# user9915

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 Dec2 asked Finding social cost in game theory paper Nov21 revised Proving lower bounds from algorithmic game theory paper (specifically, price of anarchy is lower bounded by 3/2 for $m$ links) edited tags Nov21 revised Proving lower bounds from algorithmic game theory paper (specifically, price of anarchy is lower bounded by 3/2 for $m$ links) added 532 characters in body Nov21 asked Proving lower bounds from algorithmic game theory paper (specifically, price of anarchy is lower bounded by 3/2 for $m$ links) Nov13 accepted Expected Value of a Max vs Max of an Expected value Nov13 revised Optimal social cost = 1 … Game Theory paper added 77 characters in body Nov13 revised Optimal social cost = 1 … Game Theory paper added 13 characters in body; edited title Nov13 comment Optimal social cost = 1 … Game Theory paper Look it's a massive assumption, and one that I'm not sure is warranted to say that the cost of the optimal solution is the same as optimal individual cost. Which is what you are saying in second comment. Nov13 comment Optimal social cost = 1 … Game Theory paper So I'm still left with original question: how are they deriving 1 for the optimal social cost? Nor am I sure why I should interpret optimal social cost as optimal individual social cost? Nov13 comment Optimal social cost = 1 … Game Theory paper Yes, you understood me correctly. Also, it won't let me enter the chat. Nov13 accepted Sum of random variables and expectation … difference? Nov13 comment Optimal social cost = 1 … Game Theory paper So why did you interpret optimal solution as optimal individual cost? Nov13 comment Optimal social cost = 1 … Game Theory paper socially optimal refers to the overall optimal. It is as if you had benevolent dictator could guide everyone to reduce the overall cost. I had assumed that optimal solution = socially optimal, which I had thought meant optimal solution means optimal total delay. Nov13 revised Trying to understand proof that price of anarchy O(logm/loglogm) for m links added 11 characters in body Nov13 comment Trying to understand proof that price of anarchy O(logm/loglogm) for m links Is m a constant? (the 'm' before the $(4e)^\tau$) Nov13 comment Optimal social cost = 1 … Game Theory paper if each $w_i$ = 1, then the opt = 1 because .5*1+.5*1 = 1? Nov13 comment Optimal social cost = 1 … Game Theory paper So it seems that we have the optimal solution is when the agents choose different edges to send their traffic. If that is correct, I can't tell if the authors just reweighted the $w_i$'s to get an opt of 1 or if the arithmetic works out s.t. the opt = 1. Nov12 revised Optimal social cost = 1 … Game Theory paper added 71 characters in body Nov12 revised Sum of random variables and expectation … difference? added 36 characters in body Nov12 comment Sum of random variables and expectation … difference? fair question. $s_j$ can be thought of as either speed or capacity of link $j$. It is a constant number for each edge or link $j$.