Related papers: Dynamic Peer-to-Peer Competition
In this work, we formulate a two-species Lotka--Volterra competition model on time scales. To derive the global dynamics of solutions of this planar model, we introduce a dynamic augmented phase plane analysis that extends the traditional…
Over the past few decades, the research community has been interested in the study of multi-agent systems and their emerging collective dynamics. These systems are all around us in nature, like bacterial colonies, fish schools, bird flocks,…
Firms compete for clients, creating distributions of market shares ranging from domination by a few giant companies to markets in which there are many small firms. These market structures evolve in time, and may remain stable for many years…
A competitive resource-consumer dynamical model is analyzed based on an integrated model of a competitive Lotka-Volterra model and a prey-predator Rosenzweig-MacArthur model that we call that LV-RM model throughout this paper. Resource…
In financial trading, large language model (LLM)-based agents demonstrate significant potential. However, the high sensitivity to market noise undermines the performance of LLM-based trading systems. To address this limitation, we propose a…
This paper describes the structure of the nodal set of segregation profiles arising in the singular limit of planar, stationary, reaction-diffusion systems with strongly competitive interactions of Lotka-Volterra type, when the matrix of…
Demand outstrips available resources in most situations, which gives rise to competition, interaction and learning. In this article, we review a broad spectrum of multi-agent models of competition (El Farol Bar problem, Minority Game,…
We investigate the spreading behavior of two invasive species modeled by a Lotka-Volterra diffusive competition system with two free boundaries in a spherically symmetric setting. We show that, for the weak-strong competition case, under…
Recently, a theory for stochastic optimal control in non-linear dynamical systems in continuous space-time has been developed (Kappen, 2005). We apply this theory to collaborative multi-agent systems. The agents evolve according to a given…
Robert May famously used random matrix theory to predict that large, complex systems cannot admit stable fixed points. However, this general conclusion is not always supported by empirical observation: from cells to biomes, biological…
We study systems of interacting reinforced stochastic processes, where agents' decisions evolve under reinforcement, network-mediated interactions, and environmental influences. In competitive environments with irreducible networks, we…
We study a simple continuous-time multi-agent system related to Krause's model of opinion dynamics: each agent holds a real value, and this value is continuously attracted by every other value differing from it by less than 1, with an…
This essay discusses the advantages of a probabilistic agent-based approach to questions in theoretical economics, from the nature of economic agents, to the nature of the equilibria supported by their interactions. One idea we propose is…
We study the conditions under which species interaction, as described by continuous versions of the competitive Lotka-Volterra model (namely the nonlocal Kolmogorov-Fisher model, and its differential approximation), can support the…
We study the multi-scale description of large-time collective behavior of agents driven by alignment. The resulting multi-flock dynamics arises naturally with realistic initial configurations consisting of multiple spatial scaling, which in…
We consider cyclic Lotka-Volterra models with three and four strategies where at every interaction agents play a strategy using a time-dependent probability distribution. Agents learn from a loss by reducing the probability to play a losing…
We analyze from basic physical considerations the Darwinian competition for reproduction (evolutionary dynamics) of strategists in a Public Goods Game, the archetype for $n$-agent (group) economical and biological interactions. In the…
We give a microscopic representation of the stock-market in which the microscopic agents are the individual traders and their capital. Their basic dynamics consists in the auto-catalysis of the individual capital and in the global…
We study a variant of the cyclic Lotka-Volterra model with three-agent interactions. Inspired by a multiplayer variation of the Rock-Paper-Scissors game, the model describes an ideal ecosystem in which cyclic competition among three species…
We introduce and study a model of an interacting population of agents who collaborate in groups which compete for limited resources. Groups are formed by random matching agents and their worth is determined by the sum of the efforts…