First, some data: Roughly 50% of authors I know have some presence on RG, but most of them do not maintain their site. In fact, I suspect many of them don’t know they are on RG since a page for author X seems to be automatically created when his co-author Y uploads a paper. Nobody I know of is actively using RG as a way to collaborate with other users by posting questions and answers, which seems to be a big part of the purported RG experience. But there are quite a few who upload their working and published papers.

Some RG features that make it different from other social networks are designed especially for academics types. There is for example the RG score. Academics are obsessed about ranking each other. One of the more difficult requirements for graduating in a top econ program is to memorize the publication records of all economists in the world, who got offers where, how much JETs are worth one ECMA and the historical record of these exchange rates. Well, students will have much easier life if Bill Gates and his fellow RG investors have their way: you will only be tested on a single score for each researcher, his RG score, “a metric that measures scientific reputation based on how all of your research is received by your peers.” I should say though that, at least in games and decision theory, it will probably take some time until the age of the RG score arrives. The current score is, not to put a too fine point on it, totally useless. There is a more or less universally agreed on ranking of scholars which is based on CVs and the offers they get. There is also a correct ranking based on the originality and quality of research. These two rankings are typically very different. The RG score is similar to neither.

If the score is the most useless feature of RG, the most annoying feature is the aggressive way in which they try to force you to update your site. First, their minions search the web for every old version of your papers, and once they find it they will suggest that you add it you your profile. I say `suggest’ but it’s not like you can refuse. You can choose between `yes’ and `maybe later’. And by `later’ they mean next time you log in. In the end you either surrender or accidentally click yes. Even worse is when they nag you to mind other people’s profiles. Here is for example what I get when I go to Janos’ page.

And here is what I go to Rakesh’s

Hey Ricky, just pick one, they are all nice :)

]]>After I corresponded with the editors of *Games and Economic Behavior* and *Journal of Mathematical Economics* and with the Economics Editor of Elsevier, the reason for the privacy breach became clear: the e-system allows each editor to choose whether the blinded comments of one referee to the author and the blinded comments of one referee to the editor will be seen by other reviewers. For each type of blinded comments the editor can decide whether to show it to all reviewers or not. Each editor makes his or her own choice. I guess that often editors are not aware of this option, and they do not know what was the choice that the previous editor, or the one before him, made.

Apparently, the configuration of *Games and Economic Behavior* was to allow reviewers to see only the blinded comments to the author, while the configuration of *Journal of Mathematical Economics* was to allow reviewers to see both types of blinded comments. Once the source of the problem became clear, Atsushi Kajii, the editor of *Journal of Mathematical Economics* decided to change the configuration, so that the blinded comments of reviewers to the editor will not be seen by other reviewers. I guess that in few days this change will become effective. Elsevier also promised to notify all of its journals, in which the configuration was like that of JME, about this privacy issue, and let the editors decide whether they want to keep this configuration or change it. In case this configuration remains, they will add a warning that warns the referee that the blinded comments can be read by other reviewers.

I am happy that the privacy breach came to a good end, and that in the future the e-system will keep the privacy the referees.

Regarding the second issue, Elsevier is not willing to change its user agreement. Reading the user agreements of other publishers, like Springer and INFORMS, shows that user agreements can be reasonable, and not all publishers keep the right to change the user agreement without notifying the users. The Economics Editor of Elsevier wrote: “This clause is not unreasonable as the user can choose to discontinue the services at any time.” As I already wrote in the previous post, I choose to discontinue the service.

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First, a definition: A *stationary process* is a sequence of random variables such that the joint distribution of is the same for all -s. More explicitly, suppose that the variables assume values in some finite set of *outcomes*. Stationarity means that for every , the probability is independent in . As usual, one can talk in the language of random variables or in the language of distributions, which we Bayesianists also call beliefs. A belief about the infinite future is stationary if it is the distribution of a stationary process.

Stationarity means that Bob, who starts observing the process at day , does not view this specific day as having any cosmic significance. When Alice arrives two weeks later at day and starts observing the process she has the same belief about her future as Bob had when he first arrives (Note that Bob’s view at day about what comes ahead might be different than Alice’s since he has learned something meanwhile, more on that later). In other words, each agent can denote by the first day in which they start observing the process, but there is nothing in the process itself that day corresponds to. In fact, when talking about stationary processes it will clear our thinking if we think of them as having infinite past and infinite future . We just happen to pop up at day .

The first example of a stationary process is an i.i.d. process, such as the outcomes of repeated tossing of a coin with hsome probability of success. If the probability of success is unknown then a Bayesian agent must have some prior about : The agent believes that is randomized according to and then the outcomes are i.i.d. conditioned on . A famous theorem of De-Finetti (wikipedia) characterizes all beliefs that are `mixtures of i.i.d.’ in this sense. All these beliefs are stationary.

Another example of stationary processes is Markov processes in their steady state. Again, we can generalize to situations in which the transition matrix is not known and one has some belief about it. Such situations are rather natural, but I don’t think there is a nice characterization of the processes that are mixtures of markov processes in this sense (that is, I don’t know of a De-Finetti Theorem for markov processes.) Still more general example is Markov process of some finite memory, for example when the outcome today depends on the history only through the outcomes of the last two days.

As an example of a stationary process which is not a Markov process of any finite memory consider a Hidden Markov model, according to which the outcome at every day is a function of an underlying, unobserved Markov process. If the hidden process is stationary then so is the observed process. This is an important property of stationary processes, which is obvious from the definition:

Theorem 1Let be a stationary process with values in some finite set . Then the process is stationary for every function .

As can be seen in all these examples, when one lives in a stationary environment then one has some (possibly degenerated) uncertainty about the parameters of the process. For example we have some uncertainty about the parameter of the coin or the markov chain or the hidden markov process. I still haven’t defined however what I mean by parameters of the process; What lurks behind is the ergodic decomposition theorem, which is an analogue of De-Finetti’s Theorem for stationary processes. I will talk about it in my next post. For now, let me say a word about the implications of uncertainty about parameters in economic modeling, which may account in part for the relative rareness of stationary processes in microeconomics (I will give another reason for that misfortune later):

Let Craig be a rational agent (=Bayesian expected utility maximizer) who lives in a stationary environment in which a coin is tossed every day. Craig has some uncertainty over the parameter of the coin, represented by a belief . At every day, before observing the outcome of the coin, Craig takes an action. Craig’s payoff at every day depends on the action he took, the outcome of the coin, and possibly some other random objects which follow a stationary process observed by Craig. We observe the sequence of Craig’s actions. This process is not generally a stationary process. The reason is that Craig’s actions are functions of his posterior beliefs about the parameter of the coin, and this posterior belief does not follow a stationary process: as time goes by, Craig learns the parameter of the coin. His behavior in day , when he doesn’t know the parameter is typically different from his behavior at day when he already has a good idea about the parameter.

I said earlier that in stationarity environment, the point in time which we denote by does not correspond to anything about the process itself but only reflect the point in time in which we start observing the process. In this example this is indeed the case with Craig, who starts observing the coin process at time . It is not true for us. Our subject matter is not the coin, but Craig. And time has a special meaning for Craig. Bottom line: Rational agent in a stationary environment will typically not behave in a stationary way.

To be continued…

]]>William Karush, who passed in 1997, had arrived at the same theorem many years earlier in his 1939 University of Chicago Masters Thesis (Kuhn-Tucker is 1951). When Kuhn learned of Karush’s contribution through a reading of Takayama’s book on Mathematical Economics. Upon doing so he wrote Karush:

In March I am talking at an AMS Symposium on “Nonlinear Programming – A Historical View.” Last summer I learned through reading Takayama’s Mathematical Economics of your 1939 Master’s Thesis and have obtained a copy. First, let me say that you have clear priority on the results known as the Kuhn–Tucker conditions (including the constraint qualification). I intend to set the record as straight as I can in my talk.

The missive closes with this paragraph:

Dick Cottle, who organized the session, has been told of my plans to rewrite history and says `you must be a saint’ not to complain about the absence of recognition. Al Tucker remembers you from RAND, wonders why you never called this to his attention and sends his best regards.

Karush’s reply, 6 days later, equally gracious:

Thank you for your most gracious letter. I appreciate your thoughtfulness in wanting to draw attention to my early work. If you ask why I did not bring up the matter of priority before, perhaps the answer lies in what is now happening – I am not only going to get credit for my work, but I am going to crowned a “saint”.

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**1) The e-system seems to be sometimes insecure.**

I was surprised when a referee with whom I consulted on the evaluation a paper (for GEB) told me that the system showed to him the private message that the other referee wrote to me, and that the same thing happened to him with JME. To prove his point, he sent to me screenshots with the private letter of the other referee for JME.

**2) The user agreement of Elsevier is a contract that one should never agree to sign.**

I guess no one bothered to read the user agreement of Elsevier. I did. The first paragraph binds us to the agreement:

This Registered User Agreement (“Agreement”) sets forth the terms and conditions governing the use of the Elsevier websites, online services and interactive applications (each, a “Service”) by registered users. By becoming a registered user, completing the online registration process and checking the box “I have read and understand the Registered User Agreement and agree to be bound by all of its terms” on the registration page, and using the Service, you agree to be bound by all of the terms and conditions of this Agreement.

The fourth paragraph, titled “changes” says that any change made to the contract is effective immediately, and so it binds you. If you want to make sure they did not add some paragraph to which you disagree, you must read the whole user agreement every time you use the system.

Elsevier reserves the right to update, revise, supplement and otherwise modify this Agreement from time to time. Any such changes will be effective immediately and incorporated into this Agreement. Registered users are encouraged to review the most current version of the Agreement on a periodic basis for changes. Your continued use of a Service following the posting of any changes constitutes your acceptance of those changes.

I contacted Elsevier about the user agreement and got the following response:

The Elsevier website terms and conditions (see http://www.elsevier.com/legal/elsevier-website-terms-and-conditions) cannot be customized upon request; however, these terms and conditions do not often change and notification would be provided via the “Last revised” date at the bottom of this page. The current terms and conditions were Last revised: 26 August 2010.

Well, it is comforting that they did not make any change in the past four years, but will Elsevier’s CEO agree to open an account in a bank that has the “change” paragraph in the contract?

I stopped using the e-system of Elsevier, both as a referee and as an editor.

]]>From Swansea comes another example of the inability to resist something that felt good on the tongue. A note from the head of Swansea University’s school of management to his colleagues (do they still have those at UK universities?):

]]>Some wags call for the removal of some or all of the school’s top management team. Yes, well don’t hold your breath. Or actually, do.

As far as I understood, the most common sights in the area are tourists and sea food. As far as I can tell, the main advantage of Roscoff is the Laboratoire Biologique, which is used to host conferences. Every now and then the French game theory group makes use of this facility and organizes a conference in this secluded place. The first week of July was one of these nows and thens. This is my third time to attend the Roscoff conference, and I enjoyed meeting colleagues, the talks, and the vegetarian food that all non-sea-food eaters got.

Here I will tell you about one of the talks by Roberto Cominetti.

Brouwer’s fixed point theorem states that every continuous function $f$ that is defined on a compact and convex subset $X$ of a Euclidean space has a fixed point. When the function $f$ is a contraction, that is, when there is $ρ ∈ [0,1)$ such that $d(f(x),f(y)) ≤ ρ d(x,y)$ for every $x,y \in X$, then Banach’s fixed point theorem tell us that there is a unique fixed point $x*$ and there is an algorithm to approximate it: choose an arbitrary point $x_0 ∈ X$ and define inductively $x_{k+1} = f(x_k)$. The sequence $(x_k)$ converges to $x*$ at an exponential rate.

When the function $f$ is non-expansive, that is, $d(f(x),f(y)) \leq d(x,y)$ for every $x,y \in X$, there may be more than a single fixed point (e.g., $f$ is the identity) and the sequence defined above need not converge to a fixed point (e.g., a rotation in the unit circle).

In his talk, Roberto talked about a procedure that does converge to a fixed point when $f$ is non-expansive. Let $(α_k)$ be a sequence of numbers in $(0,1)$. Choose $x_0 ∈ X$ in an arbitrary way and define inductively $x_{k+1} = α_{k+1} f(x_k) + (1-α_{k+1}) x_k$. Surprisingly enough, under this definition the distance $d(x_k,f(x_k))$ is bounded by

d(x_k,f(x_k)) ≤ C diameter(X) / \sqrt( α_1 (1-α_1) + α_2 (1-α_2) + … + α_n (1-α_n) ),

where C = 1/\sqrt(π).

In particular, if the denominator goes to infinity, which happens, for example, if the sequence $(α_k)$ is constant, then the sequence $(x_k)$ converges to a fixed point. Since the function that assigns to each two-player zero-sum strategic-form game its value is non-expansive, this result can become handy in various situations.

This is a good opportunity to thank the organizers of the conference, mainly Marc Quincampoix and Catherine Rainer, who made a great job in organizing the week.

]]>In the good old days, when men were men and sheep were nervous, prizes were awarded for accomplishing particular tasks. The French academy of sciences, for example, established in 1781, I think, a system of prizes or contests. A committee would set a goal (in 1766 it was to solve the 6 body problem, in 1818 it was explain the properties of light) and submissions judged after a deadline and a prize, if merited, awarded. One sees that today with the X -prize and the Clay prize. The puzzle with these prizes is would the challenge they highlight not be undertaken in their absence? For example, resolving P = NP has been around well before the Clay prize and many a bright young thing had already given it serious thought.

Many prizes are `achievement’ awards, given out in recognition of a great accomplishment after the fact. Some are awarded by learned societies and named in honor of an ancient worthy (Leibniz, Lagrange, Laplace etc.) Others are funded by private individuals (Nobel, Nemmers, Simons etc.).

Some learned societies have a surfeit of prizes (Mathematics) that are concentrated in the hands of a few. Indeed, one might be able to construct a partial order of the prizes and come to the conclusion that some prize X can only be awarded provided prize Y has already been secured. Once again, there is the incentive question. It is hard to imagine the prize winner strives and continues to do so in the anticipation of winning further prizes. If the purpose of the prize is to honor the work (rather than the individual) why give the $$’s to the individual? Perhaps better to take the $$’s, divide them up and hand it to junior researchers in the same area telling them they have received it in honor of X, a pioneer of the field.

Other learned societies have very few prizes (American Economic Association). There is the Clark medal (famous), Walker medal (discontinued after Nobel), Ely Lecture and the Distinguished Fellow (who?). No doubt, this is a great comfort for the members’ status anxiety. Although I have it heard it said that a paucity of awards can adversely affect a discipline in that it lessens its members chances of securing grants. No doubt this is why some learned societies have prizes for every age group and speciality one can imagine: best under 40 in applied nobble nozing theory.

Why do private individuals fund prizes? Nobel is the archetype. Is it a way to purchase reflected glory? The founders of Facebook and Google are famous in their own right, so it is hard to see how a prize will burnish their images. Perhaps they genuinely wish to support research into topic X. One can easily imagine more effective ways to do this via grants, fellowships and conferences. Indeed, both the Kavli and Simons do just this (in addition to handing out prizes). Perhaps its advertising. If one wishes to publicize the importance of some field, does awarding a generous prize buy more publicity than a simple advertisement or cultivating journalists? Unclear. How many have heard of the recent `breakthrough’ prizes?

]]>One (among many) remarkable talks was given by Roger Myerson on his 1983 paper entitled `Mechanism Design by an Informed Principal‘. Kudos to Thomas and Tymofiy for coming up with the idea of doing this. It brought to mind some couplets from Locksley Hall:

When the centuries behind me like a fruitful land reposed;

When I clung to all the present for the promise that it closed:When I dipt into the future far as human eye could see;

Saw the Vision of the world and all the wonder that would be.—

By the way, the last pair of lines appears on the dedication plaque that graces the USS Voyager (of the Star Trek franchise).

What did Roger do? He tried as best as possible, given the gulf of time, to explain why he had chosen the tack that he did in the paper (axiomatic) and his hope for how it would influence research on the subject.

A principal with private information must propose a mechanism to an agent. However, the choice of mechanism will reveal something of the principal’s private information to the agent. Thus, the problem of mechanism design in this setting is not a straight optimization problem. It is, at a high level, a signaling game. The signals are the set of mechanisms that the principal can propose. Thus, one seeks an equilibrium of this game. But which equilibrium?

In section 7 of the paper, Roger approaches the question axiomatically in the spirit of Nash bargaining. Indeed, Roger made just such an analogy in his talk. Nash did not have in mind any particular bargaining protocol, but a conviction that any reasonable protocol must satisfy some natural invariance conditions. Some decades later Rubinstein arrives with a bargaining protocol to justify Nash’s conviction. So, Roger sought the same here and expressed the wish to see this year a vindication of his hopes.

Lest you think the audience accepted Roger’s axioms uncritically, Thomas Troeger, pointed out Roger’s axiom 1 ruled out some possibly natural settings like Rothschild & Stiglitz. Roger argued that it was right and proper to rule this out and battle joined!

]]>Three main candidates survived until the final stage, Rivlin, Itzik, and Shitrit (in addition to two candidates who did not stand much chance). Election is done by a two-round system: Each of the 120 Parliament members secretly votes for a candidate. If no candidate gets more than 60 votes, then all candidates except the leading two leave the arena, and the Parliament members secretly vote to either one of the two leaders. The candidate who got more than 60 votes is the new proud president of the state.

Politics was ugly. Rivlin, who is a member of the largest party, was the leading candidate, but the Prime Minister, who comes from the very same party, was against him. Many members of the opposition voted for Rivlin. In the first round, Rivlin and Shitrit got the highest number of votes, but none of them had a majority of votes. In the second round, Rivlin won.

What I found interesting in this process is what one of the Parliament members of the second largest party said. He said that in the first round some members of his party voted for Shitrit, but then, in the second round, they voted for Rivlin. Why? “It was a tactical vote.” This way they ensured that the final election will be between Rivlin and Shitrit and *not *between Rivlin and Itzik. Politics is ugly, but at least as long as the election process does not satisfy Independence of Irrelevant Alternatives, we do not have dictatorship.

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