scholarly journals Following a “Balanced” Trajectory from an Infeasible Point to an Optimal Linear Programming Solution with a Polynomial-Time Algorithm

1996 ◽  
Vol 21 (4) ◽  
pp. 839-859
Author(s):  
Robert M. Freund
Keyword(s):  
Linear Programming ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Optimal Linear ◽  
Programming Solution ◽  
Linear Programming Solution

scholarly journals On the exact polynomial time algorithm for a special class of bimatrix game

2013 ◽  
Vol 54 ◽  
Author(s):  
Jonas Mockus ◽  
Martynas Sabaliauskas
Keyword(s):  
Game Theory ◽  
Linear Programming ◽  
Nash Equilibrium ◽  
Polynomial Time ◽  
Explicit Solution ◽  
Special Class ◽  
Polynomial Algorithm ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Bimatrix Game

The Strategy Elimination (SE) algorithm was proposed in [2] and implemented by a sequence of Linear Programming (LP) problems. In this paper an efficient explicit solution is developed and the convergence to the Nash Equilibrium is proven.Keywords: game theory, polynomial algorithm, Nash equilibrium.

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.

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