Chaos in social learning with multiple true states

Most existing social learning models assume that there is only one underlying true state. In this work, we consider a social learning model with multiple true states, in which agents in different groups receive different signal sequences generated by their corresponding underlying true states. Each agent updates his belief by combining his rational self-adjustment based on the external signals he received and the influence of his neighbors according to their communication. We observe chaotic oscillation in the belief evolution, which implies that neither true state could be learnt correctly by calculating the largest Lyapunov exponents and Hurst exponents.     

Memory distribution in complex fitness landscapes

In a co-evolutionary context, the survive probability of individual elements of a system depends on their relation with their neighbors. The natural selection process depends on the whole population, which is determined by local events between individuals. Particular characteristics assigned to each individual, as larger memory, usually improve the individual fitness, but an agent possesses also endogenous characteristics that induce to re-evaluate her fitness landscape and choose the best-suited kind of interaction, inducing a non-absolute value of the outcomes of the interaction. In this work, a novel model with agents combining memory and rational choice is introduced, where individual choices in a complex fitness landscape induce changes in the distribution of the number of agents as a function of time. In particular, the tail of this distribution is fat compared with distributions for agents interacting only with memory.     

An exploration of commonly observed stylized facts with data from experimental asset markets

We analyze data from experimental asset markets with pooled linear regression models to shed some light on the emergence of fat tails and volatility clustering in return distributions. Our data suggest that the arrival of new information is the most important cause for both stylized facts. After new information arrives we see spikes in volatility as this information is digested in the market. We also find that uninformed traders contribute significantly more to fat tails than do informed traders and that the heterogeneity in fundamental information leads to larger returns.     

The Role of Noise and Initial Conditions in the Asymptotic Solution of a Bounded Confidence, Continuous-Opinion Model

We study a model for continuous-opinion dynamics under bounded confidence. In particular, we analyze the importance of the initial distribution of opinions in determining the asymptotic configuration. Thus, we sketch the structure of attractors of the dynamical system, by means of the numerical computation of the time evolution of the agents density. We show that, for a given bound of confidence, a consensus can be encouraged or prevented by certain initial conditions. Furthermore, a noisy perturbation is added to the system with the purpose of modeling the free will of the agents. As a consequence, the importance of the initial condition is partially replaced by that of the statistical distribution of the noise. Nevertheless, we still find evidence of the influence of the initial state upon the final configuration for a short range of the bound of confidence parameter.     

Influence of spin fluctuations in the ground state on the coherent motion of holes in high-T c superconductors

The coherent two-dimensional motion of a hole generated in a high-T _c superconductor at half-filling is discussed. The system is described by thet-J model which reduces to the Heisenberg antiferromagnet (HAF) at half-filling. Special attention is payed to the influence of spin fluctuations in the ground state on the hole motion. Spin fluctuations can be considered as deviations of the true ground state of the Heisenberg antiferromagnet from the Néel state. The calculations are based on the introduction of a new trial wave function. It generalizes a wave function which was originally proposed by Shraiman and Siggia for the hole motion in the Néel state. As a result, we find that the excitation energy for the hole has a bandwidth which is reduced by a factor 0.7 as compared to the case without spin fluctuations. Moreover, the dispersion relation contains cubic harmonics which are due to effective hopping processes to more distant than second-or third-nearest neighbors. For larger values of the ratiot/J the band is substantially deformed. We compare our theory with results obtained from the exact diagonalization of finite clusters and find good agreement.     

The coevolution of partner switching and strategy updating in non-excludable public goods game

Spatial public goods game is a popular metaphor to model the dilemma of collective cooperation on graphs, yet the non-excludable property of public goods has seldom been considered in previous models. Based upon a coevolutionary model where agents play public goods games and adjust their partnerships, the present model incorporates the non-excludable property of public goods: agents are able to adjust their participation in the games hosted by others, whereas they cannot exclude others from their own games. In the coevolution, a directed and dynamical network which represents partnerships among autonomous agents is evolved. We find that non-excludable property counteracts the positive effect of partner switching, i.e., the equilibrium level of cooperation is lower than that in the situation of excludable public goods game. Therefore, we study the effect of individual punishment that cooperative agents pay a personal cost to decrease benefits of those defective neighbors who participate in their hosted games. It is found that the cooperation level in the whole population is heightened in the presence of such a costly behavior.     

An opinion formation model with dissipative structure

We propose an opinion formation model which includes both the influence of internal motivation and dissipation. Active agents adopt their neighbors’ opinions according to a simplified set of rules, but they may gradually lose their interests in the discussion and drop out of it. On the other hand, inert agents can become active by initial activation or internal motivation from neighbors, and participate in the discussion. The initial activation is usually due to occurrence of a social event. The internal motivation, opinion update and dissipation procedure take place simultaneously. We apply the voter rule in our model, and carry out analysis and numerical simulations. Results show if nonzero dissipation stays below a threshold value, the system evolves to a balance state where the average concentration of one opinion is equal to that of the other. With dissipation, a number of small-size opinion clusters exist in the end, but the system gains a fast relaxation rate. The final average opinion is closely related to the dissipation intensity and the length of time for initial activation.     

Spin-glass-like transition in the majority-vote model with anticonformists

Majority-vote model on scale-free networks and random graphs is investigated in which a randomly chosen fraction p of agents (called anticonformists) follows an antiferromagnetic update rule, i.e., they assume, with probability governed by a parameter q (0 < q < 1∕2), the opinion opposite to that of the majority of their neighbors, while the remaining 1 ? p fraction of agents (conformists) follows the usual ferromagnetic update rule assuming, with probability governed by the same parameter q, the opinion in accordance with that of the majority of their neighbors. For p = 1 it is shown by Monte Carlo simulations and using the Binder cumulants method that for decreasing q the model undergoes second-order phase transition from a disordered (paramagnetic) state to a spin-glass-like state, characterized by a non-zero value of the spin-glass order parameter measuring the overlap of agents’ opinions in two replicas of the system, and simultaneously by the magnetization close to zero. In the case of the model on scale-free networks the critical value of the parameter q weakly depends on the details of the degree distribution. As p is decreased, the critical value of q falls quickly to zero and only the disordered phase is observed. On the other hand, for p close to zero for decreasing q the usual ferromagnetic transition is observed.     

Statistical physics approach to graphical games: local and global interactions

In a graphical game agents play with their neighbors on a graph to achieve an appropriate state of equilibrium. Here relevant problems are characterizing the equilibrium set and discovering efficient algorithms to find such an equilibrium (solution). We consider a representation of games that extends over graphical games to deal conveniently with both local a global interactions and use the cavity method of statistical physics to study the geometrical structure of the equilibria space. The method also provides a distributive and local algorithm to find an equilibrium. For simplicity we consider only pure Nash equilibria but the methods can as well be extended to deal with (approximated) mixed Nash equilirbia.     

Heterogeneous attachment strategies optimize the topology of dynamic wireless networks

In optimizing the topology of wireless networks built of a dynamic set of spatially embedded agents, there are many trade-offs to be dealt with. The network should preferably be as small (in the sense that the average, or maximal, pathlength is short) as possible, it should be robust to failures, not consume too much power, and so on. In this paper, we investigate simple models of how agents can choose their neighbors in such an environment. In our model of attachment, we can tune from one situation where agents prefer to attach to others in closest proximity, to a situation where agents attach to random others regardless of distance (which thus are, on average, further away than the connections to the spatial neighbors). We evaluate this scenario with several performance measures and find that the optimal topologies, for most of the quantities, is obtained for strategies resulting in a mix of most local and a few random connections.     

Birth and death in a continuous opinion dynamics model

We here discuss the process of opinion formation in an open community where agents are made to interact and consequently update their beliefs. New actors (birth) are assumed to replace individuals that abandon the community (deaths). This dynamics is simulated in the framework of a simplified model that accounts for mutual affinity between agents. A rich phenomenology is presented and discussed with reference to the original (closed group) setting. Numerical findings are supported by analytical calculations.     

Universal Dynamical Computation in Multidimensional Excitable Lattices

We study two- and three-dimensional latticesnodes of which take three states: rest, eccited, andrefractory, and deterministically update their states indiscrete time depending on the number of excited closest neighbors. Every resting node isexcited if exactly 2 of its 8 (in two-dimensionallattice) or exactly 4 of its 26 (in three-dimensionallattice) closest neighbors are excited. A node changesits excited state into the refractory state and itsrefractory state into the rest state unconditionally. Weprove that such lattices are the minimal models oflattice excitation that exhibit bounded movable patterns of self-localized excitation(particle-like waves). The minimal, compact, stable,indivisible, and capable of nonstop movementparticle-like waves represent quanta of information.Exploring all possible binary collisions betweenparticle-like waves, we construct the catalogue of thelogical gates that are realized in the excitablelattices. The space and time complexity of the logicaloperations is evaluated and the possible realizations ofthe registers, counters, and reflectors are discussed.The place of the excitable lattices in the hierarchy ofcomputation universal models and their high affinity to real-life analogues affirm that excitablelattices may be the minimal models of real-likedynamical universal computation.     

Theoretical and experimental update on a model featuring a second Z-boson

An update is provided on theoretical and experimental aspects of a simple extension of the standard model featuring right-handed neutrinos and a second neutral gauge boson (Z′). We identify an ambiguity which a priori exists in the definition of electric charge in this model, and show spontaneous symmetry breaking can resolve it. We then re-analyse the experimental bounds on the mass of Z′ in the light of recent measurements of the standard Z boson mass and width at LEP and SLC. We find that the lower bound at 90% confidence level for the Z′ mass is 460 GeV.     

Sub-strategy updating evolution in minority game

In this paper, we propose and study a new evolution model of minority game. Any strategy in minority game can be regarded as composed of sub-strategies corresponding to different histories. Based on the evolution model proposed by Li－Riolo－Savit, in which those agents that perform poorly may update their strategies randomly. This paper presents a new evolution model in which poor agents update their strategies by changing only a part of sub-strategy sets with low success rate. Simulation result shows that the new model with sub-strategy-set updating evolution mechanism may approach its steady state more quickly than the Li－Riolo－Savit model. In the steady state of the new model, stronger adaptive cooperation among agents will appear, implying that the social resource can be allocated more rationally and utilized more effectively compared with the Li－Riolo－Savit model.     

In social complex systems,the whole can be more or less than (the sum of) the parts

We discuss in a statistical physics framework the idea that “the whole is less than the parts”, as sometimes advocated by sociologists in view of the intrinsic complexity of humans, and try to reconcile this idea with the statistical physicists wisdom according to which “the whole is more than the sum of its parts” due to collective phenomena. We consider a simple mean-field model of interacting agents having an intrinsic complexity modeled by a large number of internal configurations. We show, by analytically solving the model, that interactions between agents lead, in some parameter range, to a ‘standardization’ of agents in the sense that all agents collapse in the same internal state, thereby drastically suppressing their complexity. Slightly generalizing the model, we find that agents standardization may lead to a global order if appropriate interactions are included. Hence, in this simple model, both agents standardization and collective organization may be viewed as two sides of the same coin.     

Effect of initial concentration and spatial heterogeneity of active agent distribution on opinion dynamics

We analyze the effect of spatial heterogeneity in the initial spin distribution on spin dynamics in a three-state square lattice divided into spatial cells (districts). In the spirit of the statistical mechanics of social impact, we introduce a dominant influence rule (DIR), according to which, in a single update step, a chosen node adopts the state determined by the influence of its discussion group formed by the node itself and its neighbors within one or more coordination spheres. In contrast to models based on some form of majority rule (MR), a system governed by the DIR is easily trapped in a stable non-consensus state, if all nodes of the discussion group have the same weight of influence. To ensure that a consensus in the DIR system is necessarily reached, we need to put a stochastic process in the update rule. Further, the stochastic DIR model is used as a starting point for understanding the effect of spatial heterogeneity of active agent (non-zero spin) distribution on the exit probabilities. Initially, the positive and negative spins (active agents) are assigned to some nodes with non-uniform spatial distributions; while the rest of the nodes remain in the state with spin zero (uncommitted voters). By varying the relative means and skewness of the initial spin distributions, we observe critical behaviors of exit probabilities in finite size systems. The critical exponents are obtained by Monte Carlo simulations. The results of numerical simulations are discussed in the context of social dynamics.     

Dynamics of majority rule in two-state interacting spin systems

We introduce a two-state opinion dynamics model where agents evolve by majority rule. In each update, a group of agents is specified whose members then all adopt the local majority state. In the mean-field limit, where a group consists of randomly selected agents, consensus is reached in a time that scales ln(N, where N is the number of agents. On finite-dimensional lattices, where a group is a contiguous cluster, the consensus time fluctuates strongly between realizations and grows as a dimension-dependent power of N. The upper critical dimension appears to be larger than 4. The final opinion always equals that of the initial majority except in one dimension.     

Creating informed public opinion: citizen deliberation about nanotechnologies for human enhancements

Many people believe that ordinary citizens should influence scientific and technological developments, but the American public is routinely uninformed about these issues. As a solution, some scholars advocate creating informed public opinions by encouraging citizens to deliberate about the issues. Although this idea is currently widely applauded in the science and technology literature, deliberative outcomes are infrequently measured and the practice of deliberation is routinely criticized in other disciplines. This research contributes to our understanding of the effectiveness of citizen deliberation as a method for increasing public engagement with science. I report data measuring results of deliberation in a national citizens’ technology forum (NCTF) about nanotechnologies for human enhancement. The NCTF was a month-long process involving six groups of 9–15 ordinary citizens who deliberated in different locations across the United States with the goal of reaching consensus about policy recommendations within their groups. I find that structured deliberation generated informed opinions, sometimes meaningful shifts in preferences, and increased trust and internal efficacy among the participants. Nevertheless, the NCTF has important shortcomings, and it is not obvious that consensus conferences should be preferred over other mechanisms for creating informed opinions. Future research is needed to corroborate the findings of this study and to systematically compare outcomes of structured citizen deliberation to other less resource intensive forms of engagement.     

Promoting cooperation by local contribution under stochastic win-stay-lose-shift mechanism

We introduce a stochastic win-stay-lose-shift (WSLS) mechanism into evolutionary Prisoner’s Dilemma on small-world networks. At each time step, after playing with all its immediate neighbors, each individual gets a score to evaluate its performance in the game. The score is a linear combination of an individual’s total payoff (i.e., individual gain from the group) and local contribution to its neighbors (i.e., individual donation to the group). If one’s actual score is not larger than its desired score aspiration, it switches current strategy to the opposite one with the probability depending on the difference between the two scores. Under this stochastic WSLS regime, we assume that each focal individual gains its fixed score aspiration under the condition of full cooperation in its neighborhood, and find that cooperation is significantly enhanced under some certain parameters of the model by studying the evolution of cooperation. We also explore the influences of different values of learning rate and intensity of deterministic switch on the evolution of cooperation. Simulation results show that cooperation level monotonically increases with the relative weight of the local contribution to the score. For much low intensity of deterministic switch, cooperation is to a large extent independent of learning rate, and full cooperation can be reached when relative weight is not less than 0.5. Otherwise, cooperation level is affected by the value of learning rate. Besides, we find that the cooperation level is not sensitive to the topological parameters. To explain these simulation results, we provide corresponding analytical results based on mean-field approximation, and find out that simulation results are in close agreement with the analytical ones. Our work may be helpful in understanding the cooperative behavior in social systems based on this stochastic WSLS mechanism.     

What types of investors generate the two-phase phenomenon?

We examine the two-phase phenomenon described by Plerou, Gopikrishnan, and Stanley (2003)  [1] in the KOSPI 200 options market, one of the most liquid options markets in the world. By analysing a unique intraday dataset that contains information about investor type for each trade and quote, we find that the two-phase phenomenon is generated primarily by domestic individual investors, who are generally considered to be uninformed and noisy traders. In contrast, our empirical results indicate that trades by foreign institutions, who are generally considered informed and sophisticated investors, do not exhibit two-phase behaviour.