Tag Archives: game theory

Signalling by encouraging good decisionmaking

Con artists pressure people into quick decisions. Marketing mentions that the offer is for a limited time only, so buy now, no time to read the small print. Date rapists try to get victims drunk or drugged. In all these cases, the goal is to prevent careful reasoning about what is happening and the decisions to be made. Also to prevent the victim from consulting others. Being pressured, confused or bullied while deciding is a danger sign, so one way for honest sellers to distinguish themselves is by encouraging good decisionmaking. Giving people time, referring them to neutral sources of info, asking them to think things over before deciding are all ways to make decisions more accurate.
More accurate decisions distinguish between good and bad deals better, which benefits honest sellers and harms con artists. This differential effect of information on good and bad types enables signalling by precision of information, where good types want to reveal as much as possible and bad types want to obfuscate. Information unravelling results – the best type has an incentive to reveal itself, then the second best type, then the third best etc. By not revealing, one is pooled with the average of the remaining types. In the end, the only type who does not strictly prefer to reveal itself is the worst type.

Raising grandchildren, not children

Currently in all species I know of, each generation raises its children, who in turn raise their children, etc. This can be described as an overlapping generations model where each generation lives 2 periods, receives resources from the old of the previous generation in its youth and transfers resources to the young of the next generation when old. There is another equilibrium: each generation raises its grandchildren, has its children raised by its parents, and the children in turn raise their grandchildren. Instead of transferring resources to the next generation and receiving them from the previous, transfer resources two generations forward and receive them from two generations back. There are an infinite number of such equilibria: for each n, transfer resources n generations forward and receive them from n generations back. There are of course practical problems with large n, because the organisms do not live long enough to meet their level-n offspring.

There are complaints in developed countries that childbirth is postponed in life to acquire education and start a career. A possible solution is transitioning to an equilibrium of taking care of grandchildren, together with having children at a young age so that the grandparents are still alive to see the teenage years of their grandchildren. However, the equilibrium transition from taking care of children to taking care of grandchildren means that one generation must raise both children and grandchildren. The equilibrium transition in the other direction is easy – one generation does not raise its children or grandchildren, because its children are raised by its parents and its grandchildren by its children. Any other equilibrium is less stable than the raising-children one, because it is difficult to transition to it and easy to transition away.

The equilibrium stability comparision is similar to the social security equilibria in overlapping generations. In one equilibrium, everyone saves for their own retirement and consumes their savings when old. In another, every generation when young pays the social security costs of the previous generation who is old at the same time. The transition from the saving equilibrium to the equilibrium of paying the previous generation is easy, because one generation gets its savings and the contribution from the young, while the young do not save and receive the contribution of the next generation. The reverse transition is difficult, because one generation does not get a contribution from the young in its old age, but has to finance the retirement of the previous generation when young.

Coordination game in choosing a university

The ranking of universities is very stable over time (http://m.chronicle.com/article/Rank-Delusions/189919) regardless of the difference in resources, scandals and other factors affecting popularity and quality. There are several positive feedback mechanisms keeping the rankings constant. These come from the multiple coordination games when choosing a university.
1) Smart and hardworking students want to be together with other smart and hard workers. If for some reason the best are in one location, then in the future all the best people have a motive to go to the same place. So the best arrive at that location and help attract other best people in the future. Similarly, party animals want to go to a university famous for its parties, and if many party animals come to a university, then it becomes famous for its parties.
Why would smart people want to be together with other intelligent folks? Just for interesting conversation, for useful contacts, collaboration. For these reasons, even the stupid may want to be together with the smart. Then an assortative matching results, as Gary Becker predicted for the marriage market (http://public.econ.duke.edu/~vjh3/e195S/readings/Becker_Assort_Mating.pdf).
2) Students want to go to a school with the best teaching staff, and the best professors want to teach the best students. I have yet to hear anyone wish for stupider students or teachers for themselves. Again the preference is the same among smarter and stupider students and professors, so assortative matching is a reasonable prediction.
3) The best professors want to be with other similar ones. Where there are such people, more will arrive.
4) Smarter graduates are likely to earn more and can donate more to the university. Then the university can hire better teaching staff, which in turn attracts better students, who donate more… The more talented also accumulate more power after graduating, in government institutions for example, which they can use (legally or not) to benefit their alma mater. Predicting this, again many people want to go there, and in the stiff competition the best get in.
5) If the employers believe that from some place, more intelligent people come than from elsewhere, then they are ready to make better offers to those coming from there. This makes the place attractive to all future employee candidates. Due to competition, the best get in, which justifies the belief of the employers.
6) Smarter people can be taught faster, at a pace that the stupider cannot keep. This mechanism gives everyone a motive to go to a school corresponding to their level.
7) Faster teaching means more knowledge during a standard length higher education, which the employers should value. The graduates of a school giving more knowledge are favoured, which makes the place attractive to everyone and leads to only the best getting in. The ability of the average student remains high, which enables faster teaching.

Sexual signals are similar to money

Ronald Fisher analyzed signalling in biology through traits that do not confer direct fitness advantage (higher survival or fecundity), but are desired by the opposite sex. This attraction is an equilibrium in a coordination game – if a potential mate has traits desired by the opposite sex, then the offspring with that mate are likely to have these traits as well and succeed in attracting the opposite sex. The traits confer a mating advantage, which is part of a fitness advantage, justifying the desirability of the traits.
It is a coordination game, because in a different equilibrium, traits without a direct fitness advantage are not desired. Then these traits do not give a mating advantage to the offspring and therefore do not have an indirect fitness advantage either. Then it is not fitness-enhancing to desire them. In summary, if a trait is expected to be desirable in the future, then it is desirable now, and if a trait is expected to be neutral or undesirable, then it is neutral or undesirable now.
Fiat money is inherently worthless, but in one equilibrium of the money game, has positive value in terms of other goods. If everyone expects that others will accept money in return for goods in the future, then it is useful to obtain money now. So everyone is happy to deliver goods in return for (a sufficient sum of) money now. The money game is a coordination game, because if everyone expects money not to be accepted in the future, then they do not give goods for money now. If money is expected to be worthless, then it is worthless, and if money is expected to be valuable, then it is valuable.
An overview of signalling in biology is at http://en.wikipedia.org/wiki/Signalling_theory and Fisher’s theory at http://en.wikipedia.org/wiki/Fisherian_runaway
The coordination game of money is studied by Kiyotaki and Wright (1989, 1993): http://www.jstor.org/stable/1832197 http://www.jstor.org/stable/2117496 and more simply explained in van der Lecq “Money, coordination and prices” https://books.google.com.au/books?id=r1r40SB0Wn8C&pg=PA29&lpg=PA29&dq=fiat+money+coordination&source=bl&ots=iI0M96m-qz&sig=lRHBAWIXYZs2V5S-iNFeH-2yar8&hl=et&sa=X&ei=d3lqVeneJ8TvmAX4vIGgDg&ved=0CEoQ6AEwBw#v=onepage&q=fiat%20money%20coordination&f=false

Eliminating for-profit academic publishing

Much has been written about the high profits academic publishers get from the volunteer labour of their referees and editors, and how high subscription costs reduce funds available for actual research. The opinion pieces and blog posts I have seen do not suggest a concrete way to change the system. They only express hope that with more researchers putting their work on the web, the for-profit publishing industry will eventually disappear. I think this disappearance can and should be hastened. The obvious way is to boycott for-profit journals as an author, referee, editor and librarian.
The obvious objection is that one’s career depends on publishing in certain journals that often happen to be for-profit, and that “service to the profession” (refereeing and editing) is one’s duty and also helps the career a bit. A moral counterargument is that while boycotting may impose some personal costs, it benefits other researchers and the increase in research benefits everyone, so as a favour to the rest of humanity, boycott is the right thing. After all, why do people become academic researchers when the private sector pays more?
Game theoretically, the academic system (including publishing) is a coordination game, like many social norms. As long as everyone else conforms to the system, it is costly to depart from it. Thus self-interested people choose to conform to the system. This keeps the system stable. Individual deviations are costly, but a collective (coalitional) deviation may be costless or at least cheaper. An example is the whole editorial board of a for-profit journal deciding to resign and start a nonprofit copy of this journal. They announce publicly that all articles that researchers were planning to submit to the for-profit journal should now be submitted to the nonprofit copy. The refereeing and editing process goes on as before, only the library subscriptions to the new journal are cheaper. There should be no loss of prestige for the editors or loss of publishing opportunity for the authors.
A journal is not complicated – it only requires an online system to let authors upload relatively small text files, let the editors forward these files (with author identity removed) to referees, referees to upload their text files and the editors to forward these (deidentified) files to authors. Such programs surely exist, free and open-source as well.
Perhaps a proofreader could be hired for the journal and paid out of subscription fees. But the total cost of running a journal (with volunteer labour like now) is very low.

Of rankings

Many universities advertise themselves as being among the top n in the world (or region, country etc). Many more than n in fact, for any n small enough (1000, 500, 100 etc). How can this be? There are many different rankings of universities, each university picks the ranking in which it is the highest and advertises that. So if there are 10 rankings, each with a different university as number one, then there are at least 10 universities claiming to be number one.
There are many reasonable ways to rank a scientist, a journal, a university or a department. For a scientist, one can count all research articles published, or only those in the last 10 or 5 years, or only those in the top 100 journals in the field, or any of the previous weighted by some measure of quality, etc. Quality can be the number of citations, or citations in the last 5 years or from papers in the top 50 journals or quality-weighted citations (for some measure of quality)…
What are the characteristics of a good ranking? Partly depends on what one cares about. If a fresh PhD student is looking for an advisor, it is good to have an influential person who can pull strings to get the student a job. Influence is positively related to total citations or quality-weighted publications, and older publications may be better known than newer. If a department is looking to hire a professor, they would like someone who is active in research, not resting on past glory. So the department looks at recent publications, not total lifetime ones. Or at least divides the number of publications by the number of years the author has been a researcher.
Partly the characteristics of a good ranking are objective. It is the quality-weighted publications that matter, not just total publications. Similarly for citations. Coauthored publications should matter less than solo-authored. The ranking should not be manipulable by splitting one’s paper into two or more, or merging several papers into one. It should not increase if two authors with solo papers agree to add each other as the author, or if two coauthors having two papers together agree to make both papers single-authored, one under each of their names. Therefore credit for coauthored papers should be split between authors so that the shares sum to one.
How to measure the quality of a publication? One never knows the true impact that a discovery will have over the infinite future. Only noisy signals about this can be observed. There currently is no better measure than the opinion of other scientists, but how to transform vague opinions into numerical rankings?  The process seems to start with peer review.
Peer review is not a zero-one thing that a journal either has or not. There are a continuum of quality levels of it, from the top journals with very stringent requirements to middle ones where the referees only partly read or understand the paper, to fake journals that claim to have peer review but really don’t. There have been plenty of experiments where someone has submitted a clearly wrong or joke article to (ostensibly peer-reviewed) journals and got it accepted. Even top journals are not perfect, as evidenced by corrigenda published by authors and critical comments on published articles by other researchers. Even fake journals are unlikely to accept a paper where every word is “blah” – it would make their lack of review obvious and reduce revenue from other authors.
The rankings (of journals, researchers, universities) I have seen distinguish peer-reviewed journals from other publications in a zero-one way, not acknowledging the shades of grey between lack of review and competent review.
How to measure the quality of peer-review in a journal? One could look at the ranking of the researchers who are the reviewers and editors, but then how to rank the researchers? One could look at the quality-weighted citations per year to papers in the journal, but then what is the q    uality of a citation?
Explicit measurement of the quality of peer-review is possible: each author submitting a paper is asked to introduce a hard-to-notice mistake into the paper deliberately, report that mistake to an independent database and the referees are asked to report all mistakes they find to the same database. The author can dispute claimed mistakes and some editor has to have final judgement. It is then easy to compare the quality of review across journals and reviewers by the fraction of introduced mistakes they find. This is the who-watches-the-watchmen situation studied in Rahman (2010) “But who will monitor the monitor?” (http://www.aeaweb.org/articles.php?doi=10.1257/aer.102.6.2767).
One could disregard the journal altogether and focus on quality-weighted citations of the papers, but there is useful information contained in the reputation of a journal. The question is measuring that reputation explicitly.
If there is no objective measure of paper quality (does the chemical process described in it work, the algorithm give a correct solution, the material have the claimed properties etc), then a ranking of papers must be based on people’s opinions. This is like voting. Each alternative to be voted on is a ranking of papers, or there may simply be voting for the best paper. Arrow’s impossibility theorem applies – it is not possible to establish an overall ranking of papers (that is Pareto efficient, independent of irrelevant alternatives, non-dictatorial) using people’s individual rankings.
Theorists have weakened independence of irrelevant alternatives (ranking of A and B does not depend on preferences about other options). If preferences are cardinal (utility values have meaning beyond their ordering), then some reformulations of Arrow’s criteria can be simultaneously satisfied and a cardinal ordering of papers may be derivable from individual orderings.
If the weight of a person’s vote on the ranking of papers or researchers depends on the rank this person or their papers get, then the preference aggregation becomes a fixed point problem even with truthful (nonstrategic) voting. (This is the website relevance ranking problem, addressed by Google’s PageRank and similar algorithms.) There may be multiple fixed points, i.e. multiple different rankings that weight the votes of individuals by their rank and derive their rank from everyone’s votes.
For example, A, B and C are voting on their ranking. Whoever is top-ranked by voting gets to be the dictator and determines everyone’s ranking. A, B, C would most prefer the ranking of themselves to be ABC, BCA and CAB respectively. Each of these rankings is a fixed point, because each person votes themselves as the dictator if they should become the dictator, and the dictator’s vote determines who becomes the dictator.
A fixed point may not exist: with voters A and B, if A thinks B should be the dictator and B thinks A should, and the dictator’s vote determines who becomes the dictator, then a contradiction results no matter whether A or B is the dictator.
If voting is strategic and more votes for you gives a greater weight to your vote, then the situation is the one studied in Acemoglu, Egorov, Sonin (2012) “Dynamics and stability of constitutions, coalitions, and clubs.” (http://www.aeaweb.org/articles.php?f=s&doi=10.1257/aer.102.4.1446). Again, multiple fixed points are possible, depending on the starting state.
Suppose now that the weights of votes are fixed in advance (they are not a fixed point of the voting process). An objective signal that ranks some alternatives, but not all, does not change the problem coming from Arrow’s impossibility theorem. An objective signal that gives some noisy information about the rank or quality of each alternative can be used to prevent strategic manipulation in voting, but does not change the outcome under truthful voting much (outcome is probably continuous in the amount of noise).