scholarly journals A Polynomial Time Algorithm for Fair Resource Allocation in Resource Exchange

2019 ◽  
pp. 1-13
Author(s):  
Xiang Yan ◽  
Wei Zhu
Keyword(s):  
Resource Allocation ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Resource Exchange

scholarly journals Equilibrium computation in resource allocation games

2021 ◽  
Author(s):  
Tobias Harks ◽  
Veerle Timmermans
Keyword(s):  
Resource Allocation ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Congestion Games ◽  
Congestion Game ◽  
Equilibrium Computation ◽  
The Difference ◽  
Price Functions ◽  
Resource Allocation Games

AbstractWe study the equilibrium computation problem for two classical resource allocation games: atomic splittable congestion games and multimarket Cournot oligopolies. For atomic splittable congestion games with singleton strategies and player-specific affine cost functions, we devise the first polynomial time algorithm computing a pure Nash equilibrium. Our algorithm is combinatorial and computes the exact equilibrium assuming rational input. The idea is to compute an equilibrium for an associated integrally-splittable singleton congestion game in which the players can only split their demands in integral multiples of a common packet size. While integral games have been considered in the literature before, no polynomial time algorithm computing an equilibrium was known. Also for this class, we devise the first polynomial time algorithm and use it as a building block for our main algorithm. We then develop a polynomial time computable transformation mapping a multimarket Cournot competition game with firm-specific affine price functions and quadratic costs to an associated atomic splittable congestion game as described above. The transformation preserves equilibria in either game and, thus, leads – via our first algorithm – to a polynomial time algorithm computing Cournot equilibria. Finally, our analysis for integrally-splittable games implies new bounds on the difference between real and integral Cournot equilibria. The bounds can be seen as a generalization of the recent bounds for single market oligopolies obtained by Todd (Math Op Res 41(3):1125–1134 2016, 10.1287/moor.2015.0771).

Learning Importance of Preferences

10.29007/v68w ◽  
2018 ◽  
Author(s):  
Ying Zhu ◽  
Mirek Truszczynski
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scoring Rules ◽  
Np Hard ◽  
Individual Preferences

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

A Polynomial-Time Algorithm for the Knapsack Problem with Two Variables

1976 ◽  
Vol 23 (1) ◽  
pp. 147-154 ◽  
Author(s):  
D. S. Hirschberg ◽  
C. K. Wong
Keyword(s):  
Polynomial Time ◽  
Knapsack Problem ◽  
Polynomial Time Algorithm ◽  
Time Algorithm

scholarly journals Polynomial Time Algorithm for Min-Ranks of Graphs with Simple Tree Structures

Algorithmica ◽  
2013 ◽  
Vol 71 (1) ◽  
pp. 152-180 ◽  
Author(s):  
Son Hoang Dau ◽  
Yeow Meng Chee
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Tree Structures ◽  
Simple Tree
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