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, $p_k(t) \in$ [0,1], is assigned to each agent $k$ at time $t$. At each time step $t$ a pair of agents, chosen at random, interact by playing the game. The players update their $p_k(t)$ 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 $\bar{p}_{eq}$ and average equilibrium per-capita-income $\bar{p}_{eq},\bar{U}_\infty$. 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