229,186 research outputs found
On the complexity of problems on simple games
Simple games cover voting systems in which a single alternative, such
as a bill or an amendment, is pitted against the status quo. A simple game
or a yes–no voting system is a set of rules that specifies exactly which
collections of “yea” votes yield passage of the issue at hand, each of these
collections of “yea” voters forms a winning coalition. We are interested in
performing a complexity analysis on problems defined on such families of
games. This analysis as usual depends on the game representation used as
input. We consider four natural explicit representations: winning, losing,
minimal winning, and maximal losing. We first analyze the complexity of
testing whether a game is simple and testing whether a game is weighted.
We show that, for the four types of representations, both problems can be
solved in polynomial time. Finally, we provide results on the complexity
of testing whether a simple game or a weighted game is of a special type.
We analyze strongness, properness, decisiveness and homogeneity, which
are desirable properties to be fulfilled for a simple game. We finalize
with some considerations on the possibility of representing a game in a
more succinct representation showing a natural representation in which
the recognition problem is hard.Preprin
Cooperation through social influence
We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this scenario by an influence game, a cooperative simple game in which a team (or coalition) of players succeeds if it is able to convince enough agents to participate in the task (to vote in favor of a decision). We take the linear threshold model as the influence model. We show first the expressiveness of influence games showing that they capture the class of simple games. Then we characterize the computational complexity of various problems on influence games, including measures (length and width), values (Shapley-Shubik and Banzhaf) and properties (of teams and players). Finally, we analyze those problems for some particular extremal cases, with respect to the propagation of influence, showing tighter complexity characterizations.Peer ReviewedPostprint (author’s final draft
Model-checking Quantitative Alternating-time Temporal Logic on One-counter Game Models
We consider quantitative extensions of the alternating-time temporal logics
ATL/ATLs called quantitative alternating-time temporal logics (QATL/QATLs) in
which the value of a counter can be compared to constants using equality,
inequality and modulo constraints. We interpret these logics in one-counter
game models which are infinite duration games played on finite control graphs
where each transition can increase or decrease the value of an unbounded
counter. That is, the state-space of these games are, generally, infinite. We
consider the model-checking problem of the logics QATL and QATLs on one-counter
game models with VASS semantics for which we develop algorithms and provide
matching lower bounds. Our algorithms are based on reductions of the
model-checking problems to model-checking games. This approach makes it quite
simple for us to deal with extensions of the logical languages as well as the
infinite state spaces. The framework generalizes on one hand qualitative
problems such as ATL/ATLs model-checking of finite-state systems,
model-checking of the branching-time temporal logics CTL and CTLs on
one-counter processes and the realizability problem of LTL specifications. On
the other hand the model-checking problem for QATL/QATLs generalizes
quantitative problems such as the fixed-initial credit problem for energy games
(in the case of QATL) and energy parity games (in the case of QATLs). Our
results are positive as we show that the generalizations are not too costly
with respect to complexity. As a byproduct we obtain new results on the
complexity of model-checking CTLs in one-counter processes and show that
deciding the winner in one-counter games with LTL objectives is
2ExpSpace-complete.Comment: 22 pages, 12 figure
Playing the wrong game: An experimental analysis of relational complexity and strategic misrepresentation
It has been suggested that players often produce simplified and/or misspecified mental representations of interactive decision problems (Kreps, 1990). We submit that the relational structure of players’ preferences in a game induces cognitive complexity, and may be an important driver of such simplifications. We provide a formal classification of order structures in two-person normal form games based on the two properties of monotonicity and projectivity, and present experiments in which subjects must first construct a representation of games of different relational complexity, and subsequently play the games according to their own representation. Experimental results support the hypothesis that relational complexity matters. More complex games are harder to represent, and this difficulty is correlated with measures of short term memory capacity. Furthermore, most erroneous representations are less complex than the correct ones. In addition, subjects who misrepresent the games behave consistently with such representations according to simple but rational decision criteria. This suggests that in many strategic settings individuals may act optimally on the ground of simplified and mistaken premises.pure motive, mixed motive, preferences, bi-orders, language, cognition, projectivity, monotonicity, short term memory, experiments
The Complexity of All-switches Strategy Improvement
Strategy improvement is a widely-used and well-studied class of algorithms
for solving graph-based infinite games. These algorithms are parameterized by a
switching rule, and one of the most natural rules is "all switches" which
switches as many edges as possible in each iteration. Continuing a recent line
of work, we study all-switches strategy improvement from the perspective of
computational complexity. We consider two natural decision problems, both of
which have as input a game , a starting strategy , and an edge . The
problems are: 1.) The edge switch problem, namely, is the edge ever
switched by all-switches strategy improvement when it is started from on
game ? 2.) The optimal strategy problem, namely, is the edge used in the
final strategy that is found by strategy improvement when it is started from
on game ? We show -completeness of the edge switch
problem and optimal strategy problem for the following settings: Parity games
with the discrete strategy improvement algorithm of V\"oge and Jurdzi\'nski;
mean-payoff games with the gain-bias algorithm [14,37]; and discounted-payoff
games and simple stochastic games with their standard strategy improvement
algorithms. We also show -completeness of an analogous problem
to edge switch for the bottom-antipodal algorithm for finding the sink of an
Acyclic Unique Sink Orientation on a cube
The Complexity of Testing Properties of Simple Games
Simple games cover voting systems in which a single alternative, such as a
bill or an amendment, is pitted against the status quo. A simple game or a
yes-no voting system is a set of rules that specifies exactly which collections
of ``yea'' votes yield passage of the issue at hand. A collection of ``yea''
voters forms a winning coalition.
We are interested on performing a complexity analysis of problems on such
games depending on the game representation. We consider four natural explicit
representations, winning, loosing, minimal winning, and maximal loosing. We
first analyze the computational complexity of obtaining a particular
representation of a simple game from a different one. We show that some cases
this transformation can be done in polynomial time while the others require
exponential time. The second question is classifying the complexity for testing
whether a game is simple or weighted. We show that for the four types of
representation both problem can be solved in polynomial time. Finally, we
provide results on the complexity of testing whether a simple game or a
weighted game is of a special type. In this way, we analyze strongness,
properness, decisiveness and homogeneity, which are desirable properties to be
fulfilled for a simple game.Comment: 18 pages, LaTex fil
One-Counter Stochastic Games
We study the computational complexity of basic decision problems for
one-counter simple stochastic games (OC-SSGs), under various objectives.
OC-SSGs are 2-player turn-based stochastic games played on the transition graph
of classic one-counter automata. We study primarily the termination objective,
where the goal of one player is to maximize the probability of reaching counter
value 0, while the other player wishes to avoid this. Partly motivated by the
goal of understanding termination objectives, we also study certain "limit" and
"long run average" reward objectives that are closely related to some
well-studied objectives for stochastic games with rewards. Examples of problems
we address include: does player 1 have a strategy to ensure that the counter
eventually hits 0, i.e., terminates, almost surely, regardless of what player 2
does? Or that the liminf (or limsup) counter value equals infinity with a
desired probability? Or that the long run average reward is >0 with desired
probability? We show that the qualitative termination problem for OC-SSGs is in
NP intersection coNP, and is in P-time for 1-player OC-SSGs, or equivalently
for one-counter Markov Decision Processes (OC-MDPs). Moreover, we show that
quantitative limit problems for OC-SSGs are in NP intersection coNP, and are in
P-time for 1-player OC-MDPs. Both qualitative limit problems and qualitative
termination problems for OC-SSGs are already at least as hard as Condon's
quantitative decision problem for finite-state SSGs.Comment: 20 pages, 1 figure. This is a full version of a paper accepted for
publication in proceedings of FSTTCS 201
The Complexity of Model Checking Higher-Order Fixpoint Logic
Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed
\lambda-calculus and the modal \lambda-calculus. This makes it a highly
expressive temporal logic that is capable of expressing various interesting
correctness properties of programs that are not expressible in the modal
\lambda-calculus.
This paper provides complexity results for its model checking problem. In
particular we consider those fragments of HFL built by using only types of
bounded order k and arity m. We establish k-fold exponential time completeness
for model checking each such fragment. For the upper bound we use fixpoint
elimination to obtain reachability games that are singly-exponential in the
size of the formula and k-fold exponential in the size of the underlying
transition system. These games can be solved in deterministic linear time. As a
simple consequence, we obtain an exponential time upper bound on the expression
complexity of each such fragment.
The lower bound is established by a reduction from the word problem for
alternating (k-1)-fold exponential space bounded Turing Machines. Since there
are fixed machines of that type whose word problems are already hard with
respect to k-fold exponential time, we obtain, as a corollary, k-fold
exponential time completeness for the data complexity of our fragments of HFL,
provided m exceeds 3. This also yields a hierarchy result in expressive power.Comment: 33 pages, 2 figures, to be published in Logical Methods in Computer
Scienc
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