scholarly journals Implementable Mechanisms for Discrete Utility Functions, A Solution Using Tropical Geometry

2019 ◽  
Author(s):  
Julian-Enrique Chitiva
Keyword(s):  
Tropical Geometry ◽  
Utility Functions

A Model for Applying Information and Utility Functions

1963 ◽  
Vol 30 (3) ◽  
pp. 267-273 ◽  
Author(s):  
David Harrah
Keyword(s):  
Utility Functions

scholarly journals Pareto Efficient Auctions with Interest Rates

2019 ◽  
Vol 33 ◽  
pp. 1989-1995
Author(s):  
Gagan Goel ◽  
Vahab Mirrokni ◽  
Renato Paes Leme
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Utility Functions ◽  
Limited Access ◽  
Incentive Compatible ◽  
Pareto Efficient ◽  
Available Resources

We consider auction settings in which agents have limited access to monetary resources but are able to make payments larger than their available resources by taking loans with a certain interest rate. This setting is a strict generalization of budget constrained utility functions (which corresponds to infinite interest rates). Our main result is an incentive compatible and Pareto-efficient auction for a divisible multi-unit setting with 2 players who are able to borrow money with the same interest rate. The auction is an ascending price clock auction that bears some similarities to the clinching auction but at the same time is a considerable departure from this framework: allocated goods can be de-allocated in future and given to other agents and prices for previously allocated goods can be raised.

scholarly journals Tropical ideals do not realise all Bergman fans

2021 ◽  
Vol 8 (3) ◽  
Author(s):  
Jan Draisma ◽  
Felipe Rincón
Keyword(s):  
Tropical Geometry ◽  
Tensor Products ◽  
Tropical Variety ◽  
Polyhedral Complex ◽  
Direct Sum ◽  
Weight One ◽  
Polyhedral Complexes

AbstractEvery tropical ideal in the sense of Maclagan–Rincón has an associated tropical variety, a finite polyhedral complex equipped with positive integral weights on its maximal cells. This leads to the realisability question, ubiquitous in tropical geometry, of which weighted polyhedral complexes arise in this manner. Using work of Las Vergnas on the non-existence of tensor products of matroids, we prove that there is no tropical ideal whose variety is the Bergman fan of the direct sum of the Vámos matroid and the uniform matroid of rank two on three elements and in which all maximal cones have weight one.

scholarly journals Algebraic singularities of scattering amplitudes from tropical geometry

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
James Drummond ◽  
Jack Foster ◽  
Ömer Gürdoğan ◽  
Chrysostomos Kalousios
Keyword(s):  
Scattering Amplitudes ◽  
Natural Language ◽  
Tropical Geometry ◽  
Cluster Algebras ◽  
Finite Alphabet ◽  
Square Root ◽  
Finite Sets ◽  
Yang Mills ◽  
Square Roots ◽  
Algebraic Singularities

Abstract We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.

scholarly journals UTILITY FUNCTIONS AND FISCAL ILLUSION FROM GRANTS

1990 ◽  
Vol 43 (2) ◽  
pp. 201-205
Author(s):  
J. PATRICK O'BRIEN ◽  
YEUNG-NAN SHIEH
Keyword(s):  
Utility Functions ◽  
Fiscal Illusion
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