Archive for game theory

Covid’s game-of-life

Posted in Books, pictures, Travel, University life with tags , , , , , , , on May 7, 2020 by xi'an

A colleague from Paris Dauphine, Miquel Oliu-Barton made a proposal in Le Monde for an easing of quarantine that sounds somehow like Conway’s game of life. The notion is to define a partition of the country into geographical zones with green versus red labels, representing the absence versus presence of contagious individuals. With weekly updates depending on the observed cases or the absence thereof. While this is a nice construct that can be processed as a game theory problem, I am not so sure that it fits the specific dynamics of the coronavirus, which is not immediately detected while active, hence inducing a loss of efficiency in returning quickly enough to a red status. Not mentioning the unreliability and unavailability of tests at this scale. Or an open society (as opposed to China or Vietnam) where (a) people will resent local lockdown more than they do with global lockdown and (b) mostly operate outside the box for work or family interactions.

Le Monde puzzle [#1115]

Posted in Kids, R with tags , , , , , on October 28, 2019 by xi'an

A two-person game as Le weekly Monde current mathematical puzzle:

Two players Amaruq and Atiqtalik are in a game with n tokens where Amaruq chooses a number 1<A<10 and then Atiqtalik chooses a different 1<B<10, and then each in her turn takes either 1, A or B tokens out of the pile.The player taking the last token wins. If n=150, who between Amaruq and Atiqtalik win if both are acting in an optimal manner? Same question for n=210.

The run of a brute force R code like

B=rep(-1,200);B[1:9]=1
for (i in 10:200){
    v=matrix(-2,9,9)
    for (b in 2:9){
       for (a in (2:9)[-b+1])
       for (d in c(1,a,b)){
        e=i-d-c(1,a,b)
        if (max(!e)){v[a,b]=max(-1,v[a,b])}else{
         if (max(e)>0) v[a,b]=max(v[a,b],min(B[e[which(e>0)]]))}}
     B[i]=max(B[i],min(v[v[,b]>-2,b]))}

always produces 1’s in B, which means the first player wins no matter… I thus found out (from the published solution) that my interpretation of the game rules were wrong. The values A and B are fixed once for all and each player only has the choice between withdrawing 1, A, and B on her turn. With the following code showing that Amaruq looses both times.

B=rep(1,210)
for(b in(2:9))
 for(a in(2:9)[-b+1])
  for(i in(2:210)){
   be=-2
   for(d in c(1,a,b)){
    if (d==i){best=1}else{
      e=i-d-c(1,a,b)
      if (max(!e)){be=max(-1,be)}else{
       if (max(e)>0)be=max(be,min(B[e[which(e>0)]]))}}}
   B[i]=be}

Le Monde puzzle [#1085]

Posted in Books, Kids, R with tags , , , , , on February 18, 2019 by xi'an

A new Le Monde mathematical puzzle in the digit category:

Given 13 arbitrary relative integers chosen by Bo, Abigail can select any subset of them to be drifted by plus or minus one by Bo, repeatedly until Abigail reaches the largest possible number N of multiples of 5. What is the minimal possible value of N under the assumption that Bo tries to minimise it?

I got stuck on that one, as building a recursive functiion led me nowhere: the potential for infinite loop (add one, subtract one, add one, …) rather than memory issues forced me into a finite horizon for the R function, which then did not return anything substantial in a manageable time. Over the week and the swimming sessions, I thought of simplifying the steps, like (a) work modulo 5, (b) bias moves towards 1 or 4, away from 2 and 3, by keeping only one entry in 2 and 3, and all but one at 1 and 4, but could only produce five 0’s upon a sequence of attempts… With the intuition that only 3 entries should remain in the end, which was comforted by Le Monde solution the week after.

the incomprehensible challenge of poker

Posted in Statistics with tags , , , , , , , , on April 6, 2017 by xi'an

When reading in Nature about two deep learning algorithms winning at a version of poker within a few weeks of difference, I came back to my “usual” wonder about poker, as I cannot understand it as a game. (Although I can see the point, albeit dubious, in playing to win money.) And [definitely] correlatively do not understand the difficulty in building an AI that plays the game. [I know, I know nothing!]

round-table on Bayes[ian[ism]]

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , , , , , on March 7, 2017 by xi'an

In a [sort of] coincidence, shortly after writing my review on Le bayésianisme aujourd’hui, I got invited by the book editor, Isabelle Drouet, to take part in a round-table on Bayesianism in La Sorbonne. Which constituted the first seminar in the monthly series of the séminaire “Probabilités, Décision, Incertitude”. Invitation that I accepted and honoured by taking place in this public debate (if not dispute) on all [or most] things Bayes. Along with Paul Egré (CNRS, Institut Jean Nicod) and Pascal Pernot (CNRS, Laboratoire de chimie physique). And without a neuroscientist, who could not or would not attend.

While nothing earthshaking came out of the seminar, and certainly not from me!, it was interesting to hear of the perspectives of my philosophy+psychology and chemistry colleagues, the former explaining his path from classical to Bayesian testing—while mentioning trying to read the book Statistical rethinking reviewed a few months ago—and the later the difficulty to teach both colleagues and students the need for an assessment of uncertainty in measurements. And alluding to GUM, developed by the Bureau International des Poids et Mesures I visited last year. I tried to present my relativity viewpoints on the [relative] nature of the prior, to avoid the usual morass of debates on the nature and subjectivity of the prior, tried to explain Bayesian posteriors via ABC, mentioned examples from The Theorem that Would not Die, yet untranslated into French, and expressed reserves about the glorious future of Bayesian statistics as we know it. This seminar was fairly enjoyable, with none of the stress induced by the constraints of a radio-show. Just too bad it did not attract a wider audience!

le bayésianisme aujourd’hui [book review]

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , , , , , , , , , on March 4, 2017 by xi'an

It is quite rare to see a book published in French about Bayesian statistics and even rarer to find one that connects philosophy of science, foundations of probability, statistics, and applications in neurosciences and artificial intelligence. Le bayésianisme aujourd’hui (Bayesianism today) was edited by Isabelle Drouet, a Reader in Philosophy at La Sorbonne. And includes a chapter of mine on the basics of Bayesian inference (à la Bayesian Choice), written in French like the rest of the book.

The title of the book is rather surprising (to me) as I had never heard the term Bayesianism mentioned before. As shown by this link, the term apparently exists. (Even though I dislike the sound of it!) The notion is one of a probabilistic structure of knowledge and learning, à la Poincaré. As described in the beginning of the book. But I fear the arguments minimising the subjectivity of the Bayesian approach should not be advanced, following my new stance on the relativity of probabilistic statements, if only because they are defensive and open the path all too easily to counterarguments. Similarly, the argument according to which the “Big Data” era makesp the impact of the prior negligible and paradoxically justifies the use of Bayesian methods is limited to the case of little Big Data, i.e., when the observations are more or less iid with a limited number of parameters. Not when the number of parameters explodes. Another set of arguments that I find both more modern and compelling [for being modern is not necessarily a plus!] is the ease with which the Bayesian framework allows for integrative and cooperative learning. Along with its ultimate modularity, since each component of the learning mechanism can be extracted and replaced with an alternative. Continue reading

Le bayésianisme aujourd’hui

Posted in Books, Statistics with tags , , , , , , , on September 19, 2016 by xi'an

A few years ago, I was asked by Isabelle Drouet to contribute a chapter to a multi-disciplinary book on the Bayesian paradigm, book that is now soon to appear. In French. It has this rather ugly title of Bayesianism today. Not that I had hear of Bayesianism or bayésianime previously. There are chapters on the Bayesian notion(s) of probability, game theory, statistics, on applications, and on the (potentially) Bayesian structure of human intelligence. Most of it is thus outside statistics, but I will certainly read through it when I receive my copy.