arXiv subjects

Azadeh Aghaeeyan

Publications and source records attributed to Azadeh Aghaeeyan.

6 recordsLinked to original sources

arXiv2026

From Discrete to Continuous Highest-earning Imitation Dynamics

Imitating the highest earners is a common decision-making heuristic, but in finite populations it can generate persistent fluctuations between strategies. This paper studies whether such fluctuations persist as population size grows in heterogeneous two-strategy populations. We show that the Markov chains describing the discrete imitation dynamics form generalized stochastic approximation processes for a good upper semicontinuous differential inclusion, which defines the associated mean dynamics. We prove that these mean dynamics always converge to equilibria. Using stochastic approximation results, we then show that the amplitudes of fluctuations in the population proportions of the two strategies vanish almost surely as population size tends to infinity. Thus, in well-mixed large populations, highest-earning imitation is unlikely to produce large-scale perpetual fluctuations.

physics.soc-ph↗

arXiv2026

From Discrete to Continuous Mixed Populations of Conformists, Nonconformists, and Imitators

In two-strategy decision-making problems, individuals often imitate the highest earners or choose either the common or rare strategy. Individuals who benefit from the common strategy are conformists, whereas those who profit by choosing the less common one are called nonconformists. The population proportions of the two strategies may undergo perpetual fluctuations in finite, discrete, heterogeneous populations of imitators, conformists, and nonconformists. How these fluctuations evolve as population size increases was left as an open question and is addressed in this paper. We show that the family of Markov chains describing the discrete population dynamics forms a generalized stochastic approximation process for a differential inclusion--the continuous-time dynamics. Furthermore, we prove that the continuous-time dynamics always equilibrate. Then, by leveraging results from the stochastic approximation theory, we show that the amplitudes of fluctuations in the proportions of the two strategies in the population approach zero with probability one when the population size grows to infinity. Our results suggest that large-scale perpetual fluctuations are unlikely in large, well-mixed populations consisting of these three types, particularly when imitators follow the highest earners.

q-bio.PE↗

arXiv2024

Identifiability analysis of vaccination decision-making dynamics

Variations in individuals' perceptions of vaccination and decision-making processes can give rise to poor vaccination coverage. The future vaccination promotion programs will benefit from understanding this heterogeneity amongst groups within a population and, accordingly, tailoring the communication strategies. Motivated by this, we developed a mechanistic model consisting of a system of ordinary differential equations that categorizes individuals based on two factors: (i) perceived payoff gains for vaccination and (ii} decision-making strategies where we assumed that individuals may behave as either myopic rationalists, going for a dose of vaccine if doing so maximizes their perceived payoff gain, or success-based learners, waiting to observe feedback on vaccination before deciding. We then investigated the global identifiability of group proportions and perceived payoff gains, that is, the possibility of globally retrieving these parameters by observing the error-free cumulative proportion of vaccinated individuals over time. To do so, for each group, we assumed a piecewise constant payoff gain and, for each time interval, obtained the so-called generalized input-output equation. We then proved the global identifiability of these parameters under certain conditions. Global identifiability opens the door to reliable estimations of the group proportions and their perceived payoffs.

q-bio.QM↗

arXiv2024

Extending Identifiability Results from Continuous to Discrete-Space Systems

Researchers develop models to explain the unknowns. These models typically involve parameters that capture tangible quantities, the estimation of which is desired. Parameter identifiability investigates the recoverability of the unknown parameters given the error-free outputs, inputs, and the developed equations of the model. Different notions of and methods to test identifiability exist for dynamical systems defined in the continuous space. Yet little attention was paid to the identifiability of discrete space systems, where variables and parameters are defined in a discrete space. We develop the identifiability framework for discrete space systems and highlight that this is not an immediate extension of the continuous space framework. Unlike the continuous case, local identifiability concepts are sensitive to how a ``neighborhood'' is defined. Moreover, results on algebraic identifiability that proved useful in the continuous space are less so in their discrete form as the notion of differentiability disappears.

math.OC↗

arXiv2023

From Discrete to Continuous Binary Best-Response Dynamics: Discrete Fluctuations Almost Surely Vanish with Population Size

In binary decision-making, individuals often choose either the rare or the common action. In the framework of evolutionary game theory, the best-response update rule can be used to model this dichotomy. Those who prefer the common action are called \emph{coordinators}, and those who prefer the rare one are called \emph{anticoordinators}. A finite mixed population of the two types may undergo perpetual fluctuations, the characterization of which appears to be challenging. It is particularly unknown whether the fluctuations persist as population size grows. To fill this gap, we approximate the discrete finite population dynamics of coordinators and anticoordinators with the associated mean dynamics in the form of differential inclusions. We show that the family of the state sequences of the discrete dynamics for increasing population sizes forms a generalized stochastic approximation process for the differential inclusion. On the other hand, we show that the differential inclusions always converge to an equilibrium. This implies that the reported perpetual fluctuations in the finite discrete dynamics of coordinators and anticoordinators almost surely vanish with population size. The results encourage to first analyze the often simpler {continuous-time} mean dynamics of the discrete population dynamics as the continuous-time dynamics partly reveal the asymptotic behavior of the discrete dynamics.

eess.SY↗

arXiv2023

Revealing the unseen: Likely half of the Americans relied on others' experience when deciding on taking the COVID-19 vaccine

Efficient coverage for newly developed vaccines requires knowing which groups of individuals will accept the vaccine immediately and which will take longer to accept or never accept. Of those who may eventually accept the vaccine, there are two main types: success-based learners, basing their decisions on others' satisfaction, and myopic rationalists, attending to their own immediate perceived benefit. We used COVID-19 vaccination data to fit a mechanistic model capturing the distinct effects of the two types on the vaccination progress. We estimated that 47 percent of Americans behaved as myopic rationalist with a high variations across the jurisdictions, from 31 percent in Mississippi to 76 percent in Vermont. The proportion was correlated with the vaccination coverage, proportion of votes in favor of Democrats in 2020 presidential election, and education score.

q-bio.PE↗