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You may have heard about ResearchGate, the so called facebook of scientists. Yes, another social network. Its structure is actually more similar to twitter: each user is a node and you can create directed edges from yourself to other users. Since I finally got rid of my facebook account (I am a Bellwether. In five years all the cool guys will not be on facebook), I decided to try ResearchGate. I wanted a stable platform to upload my preferable versions of my papers so that they will be the first to pop up on google. Also, I figured if I am returning to blogging then I need stuff to bitch about. ResearchGate only partially fulfill the first goal, but it does pretty well with the second.

Last week I wrote a post about two issues with Elsevier’s e-system, which is the system that all journals run by Elsevier, including *Games and Economic Behavior* and *Journal of Mathematical Economics*, use for handling submissions: the fact that sometimes reviewers can see the blinded comments that other reviewers wrote to the editor, and the user agreement that allows Elsevier to change its terms without notifying the users.

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.

When I give a presentation about expert testing there is often a moment in which it dawns for the first time on somebody in the audience that I am not assuming that the processes are stationary or i.i.d. This is understandable. In most modeling sciences and in statistics stationarity is a natural assumption about a stochastic process and is often made without stating. In fact most processes one comes around are stationary or some derivation of a stationary process (think the white noise, or i.i.d. sampling, or markov chains in their steady state). On the other hand, most game theorists and micro-economists who work with uncertainty don’t know what is a stationary process even if they have heard the word (This is a time for you to pause and ask yourself if you know what’s stationary process). So a couple of introductory words about stationary processes is a good starting point to promote my paper with Nabil

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 .

*Games and Economic Behavior*, *Journal of Economic Theory*, *Journal of Mathematical Economics*, and *Economics Letters* are four journals that publish game theoretic papers and are published by Elsevier. They all use Elsevier e-system to handle submissions. I already talked in the past about the difficulty of operating these e-systems. Rakesh discussed the boycott against Elsevier. Recently I had some experience that made me stop using the Elsevier’s system altogether, even though I serve on the editorial board of *Games and Economic Behavior*. I will not use Émile Zola’s everlasting words for such an earthly matter; I will simply tell my experience.

**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.

Roscoff is a village at the north-west corner of France, located on a small piece of land that protrudes into the English canal. Right here, in 1548, the six-year-old Mary, Queen of Scots, having been betrothed to the Dauphin François, disembarks.

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.

Its not: why haven’t I one won? I have. A sixth form science prize. In my salad days I would day dream about winning the big one (to the sound of Freddy Mercury crooning `We Are The Champions’). But, one ages and comes to term with one’s mediocrity.

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?

I had the opportunity to participate in a delightful workshop on mechanism design and the informed principal organized by Thomas Troeger and Tymofiy Mylovavnov. The setting was a charming `schloss‘ (manse rather than castle) an hour and half outside of Mannheim. They had gathered together a murderer’s row of speakers and auditors. Suffice it to say I was the infimum of the group and lucky to be there.

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!

Yesterday the Israeli Parliament elected the state’s new president. This position is mostly ceremonial, and does not carry any significant duty. Nevertheless, quite a few people, mostly current and past Parliament members, wanted to get this job. The race was fruitful, as a couple of them were forced to withdraw their candidacy after secrets of weird sex stories and bribes were published in the press.

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.

Abraham Neyman had numerous contributions to game theory. He extended the analysis of the Shapley value in coalitional games with player set which is a measurable space, he proved the existence of the uniform value in stochastic games, and he developed the study of repeated games with boundedly rational players, among others. Abraham Neyman was also one of the founding fathers of the Center for Game Theory at the State University of New York at Stony Brook, which hosts the annual conference of the community for the past 25 years.

The *International Journal of Game Theory* will honor Abraham Neyman on his 66th birthday, which will take place in 2015, by a special issue, see the announcement here. Everyone is encouraged to submit a paper.

This post is dedicated to a new and important result in game theory – the refutation of Mertens’ conjecture by Bruno Zilliotto. **Stochastic games** were defined by Shapley (1953). Such a game is given by

- a set Z of
**states**, - a set N = {1,2,…,n} of
**players**, - for every state z and every player i a set A_i(z) of
**actions**available to player i at state z. Denote by Λ = { (z,(a_i)_{i ∈ N}) : a_i ∈ A_i(z) for every i} the set of all pairs (state, action profile at that state). - for every player i, a
**stage payoff function**u_i : Λ → R, and - a
**transition function**q : Λ → Δ(Z), where Δ(Z) is the set of probability distributions over Z.

The game starts at an initial state z^1 ∈ Z and is played as follows. At every stage t, each player i chooses an action a_i^t ∈ A_i(z^t), receives a stage payoff u_i(a_1^t,…,a_n^t), and the play moves to a new state, z^{t+1}, that is chosen according to q(z^t;a_1^t,…,a_n^t).

In this post I assume that all sets are finite. The N-stage game is a finite game, and therefore by backwards induction it has an equilibrium. As I mentioned in my previous post, the discounted game has an equilibrium (even a stationary equilibrium) because of continuity-compactness arguments.

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