Adjustment and social choice

We discuss the influence of information contagion on the dynamics of choices in social networks of heterogeneous buyers. Starting from an inhomogeneous cellular automata model of buyers dynamics, we show that when agents try to adjust their reservation price, the tatonement process does not converge to equilibrium at some intermediate market share and that large amplitude fluctuations are actually observed. When the tatonnement dynamics is slow with respect to the contagion dynamics, large periodic oscillations reminiscent of business cycles appear.Comment: 13 pages, 6 figure

Strong gender differences in reproductive success variance, and the times to the most recent common ancestors

The Time To the Most Recent Common Ancestor (TMRCA) based on human mitochondrial DNA (mtDNA) is estimated to be twice that based on the non-recombining part of the Y chromosome (NRY). These TMRCAs have special demographic implications because mtDNA is transmitted only from mother to child, and NRY from father to son. Therefore, mtDNA reflects female history, and NRY, male history. To investigate what caused the two-to-one female-male TMRCA ratio in humans, we develop a forward-looking agent-based model (ABM) with overlapping generations and individual life cycles. We implement two main mating systems: polygynandry and polygyny with different degrees in between. In each mating system, the male population can be either homogeneous or heterogeneous. In the latter case, some males are `alphas' and others are `betas', which reflects the extent to which they are favored by female mates. A heterogeneous male population implies a competition among males with the purpose of signaling as alphas. The introduction of a heterogeneous male population is found to reduce by a factor 2 the probability of finding equal female and male TMRCAs and shifts the distribution of the TMRCA ratio to higher values. We find that high male-male competition is necessary to reproduce a TMRCA ratio of 2: less than half the males can be alphas and betas can have at most half the fitness of alphas. In addition, in the modes that maximize the probability of having a TMRCA ratio between 1.5 and 2.5, the present generation has 1.4 times as many female as male ancestors. We also tested the effect of sex-biased migration and sex-specific death rates and found that these are unlikely to explain alone the sex-biased TMRCA ratio observed in humans. Our results support the view that we are descended from males who were successful in a highly competitive context, while females were facing a much smaller female-female competition

Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in

We investigate coarse equilibrium states of a fine-scale, stochastic agent-based model of consumer lock-in in a duopolistic market. In the model, agents decide on their next purchase based on a combination of their personal preference and their neighbours' opinions. For agents with independent identically-distributed parameters and all-to-all coupling, we derive an analytic approximate coarse evolution-map for the expected average purchase. We then study the emergence of coarse fronts when spatial segregation is present in the relative perceived quality of products. We develop a novel Newton-Krylov method that is able to compute accurately and efficiently coarse fixed points when the underlying fine-scale dynamics is stochastic. The main novelty of the algorithm is in the elimination of the noise that is generated when estimating Jacobian-vector products using time-integration of perturbed initial conditions. We present numerical results that demonstrate the convergence properties of the numerical method, and use the method to show that macroscopic fronts in this model destabilise at a coarse symmetry-breaking bifurcation.Comment: This version of the manuscript was accepted for publication on SIAD

Timing interactions in social simulations: The voter model

The recent availability of huge high resolution datasets on human activities has revealed the heavy-tailed nature of the interevent time distributions. In social simulations of interacting agents the standard approach has been to use Poisson processes to update the state of the agents, which gives rise to very homogeneous activity patterns with a well defined characteristic interevent time. As a paradigmatic opinion model we investigate the voter model and review the standard update rules and propose two new update rules which are able to account for heterogeneous activity patterns. For the new update rules each node gets updated with a probability that depends on the time since the last event of the node, where an event can be an update attempt (exogenous update) or a change of state (endogenous update). We find that both update rules can give rise to power law interevent time distributions, although the endogenous one more robustly. Apart from that for the exogenous update rule and the standard update rules the voter model does not reach consensus in the infinite size limit, while for the endogenous update there exist a coarsening process that drives the system toward consensus configurations.Comment: Book Chapter, 23 pages, 9 figures, 5 table

Robust modeling of human contact networks across different scales and proximity-sensing techniques

The problem of mapping human close-range proximity networks has been tackled using a variety of technical approaches. Wearable electronic devices, in particular, have proven to be particularly successful in a variety of settings relevant for research in social science, complex networks and infectious diseases dynamics. Each device and technology used for proximity sensing (e.g., RFIDs, Bluetooth, low-power radio or infrared communication, etc.) comes with specific biases on the close-range relations it records. Hence it is important to assess which statistical features of the empirical proximity networks are robust across different measurement techniques, and which modeling frameworks generalize well across empirical data. Here we compare time-resolved proximity networks recorded in different experimental settings and show that some important statistical features are robust across all settings considered. The observed universality calls for a simplified modeling approach. We show that one such simple model is indeed able to reproduce the main statistical distributions characterizing the empirical temporal networks

The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows

In this paper we develop a model of an order-driven market where traders set bids and asks and post market or limit orders according to exogenously fixed rules. Agents are assumed to have three components to the expectation of future asset returns, namely-fundamentalist, chartist and noise trader. Furthermore agents differ in the characteristics describing these components, such as time horizon, risk aversion and the weights given to the various components. The model developed here extends a great deal of earlier literature in that the order submissions of agents are determined by utility maximisation, rather than the mechanical unit order size that is commonly assumed. In this way the order flow is better related to the ongoing evolution of the market. For the given market structure we analyze the impact of the three components of the trading strategies on the statistical properties of prices and order flows and observe that it is the chartist strategy that is mainly responsible of the fat tails and clustering in the artificial price data generated by the model. The paper provides further evidence that large price changes are likely to be generated by the presence of large gaps in the book

Evolutionary Poisson Games for Controlling Large Population Behaviors

Emerging applications in engineering such as crowd-sourcing and (mis)information propagation involve a large population of heterogeneous users or agents in a complex network who strategically make dynamic decisions. In this work, we establish an evolutionary Poisson game framework to capture the random, dynamic and heterogeneous interactions of agents in a holistic fashion, and design mechanisms to control their behaviors to achieve a system-wide objective. We use the antivirus protection challenge in cyber security to motivate the framework, where each user in the network can choose whether or not to adopt the software. We introduce the notion of evolutionary Poisson stable equilibrium for the game, and show its existence and uniqueness. Online algorithms are developed using the techniques of stochastic approximation coupled with the population dynamics, and they are shown to converge to the optimal solution of the controller problem. Numerical examples are used to illustrate and corroborate our results