685,441 research outputs found
On robustness and dynamics in (un)balanced coalitional games
We build upon control theoretic concepts like robustness and dynamics to better accommodate all the situations where the coalitions’ values are uncertain and subject to changes over time. The proposed robust dynamic framework provides an alternative perspective on the study of sequences of coalitional games or interval valued games. For a sequence of coalitional games, either balanced or unbalanced, we analyze the key roles of instantaneous and average games. Instantaneous games are obtained by freezing the coalitions’ values at a given time and come into play when coalitions’ values are known. On the other hand, average games are derived from averaging the coalitions’ values up to a given time and are key part of our analysis when coalitions’ values are unknown. The main theoretical contribution of our paper is a design method of allocation rules that return solutions in the core and/or -core of the instantaneous and average games. Theoretical results are then specialized to a simulated example to shed light on the impact of the design method and on the performance of the resulting allocation rules
On asymptotic value for dynamic games with saddle point
The paper is concerned with two-person games with saddle point. We
investigate the limits of value functions for long-time-average payoff,
discounted average payoff, and the payoff that follows a probability density.
Most of our assumptions restrict the dynamics of games. In particular, we
assume the closedness of strategies under concatenation. It is also necessary
for the value function to satisfy Bellman's optimality principle, even if in a
weakened, asymptotic sense.
We provide two results. The first one is a uniform Tauber result for games:
if the value functions for long-time-average payoff converge uniformly, then
there exists the uniform limit for probability densities from a sufficiently
broad set; moreover, these limits coincide. The second one is the uniform Abel
result: if a uniform limit for self-similar densities exists, then the uniform
limit for long-time average payoff also exists, and they coincide.Comment: for SIAM CT1
Long time average of first order mean field games and weak KAM theory
We show that the long time average of solutions of first order mean field
game systems in finite horizon is governed by an ergodic system of mean field
game type. The well-posedness of this later system and the uniqueness of the
ergodic constant rely on weak KAM theory
The mechanics of stochastic slowdown in evolutionary games
We study the stochastic dynamics of evolutionary games, and focus on the
so-called `stochastic slowdown' effect, previously observed in (Altrock et. al,
2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a
beneficial mutation may take longer to fixate than a neutral one. More
precisely, the fixation time conditioned on the mutant taking over can show a
maximum at intermediate selection strength. We show that this phenomenon is
present in the prisoner's dilemma, and also discuss counterintuitive slowdown
and speedup in coexistence games. In order to establish the microscopic origins
of these phenomena, we calculate the average sojourn times. This allows us to
identify the transient states which contribute most to the slowdown effect, and
enables us to provide an understanding of slowdown in the takeover of a small
group of cooperators by defectors: Defection spreads quickly initially, but the
final steps to takeover can be delayed substantially. The analysis of
coexistence games reveals even more intricate behavior. In small populations,
the conditional average fixation time can show multiple extrema as a function
of the selection strength, e.g., slowdown, speedup, and slowdown again. We
classify two-player games with respect to the possibility to observe
non-monotonic behavior of the conditional average fixation time as a function
of selection strength.Comment: Accepted for publication in the Journal of Theoretical Biology.
Includes changes after peer revie
The tropical shadow-vertex algorithm solves mean payoff games in polynomial time on average
We introduce an algorithm which solves mean payoff games in polynomial time
on average, assuming the distribution of the games satisfies a flip invariance
property on the set of actions associated with every state. The algorithm is a
tropical analogue of the shadow-vertex simplex algorithm, which solves mean
payoff games via linear feasibility problems over the tropical semiring
. The key ingredient in our approach is
that the shadow-vertex pivoting rule can be transferred to tropical polyhedra,
and that its computation reduces to optimal assignment problems through
Pl\"ucker relations.Comment: 17 pages, 7 figures, appears in 41st International Colloquium, ICALP
2014, Copenhagen, Denmark, July 8-11, 2014, Proceedings, Part
Limit Your Consumption! Finding Bounds in Average-energy Games
Energy games are infinite two-player games played in weighted arenas with
quantitative objectives that restrict the consumption of a resource modeled by
the weights, e.g., a battery that is charged and drained. Typically, upper
and/or lower bounds on the battery capacity are part of the problem
description. Here, we consider the problem of determining upper bounds on the
average accumulated energy or on the capacity while satisfying a given lower
bound, i.e., we do not determine whether a given bound is sufficient to meet
the specification, but if there exists a sufficient bound to meet it.
In the classical setting with positive and negative weights, we show that the
problem of determining the existence of a sufficient bound on the long-run
average accumulated energy can be solved in doubly-exponential time. Then, we
consider recharge games: here, all weights are negative, but there are recharge
edges that recharge the energy to some fixed capacity. We show that bounding
the long-run average energy in such games is complete for exponential time.
Then, we consider the existential version of the problem, which turns out to be
solvable in polynomial time: here, we ask whether there is a recharge capacity
that allows the system player to win the game.
We conclude by studying tradeoffs between the memory needed to implement
strategies and the bounds they realize. We give an example showing that memory
can be traded for bounds and vice versa. Also, we show that increasing the
capacity allows to lower the average accumulated energy.Comment: In Proceedings QAPL'16, arXiv:1610.0769
New Deterministic Algorithms for Solving Parity Games
We study parity games in which one of the two players controls only a small
number of nodes and the other player controls the other nodes of the
game. Our main result is a fixed-parameter algorithm that solves bipartite
parity games in time , and general parity games in
time , where is the number of distinct
priorities and is the number of edges. For all games with this
improves the previously fastest algorithm by Jurdzi{\'n}ski, Paterson, and
Zwick (SICOMP 2008). We also obtain novel kernelization results and an improved
deterministic algorithm for graphs with small average degree
Long Time Behavior of First Order Mean Field Games on Euclidean Space
The aim of this paper is to study the long time behavior of solutions to
deterministic mean field games systems on Euclidean space. This problem was
addressed on the torus in [P. Cardaliaguet, {\it Long time
average of first order mean field games and weak KAM theory}, Dyn. Games Appl.
3 (2013), 473-488], where solutions are shown to converge to the solution of a
certain ergodic mean field games system on . By adapting the
approach in [A. Fathi, E. Maderna, {\it Weak KAM theorem on non compact
manifolds}, NoDEA Nonlinear Differential Equations Appl. 14 (2007), 1-27], we
identify structural conditions on the Lagrangian, under which the corresponding
ergodic system can be solved in . Then we show that time
dependent solutions converge to the solution of such a stationary system on all
compact subsets of the whole space
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