linear-programming   167

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ON THE GEOMETRY OF NASH EQUILIBRIA AND CORRELATED EQUILIBRIA
Abstract: It is well known that the set of correlated equilibrium distributions of an n-player noncooperative game is a convex polytope that includes all the Nash equilibrium distributions. We demonstrate an elementary yet surprising result: the Nash equilibria all lie on the boundary of the polytope.
pdf  nibble  papers  ORFE  game-theory  optimization  geometry  dimensionality  linear-algebra  equilibrium  structure  differential  correlation  iidness  acm  linear-programming  spatial  characterization  levers 
10 weeks ago by nhaliday
Practical Optimization: A Gentle Introduction
Nice introduction to linear programming/optimization.
See Chapter 10 "The Shortest Route Problem."
0root-research  linear-programming  shortest-path 
april 2019 by brad73435
Kairouz, Oh, Viswanath, "Extremal Mechanisms for Local Differential Privacy"
"We introduce a family of extremal privatization mechanisms, which we call staircase mechanisms, and prove that it contains the optimal privatization mechanism that maximizes utility. We further show that for all information theoretic utility functions studied in this paper, maximizing utility is equivalent to solving a linear program, the outcome of which is the optimal staircase mechanism."
local-differential-privacy  differential-privacy  research-article  linear-programming  randomization 
april 2019 by arthegall
[1801.02602] Three Puzzles on Mathematics, Computation, and Games
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear programming. The second puzzle is about errors made when votes are counted during elections. The third puzzle is: are quantum computers possible?
mathematics  computational-complexity  rather-interesting  lecture  to-write-about  linear-programming 
march 2018 by Vaguery
6.896: Essential Coding Theory
- probabilistic method and Chernoff bound for Shannon coding
- probabilistic method for asymptotically good Hamming codes (Gilbert coding)
- sparsity used for LDPC codes
mit  course  yoga  tcs  complexity  coding-theory  math.AG  fields  polynomials  pigeonhole-markov  linear-algebra  probabilistic-method  lecture-notes  bits  sparsity  concentration-of-measure  linear-programming  linearity  expanders  hamming  pseudorandomness  crypto  rigorous-crypto  communication-complexity  no-go  madhu-sudan  shannon  unit  p:**  quixotic  advanced 
february 2017 by nhaliday
Lecture 11
In which we prove that the Edmonds-Karp algorithm for maximum flow is a strongly polynomial time algorithm, and we begin to talk about the push-relabel approach.
pdf  lecture-notes  exposition  optimization  algorithms  linear-programming  graphs  stanford  luca-trevisan  nibble  direction  stock-flow  tcs  constraint-satisfaction  tcstariat 
january 2017 by nhaliday

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