Related papers: Diffusion of two brands in competition: cross-bran…

Diffusion models have emerged as powerful generative models, inspiring extensive research into their underlying mechanisms. One of the key questions in this area is the loss functions these models shall train with. Multiple formulations…

We consider general multi-species models of reaction diffusion processes and obtain a set of constraints on the rates which give rise to closed systems of equations for correlation functions. Our results are valid in any dimension and on…

We use a principal-agent model to analyze the structure of a book-driven dealer market when the dealer faces competition from a crossing network or dark pool. The agents are privately informed about their types (e.g. their portfolios),…

In this work we consider the question of whether a simple diffusive model can explain the scent tracking behaviours found in nature. For this behaviour to occur, both the concentration of a scent and its gradient must be above some…

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…

There is growing concern about tacit collusion using algorithmic pricing, and regulators need tools to help detect the possibility of such collusion. This paper studies how to design a hypothesis testing framework in order to decide whether…

In this paper, we study the competition of two diffusion processes for achieving the maximum possible diffusion in an area. This competition, however, does not occur in the same circumstance; one of these processes is a normal diffusion…

The formation of agents' opinions in a social system is the result of an intricate equilibrium among several driving forces. On the one hand, the social pressure exerted by peers favours the emergence of local consensus. On the other hand,…

We propose a new model about diffusion of a product which includes a memory of how many adopters or advertisements a non-adopter met, where (non-)adopters mean people (not) possessing the product. This effect is lacking in the Bass model.…

This paper is concerned with reaction-diffusion systems of two symmetric species in spatial dimension one, having two stable symmetric equilibria connected by a symmetric standing front. The first order variation of the speed of this front…

Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…

We study scenarios where multiple sellers of a homogeneous good compete on prices, where each seller can only sell to some subset of the buyers. Crucially, sellers cannot price-discriminate between buyers. We model the structure of the…

A dynamic model of the product lifecycle of (nearly) homogeneous durables in polypoly markets is established. It describes the concurrent evolution of the unit sales and price of durable goods. The theory is based on the idea that the sales…

Diffusion of a two component fluid is studied in the framework of differential equations, but where these equations are systematically derived from a well-defined microscopic model. The model has a finite carrying capacity imposed upon it…

We introduce pricing formulas for competition and collusion models of two-sided markets with an outside option. For the competition model, we find conditions under which prices and consumer surplus may increase or decrease if the outside…

The paper deals with the spread of two competing viruses over a network of population nodes, accounting for pairwise interactions and higher-order interactions (HOI) within and between the population nodes. We study the competitive…

In this paper we consider the Shigesada-Kawasaki-Teramoto (SKT) model to account for stable inhomogeneous steady states exhibiting spatial segregation, which describe a situation of coexistence of two competing species. We provide a deeper…

A simple Ising spin model which can describe the mechanism of advertising in a duopoly market is proposed. In contrast to other agent-based models, the influence does not flow inward from the surrounding neighbors to the center site, but…

We develop a location analysis spatial model of firms' competition in multi-characteristics space, where consumers' opinions about the firms' products are distributed on multilayered networks. Firms do not compete on price but only on…

We study how to incentivize agents in a target group to produce a higher output in the context of incomplete information, by means of rank-order allocation contests. We describe a symmetric Bayes--Nash equilibrium for contests that have two…