200 research outputs found
Global culture: A noise induced transition in finite systems
We analyze the effect of cultural drift, modeled as noise, in Axelrod's model
for the dissemination of culture. The disordered multicultural configurations
are found to be metastable. This general result is proven rigorously in d=1,
where the dynamics is described in terms of a Lyapunov potential. In d=2, the
dynamics is governed by the average relaxation time T of perturbations. Noise
at a rate r 1/T sustains
disorder. In the thermodynamic limit, the relaxation time diverges and global
polarization persists in spite of a dynamics of local convergence.Comment: 4 pages, 5 figures. For related material visit
http://www.imedea.uib.es/physdept
Berezin Quantization of Gauged WZW and Coset Models
Gauged WZW and coset models are known to be useful to prove holomorphic
factorization of the partition function of WZW and coset models. In this note
we show that these gauged models can be also important to quantize the theory
in the context of the Berezin formalism. For gauged coset models Berezin
quantization procedure also admits a further holomorphic factorization in the
complex structure of the moduli space.Comment: 15+1 pages, no figures, revte
A semantical approach to equilibria and rationality
Game theoretic equilibria are mathematical expressions of rationality.
Rational agents are used to model not only humans and their software
representatives, but also organisms, populations, species and genes,
interacting with each other and with the environment. Rational behaviors are
achieved not only through conscious reasoning, but also through spontaneous
stabilization at equilibrium points.
Formal theories of rationality are usually guided by informal intuitions,
which are acquired by observing some concrete economic, biological, or network
processes. Treating such processes as instances of computation, we reconstruct
and refine some basic notions of equilibrium and rationality from the some
basic structures of computation.
It is, of course, well known that equilibria arise as fixed points; the point
is that semantics of computation of fixed points seems to be providing novel
methods, algebraic and coalgebraic, for reasoning about them.Comment: 18 pages; Proceedings of CALCO 200
Cooperation and Self-Regulation in a Model of Agents Playing Different Games
A simple model for cooperation between "selfish" agents, which play an
extended version of the Prisoner's Dilemma(PD) game, in which they use
arbitrary payoffs, is presented and studied. A continuous variable,
representing the probability of cooperation, [0,1], is assigned to
each agent at time . At each time step a pair of agents, chosen at
random, interact by playing the game. The players update their using a
criteria based on the comparison of their utilities with the simplest estimate
for expected income. The agents have no memory and use strategies not based on
direct reciprocity nor 'tags'. Depending on the payoff matrix, the systems
self-organizes - after a transient - into stationary states characterized by
their average probability of cooperation and average equilibrium
per-capita-income . It turns out that the model
exhibit some results that contradict the intuition. In particular, some games
which - {\it a priory}- seems to favor defection most, may produce a relatively
high degree of cooperation. Conversely, other games, which one would bet that
lead to maximum cooperation, indeed are not the optimal for producing
cooperation.Comment: 11 pages, 3 figures, keybords: Complex adaptive systems, Agent-based
models, Social system
Holomorphic potentials for graded D-branes
We discuss gauge-fixing, propagators and effective potentials for topological
A-brane composites in Calabi-Yau compactifications. This allows for the
construction of a holomorphic potential describing the low-energy dynamics of
such systems, which generalizes the superpotentials known from the ungraded
case. Upon using results of homotopy algebra, we show that the string field and
low energy descriptions of the moduli space agree, and that the deformations of
such backgrounds are described by a certain extended version of `off-shell
Massey products' associated with flat graded superbundles. As examples, we
consider a class of graded D-brane pairs of unit relative grade. Upon computing
the holomorphic potential, we study their moduli space of composites. In
particular, we give a general proof that such pairs can form acyclic
condensates, and, for a particular case, show that another branch of their
moduli space describes condensation of a two-form.Comment: 47 pages, 7 figure
Motion of influential players can support cooperation in Prisoner's Dilemma
We study a spatial Prisoner's dilemma game with two types (A and B) of
players located on a square lattice. Players following either cooperator or
defector strategies play Prisoner's Dilemma games with their 24 nearest
neighbors. The players are allowed to adopt one of their neighbor's strategy
with a probability dependent on the payoff difference and type of the given
neighbor. Players A and B have different efficiency in the transfer of their
own strategy therefore the strategy adoption probability is reduced by a
multiplicative factor (w < 1) from the players of type B. We report that the
motion of the influential payers (type A) can improve remarkably the
maintenance of cooperation even for their low densities.Comment: 7 pages, 7 figure
Gauge-fixing, semiclassical approximation and potentials for graded Chern-Simons theories
We perform the Batalin-Vilkovisky analysis of gauge-fixing for graded
Chern-Simons theories. Upon constructing an appropriate gauge-fixing fermion,
we implement a Landau-type constraint, finding a simple form of the gauge-fixed
action. This allows us to extract the associated Feynman rules taking into
account the role of ghosts and antighosts. Our gauge-fixing procedure allows
for zero-modes, hence is not limited to the acyclic case. We also discuss the
semiclassical approximation and the effective potential for massless modes,
thereby justifying some of our previous constructions in the Batalin-Vilkovisky
approach.Comment: 46 pages, 4 figure
On operad structures of moduli spaces and string theory
Recent algebraic structures of string theory, including homotopy Lie
algebras, gravity algebras and Batalin-Vilkovisky algebras, are deduced from
the topology of the moduli spaces of punctured Riemann spheres. The principal
reason for these structures to appear is as simple as the following. A
conformal field theory is an algebra over the operad of punctured Riemann
surfaces, this operad gives rise to certain standard operads governing the
three kinds of algebras, and that yields the structures of such algebras on the
(physical) state space naturally.Comment: 33 pages (An elaboration of minimal area metrics and new references
are added
Torus knots and mirror symmetry
We propose a spectral curve describing torus knots and links in the B-model.
In particular, the application of the topological recursion to this curve
generates all their colored HOMFLY invariants. The curve is obtained by
exploiting the full Sl(2, Z) symmetry of the spectral curve of the resolved
conifold, and should be regarded as the mirror of the topological D-brane
associated to torus knots in the large N Gopakumar-Vafa duality. Moreover, we
derive the curve as the large N limit of the matrix model computing torus knot
invariants.Comment: 30 pages + appendix, 3 figure
Game Theoretical Interactions of Moving Agents
Game theory has been one of the most successful quantitative concepts to
describe social interactions, their strategical aspects, and outcomes. Among
the payoff matrix quantifying the result of a social interaction, the
interaction conditions have been varied, such as the number of repeated
interactions, the number of interaction partners, the possibility to punish
defective behavior etc. While an extension to spatial interactions has been
considered early on such as in the "game of life", recent studies have focussed
on effects of the structure of social interaction networks.
However, the possibility of individuals to move and, thereby, evade areas
with a high level of defection, and to seek areas with a high level of
cooperation, has not been fully explored so far. This contribution presents a
model combining game theoretical interactions with success-driven motion in
space, and studies the consequences that this may have for the degree of
cooperation and the spatio-temporal dynamics in the population. It is
demonstrated that the combination of game theoretical interactions with motion
gives rise to many self-organized behavioral patterns on an aggregate level,
which can explain a variety of empirically observed social behaviors
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