47,219 research outputs found
Statistical Physics Approaches to Unique Games
We show how two techniques from statistical physics can be adapted to solve a variant of the notorious Unique Games problem, potentially opening new avenues towards the Unique Games Conjecture. The variant, which we call Count Unique Games, is a promise problem in which the "yes" case guarantees a certain number of highly satisfiable assignments to the Unique Games instance. In the standard Unique Games problem, the "yes" case only guarantees at least one such assignment. We exhibit efficient algorithms for Count Unique Games based on approximating a suitable partition function for the Unique Games instance via (i) a zero-free region and polynomial interpolation, and (ii) the cluster expansion. We also show that a modest improvement to the parameters for which we give results would be strong negative evidence for the truth of the Unique Games Conjecture
Evolutionary games and quasispecies
We discuss a population of sequences subject to mutations and
frequency-dependent selection, where the fitness of a sequence depends on the
composition of the entire population. This type of dynamics is crucial to
understand the evolution of genomic regulation. Mathematically, it takes the
form of a reaction-diffusion problem that is nonlinear in the population state.
In our model system, the fitness is determined by a simple mathematical game,
the hawk-dove game. The stationary population distribution is found to be a
quasispecies with properties different from those which hold in fixed fitness
landscapes.Comment: 7 pages, 2 figures. Typos corrected, references updated. An exact
solution for the hawks-dove game is provide
Challenges in Complex Systems Science
FuturICT foundations are social science, complex systems science, and ICT.
The main concerns and challenges in the science of complex systems in the
context of FuturICT are laid out in this paper with special emphasis on the
Complex Systems route to Social Sciences. This include complex systems having:
many heterogeneous interacting parts; multiple scales; complicated transition
laws; unexpected or unpredicted emergence; sensitive dependence on initial
conditions; path-dependent dynamics; networked hierarchical connectivities;
interaction of autonomous agents; self-organisation; non-equilibrium dynamics;
combinatorial explosion; adaptivity to changing environments; co-evolving
subsystems; ill-defined boundaries; and multilevel dynamics. In this context,
science is seen as the process of abstracting the dynamics of systems from
data. This presents many challenges including: data gathering by large-scale
experiment, participatory sensing and social computation, managing huge
distributed dynamic and heterogeneous databases; moving from data to dynamical
models, going beyond correlations to cause-effect relationships, understanding
the relationship between simple and comprehensive models with appropriate
choices of variables, ensemble modeling and data assimilation, modeling systems
of systems of systems with many levels between micro and macro; and formulating
new approaches to prediction, forecasting, and risk, especially in systems that
can reflect on and change their behaviour in response to predictions, and
systems whose apparently predictable behaviour is disrupted by apparently
unpredictable rare or extreme events. These challenges are part of the FuturICT
agenda
Minority games, evolving capitals and replicator dynamics
We discuss a simple version of the Minority Game (MG) in which agents hold
only one strategy each, but in which their capitals evolve dynamically
according to their success and in which the total trading volume varies in time
accordingly. This feature is known to be crucial for MGs to reproduce stylised
facts of real market data. The stationary states and phase diagram of the model
can be computed, and we show that the ergodicity breaking phase transition
common for MGs, and marked by a divergence of the integrated response is
present also in this simplified model. An analogous majority game turns out to
be relatively void of interesting features, and the total capital is found to
diverge in time. Introducing a restraining force leads to a model akin to
replicator dynamics of evolutionary game theory, and we demonstrate that here a
different type of phase transition is observed. Finally we briefly discuss the
relation of this model with one strategy per player to more sophisticated
Minority Games with dynamical capitals and several trading strategies per
agent.Comment: 19 pages, 7 figure
Is it "natural" to expect Economics to become a part of the Natural Sciences?
We are in the middle of a complex debate as to whether Economics is really a
proper natural science. The 'Discussion & Debate' issue of this Euro. Phys. J.
Special Topic volume is: 'Can economics be a Physical Science?' I discuss some
aspects here.Comment: 7 pages; EPJ-ST special issue on 'Can Economics be a Physical
Science?' Edited by S. Sinha, A. S. Chakrabarti & M. Mitr
- …