ideas, or neutralising factors that adversely influence the decision making process. Based on a literature survey, this paper proposes the application of the Shapley value and the nucleolus to compute coalitional strength in order to enhance the group decision making process during collaborative idea selection. This document does not represent the opinion of the European Union, and the European Union is not responsible for any use that might be made of its content.The idSpace project is partially supported/co-funded by the European Union under the Information and Communication Technologies (ICT) theme of the 7th Framework Programme for R&
An Algorithm for Probabilistic Alternating Simulation
In probabilistic game structures, probabilistic alternating simulation
(PA-simulation) relations preserve formulas defined in probabilistic
alternating-time temporal logic with respect to the behaviour of a subset of
players. We propose a partition based algorithm for computing the largest
PA-simulation, which is to our knowledge the first such algorithm that works in
polynomial time, by extending the generalised coarsest partition problem (GCPP)
in a game-based setting with mixed strategies. The algorithm has higher
complexities than those in the literature for non-probabilistic simulation and
probabilistic simulation without mixed actions, but slightly improves the
existing result for computing probabilistic simulation with respect to mixed
actions.Comment: We've fixed a problem in the SOFSEM'12 conference versio
Algorithms for Game Metrics
Simulation and bisimulation metrics for stochastic systems provide a
quantitative generalization of the classical simulation and bisimulation
relations. These metrics capture the similarity of states with respect to
quantitative specifications written in the quantitative {\mu}-calculus and
related probabilistic logics. We first show that the metrics provide a bound
for the difference in long-run average and discounted average behavior across
states, indicating that the metrics can be used both in system verification,
and in performance evaluation. For turn-based games and MDPs, we provide a
polynomial-time algorithm for the computation of the one-step metric distance
between states. The algorithm is based on linear programming; it improves on
the previous known exponential-time algorithm based on a reduction to the
theory of reals. We then present PSPACE algorithms for both the decision
problem and the problem of approximating the metric distance between two
states, matching the best known algorithms for Markov chains. For the
bisimulation kernel of the metric our algorithm works in time O(n^4) for both
turn-based games and MDPs; improving the previously best known O(n^9\cdot
log(n)) time algorithm for MDPs. For a concurrent game G, we show that
computing the exact distance between states is at least as hard as computing
the value of concurrent reachability games and the square-root-sum problem in
computational geometry. We show that checking whether the metric distance is
bounded by a rational r, can be done via a reduction to the theory of real
closed fields, involving a formula with three quantifier alternations, yielding
O(|G|^O(|G|^5)) time complexity, improving the previously known reduction,
which yielded O(|G|^O(|G|^7)) time complexity. These algorithms can be iterated
to approximate the metrics using binary search.Comment: 27 pages. Full version of the paper accepted at FSTTCS 200
Axiomatizations of two types of Shapley values for games on union closed systems
A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the Shapley value. In the literature various models of games with restricted cooperation can be found. So, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper, we consider such sets of feasible coalitions that are closed under union, i.e. for any two feasible coalitions also their union is feasible. We consider and axiomatize two solutions or rules for these games that generalize the Shapley value: one is obtained as the conjunctive permission value using a corresponding superior graph, the other is defined as the Shapley value of a modified game similar as the Myerson value for games with limited communication. © 2010 The Author(s)
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