scholarly journals Redistribution Mechanisms for Assignment of Heterogeneous Objects

2011 ◽  
Vol 41 ◽  
pp. 131-154 ◽  
Author(s):  
S. P. Gujar ◽  
Y Narahari
Keyword(s):  
Assignment Problem ◽  
Individual Rationality ◽  
Impossibility Theorem ◽  
Budget Balance ◽  
Worst Case ◽  
Heterogeneous Objects ◽  
Heterogeneous Object ◽  
Groves Mechanism ◽  
Unit Demand ◽  
Object Assignment

There are p heterogeneous objects to be assigned to n competing agents (n > p) each with unit demand. It is required to design a Groves mechanism for this assignment problem satisfying weak budget balance, individual rationality, and minimizing the budget imbalance. This calls for designing an appropriate rebate function. When the objects are identical, this problem has been solved which we refer as WCO mechanism. We measure the performance of such mechanisms by the redistribution index. We first prove an impossibility theorem which rules out linear rebate functions with non-zero redistribution index in heterogeneous object assignment. Motivated by this theorem, we explore two approaches to get around this impossibility. In the first approach, we show that linear rebate functions with non-zero redistribution index are possible when the valuations for the objects have a certain type of relationship and we design a mechanism with linear rebate function that is worst case optimal. In the second approach, we show that rebate functions with non-zero efficiency are possible if linearity is relaxed. We extend the rebate functions of the WCO mechanism to heterogeneous objects assignment and conjecture them to be worst case optimal.

scholarly journals Worst case examples of an exterior point algorithm for the assignment problem

2008 ◽  
Vol 5 (3) ◽  
pp. 605-614 ◽  
Author(s):  
Charalampos Papamanthou ◽  
Konstantinos Paparrizos ◽  
Nikolaos Samaras ◽  
Konstantinos Stergiou
Keyword(s):  
Assignment Problem ◽  
Worst Case ◽  
Case Examples

scholarly journals Efficient multiunit auctions for normal goods

2020 ◽  
Vol 15 (1) ◽  
pp. 361-413 ◽  
Author(s):  
Brian Baisa
Keyword(s):  
Incentive Compatibility ◽  
Dominant Strategy ◽  
Impossibility Theorem ◽  
Budget Balance ◽  
Auction Design ◽  
Vickrey Auction ◽  
Multiunit Auctions ◽  
Private Values ◽  
Multidimensional Types ◽  
Normal Goods

I study multiunit auction design when bidders have private values, multiunit demands, and non‐quasilinear preferences. Without quasilinearity, the Vickrey auction loses its desired incentive and efficiency properties. I give conditions under which we can design a mechanism that retains the Vickrey auction's desirable incentive and efficiency properties: (1) individual rationality, (2) dominant strategy incentive compatibility, and (3) Pareto efficiency. I show that there is a mechanism that retains the desired properties of the Vickrey auction if there are two bidders who have single‐dimensional types. I also present an impossibility theorem that shows that there is no mechanism that satisfies Vickrey's desired properties and weak budget balance when bidders have multidimensional types.

Relation Oriented Modeling for Heterogeneous Object Design

2005 ◽  
Author(s):  
X. Y. Kou ◽  
S. T. Tan ◽  
W. S. Sze
Keyword(s):  
Complex Objects ◽  
Tree Structures ◽  
Modeling Approaches ◽  
Modeling Process ◽  
Heterogeneous Objects ◽  
Model Complex ◽  
Heterogeneous Object ◽  
Linear List ◽  
Heterogeneous Object Modeling ◽  
Heterogeneous Feature

Relation oriented modeling approaches are proposed to design heterogeneous objects. The heterogeneous object modeling process is viewed as representing and manipulating complex geometrical, topological and material variation relations with proper data structures. Linear list structure, hierarchical tree structures and more general graph structures are used to represent complex heterogeneous objects. The powerful non-manifold cellular representation and the hierarchical heterogeneous feature tree representation are combined to model complex objects with simultaneous geometry intricacies and compound material variations. We demonstrate that relations play critical roles in heterogeneous object design and under the relation oriented framework, heterogeneous objects can be modeled with generic, uniform representations. The proposed relation oriented modeling approaches are tested with a prototype heterogeneous CAD modeler and presented with different types of heterogeneous object examples.

scholarly journals Iso-material contour representation for process planning of heterogeneous object model

2020 ◽  
Vol 7 (4) ◽  
pp. 498-513
Author(s):  
G K Sharma ◽  
B Gurumoorthy
Keyword(s):  
Additive Manufacturing ◽  
Material Composition ◽  
Composition Material ◽  
Object Model ◽  
Material Distribution ◽  
Process Plan ◽  
Contour Representation ◽  
Heterogeneous Objects ◽  
Raster Scan ◽  
Heterogeneous Object

Abstract Additive manufacturing is emerging as the preferred process for making heterogeneous objects. Planning the deposition of material is more complex for heterogeneous objects as the material variation has to be tracked along the path. This paper proposes an iso-material contour representation to generate the process plan for additive manufacturing given a smooth representation of heterogeneous object model. These contours represent the iso-material paths for deposition. As these paths shift along the direction of the gradation of material distribution, the deposition respects the gradient of the designed material distribution unlike iso-oriented paths generated by a raster scan method. Since the paths have the same material composition, material frequent change in the material composition is avoided, which, in turn, avoids the uneven deposition caused by the frequent start and stop of deposition while the material is being changed along the paths generated by the traditional raster scan. Associativity between the contours and the corresponding designed material feature is maintained, and therefore, changes in material composition are automatically propagated to the process plan.

scholarly journals Randomized Wagering Mechanisms

2019 ◽  
Vol 33 ◽  
pp. 1845-1852
Author(s):  
Yiling Chen ◽  
Yang Liu ◽  
Juntao Wang
Keyword(s):  
Pareto Optimality ◽  
Design Space ◽  
Incentive Compatibility ◽  
Ground Truth ◽  
Impossibility Result ◽  
Individual Rationality ◽  
Budget Balance ◽  
Information Elicitation ◽  
Recent Extension ◽  
Noisy Labels

Wagering mechanisms are one-shot betting mechanisms that elicit agents’ predictions of an event. For deterministic wagering mechanisms, an existing impossibility result has shown incompatibility of some desirable theoretical properties. In particular, Pareto optimality (no profitable side bet before allocation) can not be achieved together with weak incentive compatibility, weak budget balance and individual rationality. In this paper, we expand the design space of wagering mechanisms to allow randomization and ask whether there are randomized wagering mechanisms that can achieve all previously considered desirable properties, including Pareto optimality. We answer this question positively with two classes of randomized wagering mechanisms: i) one simple randomized lottery-type implementation of existing deterministic wagering mechanisms, and ii) another family of randomized wagering mechanisms, named surrogate wagering mechanisms, which are robust to noisy ground truth. Surrogate wagering mechanisms are inspired by an idea of learning with noisy labels (Natarajan et al. 2013) as well as a recent extension of this idea to the information elicitation without verification setting (Liu and Chen 2018). We show that a broad set of randomized wagering mechanisms satisfy all desirable theoretical properties.

Heterogeneous Object Modeling Approach Based on ACIS and HOOPS

2009 ◽  
Vol 419-420 ◽  
pp. 793-796
Author(s):  
An Ping Xu ◽  
Ting Zang ◽  
Zhen Peng Ji ◽  
Yun Xia Qu
Keyword(s):  
Inverse Distance Weighting ◽  
Material Composition ◽  
Functional Modules ◽  
Object Modeling ◽  
Modeling Approach ◽  
Heterogeneous Objects ◽  
Distance Weighting ◽  
Heterogeneous Object ◽  
Heterogeneous Object Modeling ◽  
Inverse Distance

This paper deals with the background and significance of working on heterogeneous objects modeling and briefly introduces the architecture of ACIS and HOOPS and their corresponding functional modules. Based on inverse-distance weighting algorithm to determine the material composition within the object, the general approach to modeling the heterogeneous objects by using ACIS and HOOPS is introduced and demonstrated via some simple examples.

scholarly journals Strategy-Proof and Non-Wasteful Multi-Unit Auction via Social Network

2020 ◽  
Vol 34 (02) ◽  
pp. 2062-2069
Author(s):  
Takehiro Kawasaki ◽  
Nathanael Barrot ◽  
Seiji Takanashi ◽  
Taiki Todo ◽  
Makoto Yokoo
Keyword(s):  
Social Network ◽  
Truth Telling ◽  
Worst Case ◽  
The Social ◽  
Comprehensive Comparison ◽  
Strategy Proof ◽  
Unit Demand ◽  
Social Surplus ◽  
Unit Unit ◽  
Strategy Proofness

Auctions via social network, pioneered by Li et al. (2017), have been attracting considerable attention in the literature of mechanism design for auctions. However, no known mechanism has satisfied strategy-proofness, non-deficit, non-wastefulness, and individual rationality for the multi-unit unit-demand auction, except for some naïve ones. In this paper, we first propose a mechanism that satisfies all the above properties. We then make a comprehensive comparison with two naïve mechanisms, showing that the proposed mechanism dominates them in social surplus, seller's revenue, and incentive of buyers for truth-telling. We also analyze the characteristics of the social surplus and the revenue achieved by the proposed mechanism, including the constant approximability of the worst-case efficiency loss and the complexity of optimizing revenue from the seller's perspective.

scholarly journals An Axiomatic View of the Parimutuel Consensus Mechanism

2018 ◽  
Author(s):  
Rupert Freeman ◽  
David M. Pennock
Keyword(s):  
Pareto Optimality ◽  
Incentive Compatibility ◽  
The Other ◽  
Individual Rationality ◽  
Budget Balance ◽  
Incentive Compatible

We consider an axiomatic view of the Parimutuel Consensus Mechanism defined by Eisenberg and Gale (1959). The parimutuel consensus mechanism can be interpreted as a parimutuel market for wagering with a proxy that bets optimally on behalf of the agents, depending on the bets of the other agents.  We show that the parimutuel consensus mechanism uniquely satisfies the desirable properties of Pareto optimality, individual rationality, budget balance, anonymity, sybilproofness and envy-freeness. While the parimutuel consensus mechanism does violate the key property of incentive compatibility, it is incentive compatible in the limit as the number of agents becomes large. Via simulations on real contest data, we show that violations of incentive compatibility are both rare and only minimally beneficial for the participants. This suggests that the parimutuel consensus mechanism is a reasonable mechanism for eliciting information in practice.

scholarly journals Multi-Unit Assignment Problem: FCFS Course Allocation System Data Analysis

2016 ◽  
Vol 55 (1) ◽  
pp. 70-80
Author(s):  
Gediminas Murauskas ◽  
Marijus Radavičius
Keyword(s):  
Data Analysis ◽  
Regression Model ◽  
Empirical Data ◽  
Assignment Problem ◽  
Simulated Data ◽  
Allocation System ◽  
Censored Regression Model ◽  
System Data ◽  
Unit Demand ◽  
Vilnius University

We study the allocation of courses to students with multi-unit demand. Exploratory analysis of courseallocation practices at Vilnius University (VU) is performed. The allocation of students to courses is done by a simplefirst-come first-served (FCFS) procedure. We show that FCFS procedure does not deliver desirable outcomes. Data withstudent preferences is needed in order to compare assignment algorithms. We use censored regression model to constructstudent preferences generation mechanism based on empirical data collected at VU. Using simulated data several multiunitassignment algorithms are compared.

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