Related papers: Attractors, Equilibrium, Profit, Loss
How do networks of relationships evolve over time? We analyse a dataset tracking the social interactions of 900 individuals over four years. Despite continuous shifts in individual relationships, the macroscopic structural properties of the…
We show that the law of energy conservation with the fact of matter stability imply the existence of energy complementary to that given by the function of states of interacting systems and treated, with the environment, the function of…
The backbone of nonequilibrium thermodynamics is the stability structure, where entropy is related to a Lyapunov function of thermodynamic equilibrium. Stability is the background of natural selection: unstable systems are temporary, and…
In this paper, we show that if every consumer in an economy has a quasi-linear utility function, then the normalized equilibrium price is unique, and is locally stable with respect to the t\^atonnement process. Our study can be seen as that…
We propose a dynamical model for group formation and switching behavior in systems where each group competes for members through attraction functions that are inversely proportional to their current sizes. This attraction is modulated by…
Mounting evidences are being gathered suggesting that income and wealth distribution in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium, but also deviating…
We investigate the dynamics of wealth inequality in an economy where households have positional preferences, with the strength of the positional concern determined endogenously by inequality of wealth distribution in the society. We…
The principles of static equilibrium are of special interest to civil engineers. For a rigid body to be in static equilibrium the condition is that net force and net torque acting on the body should be zero. That clearly signifies that if…
We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe…
We consider the dynamics, existence and stability of the equilibrium states for large populations of individuals who can play various types of non--cooperative games. The players imitate the most attractive strategies, and the choice is…
Suppose that an equilibrium is asymptotically stable when external inputs vanish. Then, every bounded trajectory which corresponds to a control which approaches zero and which lies in the domain of attraction of the unforced system, must…
We show that, with indivisible goods, the existence of competitive equilibrium fundamentally depends on agents' substitution effects, not their income effects. Our Equilibrium Existence Duality allows us to transport results on the…
We study the existence of equilibrium when agents' preferences may not beconvex. For some specific utility functions, we provide a necessary and sufficientcondition under which there exists an equilibrium. The standard approach cannot be…
Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For…
We present a dynamical many-body theory of money in which the value of money is a time dependent ``strategic variable'' that is chosen by the individual agents. The value of money in equilibrium is not fixed by the equations, and thus…
We consider an economy made of competing firms which are heterogeneous in their capital and use several inputs for producing goods. Their consumption policy is fixed rationally by maximizing a utility and their capital cannot fall below a…
A replicator equation with mutation processes is numerically studied. Without any mutations, two characteristics of the replicator dynamics are known: an exponential divergence of the dominance period, and hierarchical orderings of the…
The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of self-organization because energy is a local property of a configuration. For…
The stability analysis of socioeconomic systems has been centered on answering whether small perturbations when a system is in a given quantitative state will push the system permanently to a different quantitative state. However, typically…
I introduce a stability notion, dynamic stability, for two-sided dynamic matching markets where (i) matching opportunities arrive over time, (ii) matching is one-to-one, and (iii) matching is irreversible. The definition addresses two…