Related papers: Dynamical Systems Models for Market Evolution: A M…

A novel mathematical framework is proposed to describe the ecological and evolutionary consequences of consumer--resource interactions. Both the consumer and resource are assumed to consist of several (sub)species, which interact between…

The application of learning-based control methods in robotics presents significant challenges. One is that model-free reinforcement learning algorithms use observation data with low sample efficiency. To address this challenge, a prevalent…

Proportional dynamics, originated from peer-to-peer file sharing systems, models a decentralized price-learning process in Fisher markets. Previously, items in the dynamics operate independently of one another, and each is assumed to belong…

The premise of this paper is the following value proposition: Models are good when they describe a system of phenomena, and they are better when they can predict the effect of interventions upon the system. We introduce a formalism by which…

This essay provides a critical overview of the mathematical kinetic theory of active particles, which is used to model and study collective systems consisting of interacting living entities, such as those involved in behavior and evolution.…

Many complex adaptive systems contain a large diversity of specialized components. The specialization at the level of the microscopic degrees of freedom, and diversity at the level of the system as a whole are phenomena that appear during…

How to promote the innovative activities is an important problem for modern society. In this paper, combining with the evolutionary games and information spreading, we propose a lattice model to investigate dynamics of human innovative…

Prediction markets rely on liquidity to convert trades into informative prices, yet existing mechanisms fix liquidity ex ante. This restriction enforces a static trade-off between price responsiveness and worst-case loss despite inherently…

Machine learning models play a key role for service providers looking to gain market share in consumer markets. However, traditional learning approaches do not take into account the existence of additional providers, who compete with each…

This paper introduces dynamic mechanism design in an elementary fashion. We first examine optimal dynamic mechanisms: We find necessary and sufficient conditions for perfect Bayesian incentive compatibility and formulate the optimal dynamic…

Dynamics with choice is a generalization of discrete-time dynamics where instead of the same evolution operator at every time step there is a choice of operators to transform the current state of the system. This notion is new and…

In this monograph, we introduce a new model in population dynamics that describes two species sharing the same environmental resources in a situation of open hostility. The interactions among these populations are described not in terms of…

Learning processes by exploiting restricted domain knowledge is an important task across a plethora of scientific areas, with more and more hybrid training methods additively combining data-driven and model-based approaches. Although the…

We study a minimalist kinetic model for economies. A system of agents with local trading rules display emergent demand behaviour. We examine the resulting wealth distribution to look for non-thermal behaviour. We compare and contrast this…

Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit…

We propose a flexible stochastic framework for modeling the market share dynamics over time in a multiple markets setting, where firms interact within and between markets. Firms undergo stochastic idiosyncratic shocks, which contract their…

Natural selection favors the more successful individuals. This is the elementary premise that pervades common models of evolution. Under extreme conditions, however, the process may no longer be probabilistic. Those that meet certain…

Agent-based models help explain stock price dynamics as emergent phenomena driven by interacting investors. In this modeling tradition, investor behavior has typically been captured by two distinct mechanisms -- learning and heterogeneous…

Scientists investigate the dynamics of complex systems with quantitative models, employing them to synthesize knowledge, to explain observations, and to forecast future system behavior. Complete specification of systems is impossible, so…

Predators often consume multiple prey and by mutually subsidizing a shared predator, the prey may reciprocally harm each other. When predation levels are high, this apparent competition can culminate in a prey species being displaced.…