Related papers: Natural selection. IV. The Price equation
Pricing decisions of companies require an understanding of the causal effect of a price change on the demand. When real-life pricing experiments are infeasible, data-driven decision-making must be based on alternative data sources such as…
Market-based mechanisms such as auctions are being studied as an appropriate means for resource allocation in distributed and mulitagent decision problems. When agents value resources in combination rather than in isolation, they must often…
We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…
Recent studies of in vitro evolution of DNA via protein binding indicate that the evolution behavior is qualitatively different in different parameter regimes. I here present a general theory that is valid for a wide range of parameters,…
In both natural and artificial studies, evolution is often seen as synonymous to natural selection. Individuals evolve under pressures set by environments that are either reset or do not carry over significant changes from previous…
Our understanding of evolution is shaped strongly by how we conceive of its fundamental causes. In the original Modern Synthesis, evolution was defined as a process of shifting the frequencies of available alleles at many loci affecting a…
There is a growing body of work on sorting and selection in models other than the unit-cost comparison model. This work is the first treatment of a natural stochastic variant of the problem where the cost of comparing two elements is a…
Competition for available resources is natural amongst coexisting species, and the fittest contenders dominate over the rest in evolution. The dynamics of this selection is studied using a simple linear model. It has similarities to…
The key idea of this model is that firms are the result of an evolutionary process. Based on demand and supply considerations the evolutionary model presented here derives explicitly Gibrat's law of proportionate effects as the result of…
The properties of the evolution equation have been analyzed. The uniqueness and the existence of solution for the evolution equation with special value of parameter characterizing intensity of change of external conditions, of the…
We introduce a new tool for predicting the evolution of an option for the cases where at some specific time, there is a high-degree of uncertainty for identifying its price. We work over the special case where we can predict the evolution…
In sorting literature, comparative statics for multidimensional assignment models with general output functions and input distributions is an important open question. We provide a complete theory of comparative statics for technological…
We look at price formation in a retail setting, that is, companies set prices, and consumers either accept prices or go someplace else. In contrast to most other models in this context, we use a two-dimensional spatial structure for…
This research is concerned with evolution equations and their forward-backward discretizations. Our first contribution is an estimation for the distance between iterates of sequences generated by forward-backward schemes, useful in the…
Many examples of cooperation exist in biology. In chemical systems however, which can sometimes be quite complex, we do not appear to observe intricate cooperative interactions. A key question for the origin of life, is then how can…
Analogies between evolutionary dynamics and statistical mechanics, such as Fisher's second-law-like "fundamental theorem of natural selection" and Wright's "fitness landscapes", have had a deep and fruitful influence on the development of…
Algorithmic decision-making in high-stakes settings can have profound impacts on individuals and populations. While much prior work studies fairness in static settings, recent results show that enforcing static fairness constraints may…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
Species coexistence is one of the central themes in modern ecology. Coexistence is a prerequisite of biological diversity. However, the question arises how biodiversity can be reconciled with the statement of competition theory, which…
We consider the optimization of a dynamical system by switching at discrete time points between abstract evolution equations composed by nonlinearly perturbed strongly continuous semigroups, nonlinear state reset maps at mode transition…