Related papers: A note on the Cobb-Douglas function
We analyse a coalition formation game between strategic service providers of a congestible service. The key novelty of our formulation is that it is a constant sum game, i.e., the total payoff across all service providers (or coalitions of…
The Debreu Koopmans theorem restricts separable aggregation to at most one nonconvex component. We solve this by proving that a separable, additive or multiplicative, function is star quasiconvex, those with star shaped sublevel sets about…
For two-person dynamic zero-sum games (both discrete and continuous settings), we investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity and the limit of value…
We show that an arithmetic function which satisfies some weak multiplicativity properties and in addition has a non-decreasing or $\log$-uniformly continuous normal order is close to a function of the form $n\mapsto n^c$. As an application…
We study one class of continuous functions $f$ defined on segment $[0,1]$ by equality $$ f(x)=\delta_{\alpha_1(x)1}+\sum^{\infty}_{k=2}\left[\delta_{\alpha_k(x)k}\prod^{k-1}_{j=1}g_{\alpha_j…
We define an analogue of the classical Mittag-Leffler function which is applied to two variables, and establish its basic properties. Using a corresponding single-variable function with fractional powers, we define an associated fractional…
For a dynamical system on n-dimensional projective space over a number field or a function field, we show that semi-stable reduction implies the minimality of the resultant. We use this to show that every such dynamical system over a number…
Recent results, establishing evidence of intractability for such restrictive utility functions as additively separable, piecewise-linear and concave, under both Fisher and Arrow-Debreu market models, have prompted the question of whether we…
In this paper we study functions with low influences on product probability spaces. The analysis of boolean functions with low influences has become a central problem in discrete Fourier analysis. It is motivated by fundamental questions…
The global decline in the labor income share has challenged the classical Kaldor facts; however, the macroeconomic aggregation mechanism -- namely, how aggregate factor shares emerge from firm-level heterogeneity -- remains underexplored.…
A heuristic principle attributed to A. Bloch says that a family of holomorphic functions is likely to be normal if there is no nonconstant entire functions with this property. We discuss this principle and survey recent results that have…
It is shown that a real-valued formal meromorphic function on a formal generic submanifold of finite Kohn-Bloom-Graham type is necessarily constant.
We consider processes which are functions of finite-state Markov chains. It is well known that such processes are rarely Markov. However, such processes are often regular in the following sense: the distant past values of the process have…
This paper embeds a signaling friction into the continuous-time heterogeneous agent framework. A continuum of producers operate Cobb-Douglas technologies with regime-specific productivity $A_j \in \{A_L, A_H\}$. Stochastic arrival of…
We consider a model of fishery management, where $n$ agents exploit a single population with strictly concave continuously differentiable growth function of Verhulst type. If the agent actions are coordinated and directed towards the…
This paper studies estimation in functional linear quantile regression in which the dependent variable is scalar while the covariate is a function, and the conditional quantile for each fixed quantile index is modeled as a linear functional…
We examine Bourbaki's function, an easily-constructed continuous but nowhere-differentiable function, and explore properties including functional identities, the antiderivative, and the box and Hausdorff dimensions of the graph.
This paper argues that continued AI scaling requires repeated efficiency doublings. Classical AI scaling laws remain useful because they make progress predictable despite diminishing returns, but the compute variable in those laws is best…
The paper is related to the identification of firm's features which serve as determinants for firm's total factor productivity through unsupervised learning techniques (principal component analysis, self organizing maps, clustering). This…
In this paper, we provide an example of the optimal growth model in which there exist infinitely many solutions to the Hamilton-Jacobi-Bellman equation but the value function does not satisfy this equation. We consider the cause of this…