Related papers: The relationship between general equilibrium model…
An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $\alpha$-maxmin nonlinear…
The GREM-like trap model is a continuous time Markov jump process on the leaves of a finite volume $L$-level tree whose transition rates depend on a trapping landscape built on the vertices of the whole tree. We prove that the natural…
This paper is concerned with the theory of generic non-normal nonlinear evolutionary equations, with potential applications in Fluid Dynamics and Optics. Two theoretical models are presented. The first is a model two-level non-normal…
A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age,…
In this work, a theorem is first proved which presents a game theoretic formulation of a necessary and sufficient sustainizability over a set condition for a general system described by ordinary differential equations (ODEs). Then, two…
A generalization of the ABC model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) density-conserving or (ii) nonconserving dynamics. For…
We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles. We introduce a model in which visible and hidden variables interact through two…
We consider a physical model where the total energy is governed by surface tension and attractive screened Coulomb potential on the 3-dimensional space. We obtain different periodic equilibrium patterns i.e. stationary sets for this energy,…
General Equilibrium Theory is the benchmark of economics, especially its results concerning the efficient allocation of resources, known as the First and Second Welfare Theorems. Yet, General Equilibrium Theory is beyond the scope of most…
Various multi-agent models of wealth distributions defined by microscopic laws regulating the trades, with or without a saving criterion, are reviewed. We discuss and clarify the equilibrium properties of the model with constant global…
We consider piecewise linear discrete time macroeconomic models, which possess a continuum of equilibrium states. These systems are obtained by replacing rational inflation expectations with a boundedly rational, and genuinely sticky,…
Gibbs' phase rule states that two-phase coexistence of a single-component system, characterized by an n-dimensional parameter-space, may occur in an n-1-dimensional region. For example, the two equilibrium phases of the Ising model coexist…
We introduce a model of dynamic matching with transferable utility, extending the static model of Shapley and Shubik (1971). Forward-looking agents have individual states that evolve with current matches. Each period, a matching market with…
Innovation and obsolescence describe dynamics of ever-churning and adapting social and biological systems, concepts that encompass field-specific formulations. We formalize the connection with a reduced model of the dynamics of the "space…
The dynamics of wealth distribution plays a critical role in the economic market, hence an understanding of its nonequilibrium statistical mechanics is of great importance to human society. For this aim, a simple and efficient…
In a satisficing equilibrium each agent $i$ plays one of her top $k_i$ actions in response to the actions of the other agents. Our concept unifies models of bounded rationality and yields predictions that differ from canonical solution…
We investigate mean-field dynamics of a nonlinear opinion formation model with congregator and contrarian agents. Each agent assumes one of the two possible states. Congregators imitate the state of other agents with a rate that increases…
We study three non-equivalent queueing models in continuous time that each generalise the classical M/M/1 queue in a different way. Inter-event times in all models are Mittag-Leffler distributed, which is a heavy tail distribution with no…
Understanding glasses and the glass transition requires comprehending the nature of the crossover from the ergodic (or equilibrium) regime, in which the stationary properties of the system have no history dependence, to the mysterious glass…
Generative model ecosystems increasingly operate as competitive multi-platform markets, where platforms strategically select models from a shared pool and users with heterogeneous preferences choose among them. Understanding how platforms…