A piecewise-constant valuation is a kind of a function that represents the utility of an agent over a continuous resource, such as land. It occurs when...

region. Crenel function Piecewise Sigmoid function Simple function Step detection Heaviside step function Piecewise-constant valuation "Step Function". "Step...

such mechanism cannot be envy-free. Suppose all agents have piecewise-constant valuations. This means that, for each agent, the cake is partitioned into...

prove the existence of an exact division when the agents have piecewise-constant valuations. This means that the cake can be partitioned into R regions...

reveals his/her entire valuation function to the algorithm; this is possible, for example, with piecewise-constant valuations. With direct revelation...

more agents with piecewise-uniform valuations, without free disposal. There are 2 or more agents with piecewise-constant valuations, with or without free...

n} partners with general valuations: additive approximation to envy and efficiency, based on the piecewise-constant-valuations algorithm. Brams, Feldman...

Haris (2014-12-14). "Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations". Web and Internet Economics. Lecture Notes in Computer...

and addition by their tropical counterparts and each constant in K {\displaystyle K} by its valuation. That is, if f = ∑ i = 1 s c i x A i with  A 1 , …...

his mechanism using simulations. He generated piecewise-constant valuation functions, whose constants were selected at random from the uniform distribution...

entire valuation to the mechanism. This model makes sense only when the valuations can be represented succinctly, for example, when they are piecewise-uniform...

{\displaystyle O(n^{2}d)} . Another restriction on the valuations is that they are piecewise-constant - for each agent, there are at most m desired intervals...

numerical examples. These examples showed de Moivre using his hypothesis in a piecewise fashion, wherein he assumed that the overall pattern of human mortality...

"separable"), but for each item-kind, the valuation has decreasing marginal utilities (this is the meaning of "piecewise-linear concave"). They give a 2-approximation...

force the SABR model price of the option into the form of the Black model valuation formula. Then the implied volatility, which is the value of the lognormal...

function, and is hence not invertible. The real absolute value function is a piecewise linear, convex function. For both real and complex numbers the absolute...

cases: two agents with general additive valuations, or any number of agents with piecewise-linear valuations. In contrast to EF1, which is compatible...

{\displaystyle h_{i}} to be the constant function 0 {\displaystyle 0} . We say a convex function is simple piecewise-linear if it is a maximum of two...

models. Algorithms for restricted classes of valuations, such as piecewise-linear, piecewise-constant or piecewise-uniform, which can be given explicitly as...

quasilinear, in which the utility of each agent from each room can be any piecewise linear function of the rent. This setting generalizes the soft budget...

907912. S2CID 15583243. Yu, Guoshen (2012). "Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity"...

An allocation of items among n {\displaystyle n} agents with different valuations is called MMS-fair if each agent gets a bundle that is at least as good...

Haris; Ye, Chun (2014). "Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations". In Liu, Tie-Yan; Qi, Qi; Ye, Yinyu (eds.). Web...

agents with general additive valuations, and for n agents with piecewise linear valuations over the divisible goods. They also present an efficient algorithm...

They are an active area of research, linking algebraic varieties with piecewise linear structures. The Łukasiewicz semiring: the closed interval [ 0 ...

it is economically non-storable and power system stability requires a constant balance between production and consumption. At the same time, electricity...