Related papers: Ultra valuations
We revisit the setting of fairly allocating indivisible items when agents have different weights representing their entitlements. First, we propose a parameterized family of relaxations for weighted envy-freeness and the same for weighted…
A valuation theory for superrings is developed, extending classical constructions from commutative algebra to the $\mathbb Z_2$-graded and supercommutative setting. We define valuations on superrings, investigate their fundamental…
Some of the most significant high-level properties of currencies are the sums of certain account balances. Properties of such sums can ensure the integrity of currencies and transactions. For example, the sum of balances should not be…
Starting from a plausible assumption about the Total Revenue concept, a system of economic agents, that simulates the exchange of goods, is studied. Following a methodology equivalent to that used in the statistical-mechanical determination…
Ryser's max term rank formula with graph theoretic terminology is equivalent to a characterization of degree sequences of simple bipartite graphs with matching number at least $\ell$. In a previous paper by the authors, a generalization was…
A fundamental task underlying many important optimization problems, from influence maximization to sensor placement to content recommendation, is to select the optimal group of $k$ items from a larger set. Submodularity has been very…
Evolution has produced an astonishing diversity of species, each filling a different niche. Algorithms like MAP-Elites mimic this divergent evolutionary process to find a set of behaviorally diverse but high-performing solutions, called the…
We study the problem of fairly allocating indivisible goods among agents which are equipped with {\em leveled} valuation functions. Such preferences, that have been studied before in economics and fair division literature, capture a simple…
The design of optimal auctions is a problem of interest in economics, game theory and computer science. Despite decades of effort, strategyproof, revenue-maximizing auction designs are still not known outside of restricted settings.…
We study buyer-optimal procurement mechanisms when quality is contractible. When some costs are borne by every participant of a procurement auction regardless of winning, the classic analysis should be amended. We show that an optimal…
We study the problem of multi-dimensional revenue maximization when selling $m$ items to a buyer that has additive valuations for them, drawn from a (possibly correlated) prior distribution. Unlike traditional Bayesian auction design, we…
In a recent paper, an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices -- the so called `matrix properties'. In this paper we extend this algorithm to…
We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs. The set of superhedging portfolios can be obtained by a recursive…
As the widely applied method for measuring matching assortativeness in a transferable utility matching game, a matching maximum score estimation is proposed by \cite{fox2010qe}. This article reveals that combining unmatched agents,…
Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments…
The Ulam's metric is the minimal number of moves consisting in removal of one element from a permutation and its subsequent reinsertion in different place, to go between two given permutations. Thet elements that are not moved create…
We characterize the equality between ultradifferentiable function classes defined in terms of abstractly given weight matrices and in terms of the corresponding matrix of associated weight functions by using new growth indices. These…
We study the problem of designing optimal auctions under restrictions on the set of permissible allocations. In addition to allowing us to restrict to deterministic mechanisms, we can also indirectly model non-additive valuations. We prove…
A variety of optimization problems takes the form of a minimum norm optimization. In this paper, we study the change of optimal values between two incrementally constructed least norm optimization problems, with new measurements included in…
We model the role of an online platform disrupting a market with unit-demand buyers and unit-supply sellers. Each seller can transact with a subset of the buyers whom she already knows, as well as with any additional buyers to whom she is…