## Thursday, July 28, 2016

### GAMES/EC 2016

This week I report from Maastricht in the Netherlands from the GAMES 2016, the 5th World Congress of the Game Theory Society. By having their congress every four years, everyone who is anyone in the game theory community makes a strong effort to be here, including three Nobel laureates, Robert Aumann, Roger Myerson and Eric Maskin. The conference has about 750 participants and up to 19 parallel sessions.

This year the conference is co-located with the Economics and Computation conference that comes more from the CS community. By co-located we are sharing the same buildings and many of the events, effectively one larger conference (which means in reality 21 parallel sessions).

EC keeps growing, accepting 80 papers out of 242 submissions, all of which are freely downloadable.

My favorite EC talk was the best student paper, Deferred Acceptance with Compensation Chains by
Piotr Dworczak, a graduate student in the Stanford Business School. He gives an algorithm for finding stable matchings with the property that every stable matching can be found by changing the order that the agents get to choose. The paper Which Is the Fairest (Rent Division) of Them All? by
Kobi Gal, Moshe Mash, Ariel Procaccia and Yair Zick won best paper.

Also a shout out to the talk Cadet-Branch Matching in a Quasi-Linear Labor Market solely authored by Ravi Jagadeesan, a rising junior undergraduate at Harvard. I went to grad school with Ravi's mother Lalita, and yes that makes me feel old.

Tim Roughgarden gave the Kalai prize talk for his work on Intrinsic Robustness of the Price of Anarchy. The talk, attended by a good number of the game theorists, gave a general approach to generalizing bounds price of anarchy results to broader classes of equilibria. Tim followed Keith Chen who heads the analytic team for Uber and discussed how game theory and optimization ideas are driving a major e-commerce company. No major surprises but here's one trade secret: Uber covers its maps with hexagons while Lyft uses squares.

All is all a great week, with packed schedules and crowded activities, but great to see all these game theorists and computer scientists talking with each other.

## Sunday, July 24, 2016

### The College Issues that are talked about/College issues that are important

The following college issues get lots of attention:

Admissions-  high school students PLAN to do things JUST to get them into an elite college. For example nobody takes the SATs just for the fun of it anymore.

Sports- too much money spend on it?

Sports- the players treated unfairly?

Are other out-of-class activites also an issue? See here.

Jock Culture.

Free speech- Speech codes, triggers. (I've heard this talked about for about 30 years now.)

A  common core. How to make it not just dead white males.

A common core. How to get this to work when profs are overly specialized.

Professors are rewarded for research more than teaching- how to induce them to be better teachers.(I've heard about this one for about 40 years.)

Renaming buildings that are named after racists. ( Byrd Stadium at UMCP is now Maryland Stadium  see here) (If we find out that Fields or Abel was a racist will we rename the awards? Why bother naming things after Justice Scalia or Bobby Kennedy when they will be renamed at some point because of their views on gay people?)

Renaming buildings that are named after the things racists do (see here)

White privilege  (If I was black then whenever my blog had   bad spelling or grammar it would be connected to my race and assumed upbringing.)

The crushing debts of $100,000 or so that some students face after college. (Which is why some students Feel the Bern!, though others Feel the Bern! for different reasons.) Hookup culture on campus Lack of diversity in some majors (I've heard this talked about for about 30 years now.) (Examples: Across the country CS is at around 15% female. Art History is around 80% female. Why does the CS one generate much discussion and some outrage but the art history one... not so much? I would guess jobs. But the point of this list is just that these are the issues people ARE talking about.) Should college be vocational vs intellectual? Are these two disjoint? MOOCS: How will they affect education? These are important issues. But they affect few people. 65% (and dropping) high school seniors goto college. Over 1/2 of all college students go to community college. Many of those students are part timers who also work. Speech codes are not at the top of the things they have to worry about. These people face other problems that do not get attention. See the following excellent articles Shut up abour Harvard by Ben Cassleman and The other 75% by Paul Attewell and David Lavin To give one example: The number of students going to community college who need to take part time jobs to finish and end up with a crushing (to them) debt of$10,000 is a far more common problem then any of the ones above. Why so little coverage?

The articles give other examples of problems that are NOT being talked about.

The other 75% is from the excellent book What is college for edited by Lagemann and Lewis, and reviewed by me, for SIGACT News, here.   Most of the other chapters are about the issues above. We need a book, or at least  a conversation, about issues of education affecting many more people.

The Morrill Land-Grant Acts established many colleges. It was passed in a time when it was realized that its important to have an educated public. It must have been passed in a time where there were not the pressing issues we have today (like bathrooms for transgender people) so they could think about these issues clearly. It was passed in 1862 in the middle of the Civil War.

A meta-thought--- Every comment on this blog about the issues I list above as NOT affecting that many people will prove my point that those issues are discussed far more than issues that affect far more people. Even so, feel free to comment on whatever issues you want.

## Thursday, July 21, 2016

### Snowbird 2016

Earlier this week I attended the 2016 CRA Snowbird Conference, a biennial meeting of CS chairs and other leaders in the the computing community. I’ve attended every meeting since 2010, the first as a panelists on journals in CS and the last three as department chair. I enjoy this meeting mostly for the networking with other chairs across the whole CS discipline.

Computer science sits in an enviable position with booming enrollments, our graduates easily finding quality jobs in the field and computing literally changing society. Success breeds challenges, top of this list is how do we cover the dramatically increasing course load. Right now most schools are applying a variety of short-term solutions from increased use of larger classrooms, sometimes with recorded video, instructors and teaching faculty, PhD, MS and undergrad TAs and less small specialized graduate classes to allow for more core courses. What we haven’t seen is increased teaching loads. We need to be careful not to drive faculty into industry’s waiting arms.

The confrence had some interesting speakers such as John Markoff from the New York Times on the excitement and concerns over machine learning and automation, Cynthia Dwork on the theory approach to privacy and fairness in the big data era, and Robert Morse from US News on how they rank CS departments. I'm generally fine with the US News Ranking, they measure reputation and reputation is in the end what matters in recruiting students and faculty. Many at the meeting had other, less friendly, opinions towards US News and rankings in general.

One popular session discussed schools and colleges of computing beyond the department. Most of the successful transitions came out of CS programs in colleges of science, such as at CMU and Georgia Tech. Rarely do we see the transition out of engineering. With both the growth of computer science and its increasingly central role in many academic disciplines, now is a good time to make the argument for more colleges of computing. Perversely the growth makes such changes more challenging as an engineering dean would not want to give up such a large and growing part of their college.

The Snowbird conference moves the conversation away from the weeds of current results to look back at what our field has achieved and where it is going. It's never been a more exciting time to be a computer scientist and while chairs always love to grumble when we get together, we all know how lucky we are to be leaders in this era.

## Monday, July 18, 2016

### Solution to the Alice-Bob-Box problem.

In my last blog I solved one problem and asked another (when will it end!).  Damien Roberts provided an answer in the comments to the last blog, so kudos to Damien! I summarize the question asked and answer it (same answer as Damien, though more long winded)  and then some comments and further questions.

Peter Winkler told me this problem at the Joel Spencer 70th Bday conference.  He got it from Sergui Hart who does not claim to be the inventor of it.

PROBLEM:
Alice and Bob play the following (non-fun) game:

Alice puts natural numbers in the boxes 1,2,3,4,... She can put any number in any box. She can put the number 12 in two boxes. She can refuse to put primes in any box. The world is her burito!

Bob opens all but a finite number of  boxes. He chooses one of the boxes that is NOT opened and guesses what is in it and then opens it.  If his guess is correct he wins! (not clear what he wins, but he wins).If not he is, as one of our candidates for prez would say, a LOOOOOOOSER.

Would you rather be Alice or Bob?
END OF PROBLEM

(Added Later- below is an answer that I believe to be correct. Some people disagree. See some of the comments below and also the comments on this)

I would rather be Bob:

As you might have guessed, Bob takes the set of all infinite sequences of natural numbers and looks at the equivalence x==y iff x and y differ on only a finite number of positions. He then picks a representative from each part of the induced partition.

(When I tried to solve the problem thats as far as I got. Some commenters thought that was the solution, or the solution was obvious from that point. I don't see how.)

Here is what Bob does;

STEP 1: (I used to have Bob takes a random perm of the naturals and relabels the boxes but commenters pointed out that this was not needed and might not even make sense. So there is no Step 1, but I keep
it in case someone sees this post and wonders what happened to step 1.)

STEP2: Bob rearranges the boxes into (say) 100 rows.  We'll say

ROW1: BOXES: 1,101,201,301,...

ROW2: BOXES: 2,102,202,302,...
...
ROW100: BOXES: 100,200,300,...

STEP3: Bob picks a Row AT RANDOM (second use of probability). We will say ROW8:

STEP4: Bob opens the boxes in all of the rows EXCEPT ROW8 (he will open some in ROW8 later). For each Row i NE 8 he does the following:

ROWi is in one of the parts of the partition. Bob had ahead of time chosen a representative in that part. Let x(i) be such that from the x(i)th element on ROWi and the Representative AGREE.

Let x  = max of the x(i).

So, for all rows i NE 8, if you look past the xth position, ROWi and the represenative for that equivalance class are the same.

STEP5: Bob opens up, in ROW8, the boxes x+2, x+3,...

STEP6: Bob knows the part that ROW8 is in the partition. Bob looks at the representative. Bob guesses that the number in box x+1 of ROW8 is the same as the number in the (x+1)th position of the representative.

WHY is this a good idea?

Consider ROWi. Let x(i) (as above) be such that past x(i) ROWi agrees with its rep. In order for the guess to be wrong you would need x(8) > all other x(i). How likely is that? Since we began with a random perm, the prob that x(8) is the largest (for that matter, the prob that any particular i_o has max x(i_0) ) is 1/100. So Bob wins with prob 1- 1/100

Bob can do even better with 1000 rows or 10,000 rows, etc. For any eps>0 he can make the prob that he'll win 1-eps.

One issue I've been trying to get at in this post and the last one was, is this a real solution? I think so, but some students don't like it. Even those that understand it. What do you think?

There is no deterministic solution to the Alice-Bob-Box problem since if the adversary knows what box Bob will guess he can make it so that Bob gets it wrong.

Some asked if there was a computable solution. For both the infinite-hats problem and the box-problem if the players have a strategy depending on only a finite number of inputs they can't win. There are ways to measure the complexity of a strategy and it would be interesting to get upper and lower bounds on the complexity of a strategy. And one can look at the following: If the adversary's strategy is of complexity BLAH then what complexity do the players need to beat it?

Also, in both games AC is used by the players. Eddie Fisher pointed out that if you toss out AC and instead have the AC AM (all sets are measurable) then the Adversary wins the hat game. Not sure about the box game.  One can look at what happens in various axiom systems.

So many open questions, so little time!

## Thursday, July 14, 2016

### Solution to the infinite hat problem/a point/a new problem

In my last post I asked the following question (I've shortened it here but its the same really.)

An infinite number of people, labelled 1,2,3,... have hats on their head, RED or BLUE. They must all shout at the same time a color. They want only a finite number of people to not guess their own hat color correctly. Can they do this?

YES they can manage to get all but a finite number of hats wrong. Here is what they do in their strategy meeting:

1) Define an equivalence class on infinite strings of R's and B's:  x==y iff x and y differ on only a finite number of places. It is easy to show that this is an Equiv relation. We think of the string as telling us the hat colors of all the people.

2) An Equiv Rel induces a partition. Choose, for each part of the partition, a representative. They all know all of the representatives.

NOW, once the hats are put on here is how each person reacts:

Gee, I see all of those hats out there! Since I see all but my hat I KNOW which partition the hat coloring is in. I look at the representative of that partition. I guess the hat color that I have in that representative.

Note that ALL of the people will use the SAME rep, and that rep differs from reality in only a finite number of hats. Therefore the number of incorrect answers is finite.

POINT- when I show this to my class they often don't like it. Some of course do not understand it, but even those who do sometimes say that's not practical  or the people would need infinite brains!  These are both true, but I like it anyway. HOW ABOUT YOU- does the solution satisfy?

NEW PROBLEM (are any problems really new?) I heard this from Peter Winkler who heard it from Sergui Hart who does not claim to have invented it.

Alice and Bob play a game (My darling complains that when a math puzzle uses the word game its usually not a fun game. This problem will not be a counterexample.)

There are an infinite number of boxes labelled 1,2,3,....

Alice puts into each box a natural number.

(CLARIFICATION based on a comment- Alice an put any number she wants in any box.
She wants to put 18 in both box 199 and box 3999 she can do that. NO restriction on what
Alice puts in the boxes except that every box has SOME natural number. ALSO- she need not
use all the naturals- if she wants to put a 1 in every box, she can.)

Bob opens all but a finite number of boxes.

For one of the boxes Bob does NOT open he guesses what the number in it is.

They then open that box. If Bob is right, he wins. If not then Alice wins.

Would you rather be Alice or Bob?

Feel free to post thoughts in the comments, though if you want to solve it without help you may want to avoid the comments. I'll post the answer next week.

## Sunday, July 10, 2016

### An infinite hat problem and later a point

Problem: There are an infinite number of people. They are labelled 1,2,3,... (I am not a number, I am a free man!) There is the Master who I call The Master. The Master will, at the same time, put a hat on each persons head. Some of the hats are RED, some are BLUE. (Clarification  added later- everyone can see all the peoples hat colors except their own.)

The people will then all, at the same time, yell out a hat color. (Clarification added later- NO other form of communicationis allowed.)

If  only a finite number of them get their own hat color wrong they win (not sure what they win, but they win!)

If an infinite number of them get their own had color wrong, then they lose.

They can discuss strategy ahead of time; however, The Master overhears all conversation.

Assume that the people and The Master are experts at this game.

Who would you bet to win? How much and at what odds?

I'll post the answer, a meta question about it, and another math question, on Thursday.

Feel free to post your answer as comments. If you do then please also comment on if you've seen the problem before since I'm curious (1) how well known the problem is, and (2) how hard it is to solve if you haven't seen it.

If you want to try to solve it yourself, don't look at the comments in case the right solution is there.

## Monday, July 04, 2016

### Is determining if a poly over a finite field is 1-1 hard? Sure seems so.

When I teach cryptography  to High School  students I begin with shift and linear  ciphers which are

x --> x+s mod 26 (s is a shift, x is a letter of the alphabet. Hmm- x really IS a letter of the alphabet!)

x--> ax+b mod 26 (Note that a has to be rel prime to 26.)

I then ask why nobody seems to have ever used

x --> ax2 + bx + c mod 26.

I then tell them that this is because there is no quick test that will, given (a,b,c), tell if
f(x) = ax2 + bx + c mod 26 is 1-1 (and hence onto).

It recently dawned on me that I don't really know that its hard to test.
(ADDED LATER) In fact its not true. Algebra shows that f(x) is NOT 1-1 iff

a(x+y)+b =0 mod 26

has a solution. If a is rel prime to 26 then clearly there is a solution (many in fact).
If a is not rel prime to 26 then I suspect this is not hard.

How hard is the following problem?

Given a poly f(x) of degree d, and n,  is f(x)  mod n 1-1?

We will assume all coefficients are between 0 and n.. We can also assume that c is 0 since f(x) is 1-1 then f(x)-c is 1-1.
The coefficients are  given in binary so the length of the input is roughly dlog(n).

One can of course compute f(0), f(1),...,f(n-1) and see if there are any repeats, but this takes O(n) steps which is exp in the input of length log n.

I suspect that this is either a well known solved problem (either in P or NPC) or a well known open problem. Any help or references will be more appreciated than usual-- see next paragraph.

I am the new SIGACT News Open Problems Column editor. In the future I will be soliciting people to write columns for me, but the first one I'll do myself and this might be a good topic- if its open! And if it is open, would be good to know references and what is known.