In a recent post (Why Italy? Why Spain? And why the EFSF’s size does not matter), I concluded with a question that readers keep asking: “If what you are saying is right, why are Europe’s leaders so committed to the current structure of the EFSF?” More generally, the world has been watching Europeans blundering incessantly from one spectacular failure to the next and increasingly wonders whether their actions are a manifestation of irrationality or some sinister plan. In that post’s closing paragraph I suggested that there is a third explanation: Europe’s commitment to the awful EFSF, and other such disastrous policies, reflects a most peculiar form of rational idiocy. Today I shall lay bare this explanation by means of four telling illustrations: The Penny Pincher’s Conundrum, The Underbidder’s Nightmare, The Speculator’s Delight, and, lastly, The Eurozone’s Dilemma.

The Penny Pincher’s Conundrum

Imagine we place ten shiny gold sovereigns on a table (since gold is all the rage these days) and invite Angela and Bill to take turns to collect either one or two coins at a time. We tell them that if, at any visit to the table, one of them collects two coins, the game ends and the remaining coins are lost to both. But as long as each collects a single coin, they can keep coming back till all coins are collected.

[We assume that all that Angela and Bill care about is the number of coins that they receive individually, and that no enforceable agreement for sharing the coins ex post is possible.]

What should Angela do if we give her the chance to step up to the table first? Should she take a single coin, thus giving Bill a chance to play too, or take the two of the ten coins and kill the game there and then (thus causing the loss of eight gold sovereigns to both)?

Clearly, the rational outcome would be to collect one coin at the first visit, let Bill do the same at his first visit and keep doing this so that, between them, they do not let a single gold coin go to waste. Alas, this is not what will happen if they allow themselves to think in the manner that economists define as ‘rational’. Why not?

If Angela is smart, she will work out from the outset that, if the game keeps going until only two coins are left on the table (and each one of them has pocketed four), it will be her turn to play and, at that point, she will not be able to resist taking both. But if she respects Bill’s intelligence, she will know that he will have worked out this conclusion too. So, she will quickly conclude that, just before that stage is reached, when there are three coins on the table, and it is Bill’s turn to play, Bill will predict that if he takes only one coin she will then collect two and, therefore, Bill must defend his interests by collecting two coins himself, while he still has a chance.

[The adjacent figure helps follow her logic’s twists and turns. It generalises to the case where, at the beginning, there are G golden sovereigns on the table. If Angela, who plays first, takes two coins, she follows the vertical arrow downwards. The first number of coins then represents the payoff of the player who took two coins and the second the other player’s tally. Similarly at every stage of the game. Clearly, if they reach the end by taking one coin each, each ends up with G/2 coins.]

Smart Angela, therefore, ‘knows’ that if they reach the stage when there are three coins on the table, she will collect none of them (since Bill will pick up two). With this thought in mind, she will ensure that when it is her turn to play with four coins on the table, she must collect two. Then again she knows that Bill will also work this out and thus becomes convinced that he will kill the game (by collecting two coins) before they reach that stage; when he gets to choose with 5 coins on the table. And so on and so forth.

To cut a long story short, Angela has just worked out that Bill will have an incentive (courtesy of his predictions of what she thinks he will do) to pick up two coins whenever he gets a chance; even right after at the game’s beginning. So, Angela predicts that if, at the very beginning, she takes a single coin, he will take two immediately after and the game will end with her having only one gold sovereign. With this firm conclusion in her mind, one that was worked out with superb reasoning and foresight, she steps up to the table and collects two coins on her first visit. Too bad that eight sparkling gold sovereigns have gone to waste…

The story’s moral: Rational choices and infinite strategic foresight offer no defence against collective and individual idiocy. A penny-pincher may end up with pennies in her pursuit of penny maximisation when much greater riches are available. In contrast, a capacity to think in terms of the collective interest would, ironically, serve the decision maker’s private interest much, much better.

The Underbidder’s Nightmare

Angela and Bill now play a new game. We put €100 in a box and allow them to bid for it incrementally (in steps of €1 at a time) but under the following rules: The highest bid wins the box (and its contents) but both the highest and the second highest bids are paid in full. For example, if the bidding ended with Bill offering €60 and Angela €30, Bill wins the €100 but Angela must also pay us €30 as a participant’s fee. It is not hard to see that:

(A) It is always rational to enter the game by making a bid

(B) If both make a bid, the bidding process will continue until both are ruined.

The first conclusion, (A), is quite straightforward: €100 is on offer and, if one’s opponent does not bid, it makes huge sense to bid €1 to get the €100. Beyond that, if the other has made the first move, and bid €1, it makes sense to offer €2.

The second conclusion, (B), seems less self-evident but is equally simple to arrive at logically: The moment one has made any bid, one has a cast iron incentive to bid above the other. Suppose, for instance, that Angela’s €X is surpassed by a €(X+1) bid by Bill. Since she must pay her bid even if she loses the auction, she is better off bidding €(X+2). Why? Because €[100-(X+2)] always exceeds -€(X+2). But note that this is true even if X exceeds €100 by any number! That is, this auction will never end. Both players will be outbidding each other, resembling supremely rational idiots with a penchant for bankruptcy. When will this auction end? Only when one of them hits the buffers of her or his budget constraint. Or when, alas, they start wondering whether their type of rationality needs to be scrutinised…

The story’s moral: It is perfectly possible for policy makers to find themselves in a dynamic situation which compels one constantly to throw good money after bad in pursuit of an impossible objective, with the result that everyone is a loser. When caught in such a dynamic spider’s web, e.g. the EFSF’s dynamic as depicted here, the only rational thing to do is to stop. But then again it takes considerable leadership qualities to subject one’s own rationality to some higher-order scrutiny and lead the Union out of the cul-de-sac.

The Speculator’s Delight

Speculators like nothing more than an official non-credible commitment. Here is the simplest possible depiction of such a feeble assurance.

Speculator attacks Officials resist



Speculator attacks Officials capitulate



Speculator desists



Spec’s pref. order Officials’ pref. order

The idea here is that the speculator will not attack if she has reason to expect that officials will resist (nb. an attack followed by resistance yields the speculator’s third outcome, i.e. corresponds to her least preferred outcome). This may lead foolish officials (e.g. the former Greek Finance Minister, Mr G. Papakonstantinou; recall his threats to speculators that they would “lose their shirts” if they bet against Greek bonds) to threaten speculators with reprisals if they dare challenge them. Why foolish? Because, at least in this case, these threats cannot and will not be taken seriously. And why is that? Because speculators can see that, if they attack, the officials will be forced to choose between an action that yields their second best outcome (capitulation) and another action that yields their third best (i.e. their worst) outcome (resistance). Which action will officials choose? Capitulation of course, just as Europe’s leaders have been doing for the past eighteen months.

Then again, one may argue, quite plausibly, that things change when this ‘game’ between officials and speculators is repeated again and again. That then it may well make sense for officials to resist for a number of periods so as to signal to speculators that they can expect a bloody nose every time they challenge them. In this sense, the short or medium term cost of resisting speculative attacks (i.e. the cost to officials of opting repeatedly for their third, rather than their second, preferred outcome) can be seen as an investment in a reputation that will keep speculators at bay.

This may well be so. Except, to work as a proper deterrent against speculation, it must be commonly known that the officials’ planning horizon is indefinite. That it stretches well into the future. Alas, this is hardly ever true. For we all know that Mrs Merkel’s and Mr Sarkozy’s planning horizon barely stretches to the next local or national election. And since their horizon is known to be definite, even fixed, something like the rational idiocy of the Penny Pincher’s Conundrum applies: Speculators work out that, at some point in the not too distant future (determined by the electoral cycle), the officials will capitulate (just like Angela, in that game, predicts that Bill will collect, sooner or later, two as opposed to one gold sovereigns). Then, by the logic that led Angela to take two coins immediately (see The Penny Pincher’s Conundrum above), speculators predict that the officials’ resolve to take the long view will melt down instantly.

The story’s moral: Speculators can be kept at bay only when officials are not constrained by a finite horizon. Or when the game is changed so that officials’ defensive moves cost them less than capitulation. In Europe, tragically, neither applies. The short term cost of capitulation is lower than the short term cost of resistance while the officials’ horizon coincides with the core countries’ next election.

The Eurozone’s Dilemma

Suppose I am right in my conviction that implementation of The Modest Proposal would end the crisis here and now. Is it possible that, e.g., Mrs Merkel knows this and still chooses, rationally, to resist such a systemic solution? Yes, is my answer.

Suppose, for argument’s sake, that Mrs Merkel agrees with us that a combination of (A) ECB-issued eurobonds that allow for the transfer of the Maastricht compliant debt to the Centre, and (B) bank recapitalisation would resolve the euro crisis. But let us also suppose that she takes it for granted that the bankers will be allowed to make their own decisions on whether they want to draw upon EFSF funds to effect the said recapitalisation (at the expense of equity that will dilute their own holdings). Then it is very possible that we have the following strategic interaction:

Banks recapitalise Banks do not recapitalise
ECB-bonds + tranche transfer



Current EFSFbased policy



Europe’s leadership chooses its policy from the two rows whereas the bankers choose from the two columns. The numbers in the table correspond to the ranking of the outcomes of European officials, the first number, and of the bankers, the second number.

The assumption here, which one may of course contest, is that European leaders, with Mrs Merkel first and foremost among them, understand that maintaining the current strategy of EFSF loans for the ‘fallen’ states (let’s call this the EFSF strategy) will lead to their third-best outcome if bankers continue to refuse recapitalisation – notice the bottom right cell in which Europe’s leaders end up with their third best outcome and the bankers with their second best. In contrast, if Europe’s leaders were to go ahead and authorise the ECB to issue its own bonds, while the banks recapitalised, our leaders get their second best and bankers their third best outcome.

As for the worst outcomes possible, for the core countries’ politicians it is that they go ahead with ECB-bonds (and a transfer of the eurozone’s Maastricht compliant debt to the ECB) only to discover that the bankers refused to recapitalise their banks (since that would effect debt unification without stemming the banking crisis that started the whole disaster). And the worst outcome of bankers is that they recapitalise (i.e. lose much of their control over the banks) when Europe is sticking to the toxic EFSF (thus ensuring the crisis’ continuation).

Lastly, the best outcomes are exactly the opposite: For surplus country politicians, it is that the bankers recapitalise without the ECB taking the decisive step toward sovereign debt unification. And for bankers the best outcome is that the ECB unifies the debt, via the issuing of its own eurobonds, without themselves having to recapitalise their banks – notice that in the off-diagonal cells, one ‘player’ gets her least preferred outcome (number 4) while the other gets her most preferred outcome (number 1).

With all these assumptions in place, it is easy to see how instrumental thinking leads both politicians and bankers to a disastrous outcome: Rationally! Let’s start with the banks. If they predict that Europe will adopt the Modest Proposal’s ECB-issued eurobond policy (i.e. the first row), they know that they will get their third best if they recapitalise and their first best if they do not. Also, if they expect that Europe will stick to the toxic EFSF (i.e. that they will be constrained within the second row), bankers know that to recapitalise will yield their fourth-best and not to recapitalise their second best outcome. In short, whether they expect Europe to go ahead with ECB-bonds and the unification of the Maastricht compliant debt, bankers will not recapitalise. Period!

Let us now look at things from the perspective of core, or surplus, country politicians; e.g. Mrs Merkel. She knows, by perusing the table, that if the banks recapitalise, her best option requires that she does not authorise the ECB to issue bonds and unify the Maastricht compliant part of the eurozone’s debt (observe that her number 1 preference lies in the bottom left cell). And if banks are to choose not to recapitalise, ECB-bonds and Maastricht compliant debt unification gives her her worst possible outcome (notice that the top right cell contains her nightmare: preference no. 4). In brief, whatever she expects the bankers to do, to recapitalise or not to recapitalise, Mrs Merkel is  best off by sticking to the catastrophic EFSF…

The story’s moral: As suggested in my previous post’s conclusion, it is possible that surplus countries’ politicians are choosing an allegiance to the EFSF and related policies even if they know that this commitment is tantamount to a poor, even a catastrophic, choice. In this illustration we saw how a particularly narrow way of thinking rationally, what philosophers refer to as ‘instrumental rationality’, leads to an outcome that is, at once, (a) terrible for Europe’s politicians and (b) impossible for their logic to escape.

Overall moral

The difference between good and bad leadership boils down to a capacity to transcend the penny pincher’s logic. True leaders know how not to undermine their own interest by learning to resist the temptation presented by the prospect of small net political gains. Inspired politicians know not only how to manoeuvre skilfully within a game’s rules but, primarily, how to re-write the rules. Unfortunately, Europe’s politicians are proving a breed that has risen through the hierarchy of their parties and parliaments by adapting themselves brilliantly to the existing games, utterly incapable of transcending either instrumental thinking or the game  itself. While things were going swimmingly, prior to 2008, this narrow-minded, instrumental, rationality sufficed. After the Crash of 2008 it no longer does.


For the purposes of this post I had to delve into my game theoretical past. Masochistic readers who want to read more on game theory, its uses and abuses, may benefot from a book I published in 2004 by Routledge (jointly with Shaun Hargreaves Heap) entitled: GAME THEORY: A critical text.













  • Great post..my compliments on your disciplined approach and tireless effort to forge ahead with your analysis and proposals

  • Hi.

    I enjoyed that post.

    Everything interacts and everything flows.

    At least two interacting points are required for energy flow and each and everyone of these has two opposites. So there are always four(4) possible choices.
    When there is harmonic interaction ,there always exist one(1) option amongst four(4) ,that is a win-win situation.

    What the above tells me is that the systems created for “social” organisation ,the political and financial systems ,are contradicting themselves in a way that there can never be a win-win situation.

    Let us suppose that it is so. Then the only remaining element(s) that can decide for energy to flow (situations to be created and directed) ,exist only outside of the systems. This then renders the systems obsolete ,for the decisive elements can be uncontrollable and therefore corrupted. So ,representatives of the people represent themselves only. The same with bankers.

    Even if the systems were/are perfect or near perfect ,then there would still be the fear of corruption if the complexity of them would surpass everyday understanding.

    In final analysis we have reached a point ,where it doesn’t matter who is bad or good ,righteous or corrupted. For this to have an end ,interactions must become simpler and immediate.

    Life is not a system. Life is a method.
    Life is not closed in a box. We “imprison” ourselves in a “system”.

    Once more i will state my opinion that there never was ,is and will be a perfect solution or one political ideology or economic system that can superimpose all life.

    No more socialism ,communism ,capitalism or whatever. The ideologies never were the problem. Our choice to be absolute was and still is.

    Choose nothing ,be everything.

    Easy to say ,hard to do.

  • Without reading all of the above there are two critical flaws and a minor one:

    (1) The game needs to be within legal boundaries. This is anything but clear
    (2) The whole “Eurobond” hype is based on the assumption that nothing else will change. This is like introducing socialism in Singapore and believing that the GDP will remain at record highs. Why should I continue to work so dead people can get a pension in Greece?
    (3) There are more players, some of them might be irrational

    • @ Knut34
      “Why should I continue to work so dead people can get a pension in Greece?”

      Because you never paid for the dead of the WW-2 and for the ruins you left behind.

      Sorry Mr Varoufakis

    • Did the Greeks pay the Helots anything yet?

      I assume that Greek modern day, lazy corrupt and lying society would have made ruins out of whatever existed prior to WW2 in Greece anyways…

      The only thing that Greece does is ask for money since it joined the EU. Sorry, I forgot number fudging, lying etc.

      You have had your chance to get on your feet for 20 years. Why don´t you start a union with Uganda or some other African country.

    • Dear Knut,

      As you know, I have been extremely liberal in welcoming and posting each and every comment of yours on this blog. Dissent and disagreement are the spice of life and the fuel of better thinking. Insults that border on the outright racist are not. Over the last few days, permit me to say, your comments have been on a slippery slope. Calling a whole people names (corrupt, lazy etc.), without any qualification, is something that the German nation has learned to avoid – the hard way. You seem to have been one of the minority of Germans who have steadfastly refused to appreciate the importance of not generalising. This is the last time I post a comment of yours that is demonstrably offensive. The reason for stepping in is simple: If 1929 has taught us something, it is that the first victim of a massive global debt crisis (like that we have been experiencing since 2008) is the common currency of the time (the Gold Standard then the euro-as-it-was-designed now). Soon after the ammasing discontent turns one people against another (the Germans against the Greeks, the Greeks against the Germans – then the Germans against the Germans and the Greeks against the Greeks etc.). Last time we went through a crisis of that magnitude, the forces of evil, utilising language identical to yours, immersed humanity into a deadly, catastrophic mire. I strongly advise you to desist. And if you insist on this type of narrative, I invite you to use some other forum. This one is, from now on, closed to biggoted language while remaining forever open to reasoned debate.

    Winner is: Game theory REENGINEERED-Leaders Stick Head in Bush and JUST HOPE!!
    Like running a car in darkness without HEADLAMPS will ultimately lead to DISASTER
    and possible DEATH-now implicating Economic Eurozone DEFAULT and also their own
    personal DEFAULT as STATESMANS voting HELL instead of seeing themselfs as
    HEROES coming back with NEW INSIGHTS.BIG LEADERS must posses inherent
    ability to fully assimilate STATE OF AFFAIRS in MAKRO VIEW like END OF COLD WAR
    Russian Leader Gorbatjov and others before him.
    Pledging in favour of MODEST PROPOSAL TODAY MR GEORGE SOROS HEDGE FUND MANAGER of WORLD rang. This might be of critical importance to CHANGE MINDSET to EUROPEAN LEADERS in direction of REASON not just continue a LOSING GAME ending in ABYSS for them all!!


  • Doubts on the Penny Pincher’s Conundrum

    Fascinating game-article and astonishing conclusions as usual. There’s one thing I do not fully comprehend though, regarding ‘Penny Pincher’s Conundrum’.

    Let us call the assumption that ‘all that Angela and Bill care about is the number of coins that they receive individually’ Axiom 1.

    [A] If greed is out of the way, maximum profits are 5 – 5, independently of who plays first.

    [B] If greed gets in the way (which is the most probable scenario) then:

    [B1] if first player is set from the beginning and Axiom 1 stands, Angela will have to play first and they both will have to play until Angela gets 6 and Bill gets 4, which are their expected maximum (if they are instrumentally rational I assume that they will control their greed until it becomes profitable).

    [B2] if the first player has the necessary degree of freedom to choose to ‘pass’, expecting that his opponent will draw first, then either they will both wait indefinitely for the other to open the game (and end up without any gain) or one of them will begin and the game will follow the above-mentioned path.

    To conclude, I only see 3 alternatives: 5-5, 6-4 and 0-0. I think your conclusion is in contrast with Axiom 1.

    Where do I go wrong ?

  • Nice analysis!

    In “The Eurozone’s Dilemma” description , the apyoff matrix is the key for analysis and
    outcome concluded.

    If the payoff matrix was as follows : Banks recapitalise Banks do not recapitalise

    ECB-bonds + tranche transfer 1,1 1,0

    Current EFSFbased policy 0,1 0,0

    Then the (1,1 ) section is Nash Equilibrium , hence a solution
    (1,0) or (0,1) means repetion and (0,0) no solution

    • If 7 poor and 3 rich people sit around the table and they have a vote whether to introduce socialism, the vote will be 7:3 in favor of socialism. 5 years later you will have 10 poor people sitting at the table…

  • “while remaining forever open to reasoned debate”

    An interesting “debate” with a group of people that all agree to take away money from another group of people. I am not so sure, if that is the foundation to find sustainable solutions.

    I want to thank many of you for upsetting me with your posts that call for a breach of existing contracts, laws and some constitutions on top contradict the capitalist principles our economy is based upon. It gave me a lot of energy: I used it in optimizing my revenues streams that I lowered my taxes significantly (remember: why should I pay for this?), I supported a neighbor kid to set up a small business selling anti EU merchandise online and I joined, consult and financially support a nationalist right wing party.

    Maybe your socialist dream of common debt and transfers will come true (for a while). To sustain it, you will need to build a wall around Europe or accept wealth & brain drain.

    The EU has many parallels with what happened from 1930 to 1933: (1) A law (March 24th 1933) was passed to bascially get rid of the Weimar Republic and (2) Austerity program was forced on people, due to constraints set from other countries (until 1932).

    (1) a combination of the Lisbon Treaty & the bailouts without parliament control
    (2) already seen in GR, PT, ES, IT, IE


    • @Knut34
      What prof. Varoufakis is trying to say from the beginning of this crisis is that this is not just a Greek problem but a European one. I can go even further and say that this is not a European crisis but a global crisis of the current economic system. Please do take under consideration that for every real dollar or euro that is produced around the world there are 14 dollars or euros of virtual money that are wandering around the globe waiting for a chance to make easy profit for the, so called, “investors”. This means that for every cent that we earn working and producing there are 14 cents of HOT AIR which produce profits to people who are not working to earn them. In the real economy of our life this means that we must work more and be paid less so that the “investors” are getting more and more out of our pockets. This economic system that we have is greedy, inhumane and immoral. This is not the first time that economic Globalization is happening in the world. I have to remind you that at the beginning of the 20th century the situation was more or less the same as now. Then the political elites of the time were unable to understand what was coming, both liberals and the socialists were living their myth of the end of the wars. The end of this historical period found Europe destroyed twice from wars. What I am trying to say is that as long as the stock markets or the banks are free to do whatever they want, capitalizing their profits and socializing their losses, not respecting any moral codes or values, that our societies have developed over the years, then the economic crisis will go deeper and deeper. At the end of this slippery path there is the nightmare of nationalism and of course war. And everyone must have in mind that capitalism has one certain and very effective way of dealing with crisis and this is war. Taking under consideration that both EU and USA are losing their power and at the same time new economic powers – such as China, India and Brazil become stronger – which means that EU and USA are going to have less opportunities to export their problems to other places on earth, not that this is acceptable or a solution but this is what was happening until now, I am horrified of the thought of what is going to happen in Europe if we tolerate stereotypes of the lazy and corrupted south and the decent hard-working north. You are right about our tax collecting system. And we have a lot of problems here in Greece with our public domain and corruption. No excuse for us and this is something that we must deal with it asap. But you also say that it was rightfully so for Greece to have interest of 10-15% before Euro. May I ask a simple question, why; Do you think that Greece was a risk for the investors; Well if you think so you are wrong. Greece until now paid every single cent that we borrowed and no investor ever lost from us even though we declared default 4 times in our history. Actually I think we are the only country in the world that recognized loans that had to be erased after default. So not only we paid until now all our debts but we paid them with a 10-15% rate of interest. As a matter of fact until 1940 the greek people received 600 of units for every 1000 units that we borrowed. The rest was kept by the “investors” as a warranty. Interestingly we had to pay also the warranty that was already kept. The price for our independency was that Greece remained dependent to our lenders . And since you mentioned your solid finance perhaps you should recalculate your finances after you take under consideration a modest figure of about 162 billion (no interest is included so you can do the maths even with a small rate of 3-4%) Euros that Germany has to give to Greece for War Compensation. No interest is included so I am leaving it up to you to do the calculation with a reasonable figure of 3-4 %. This amount of money represents 108 billion Euros as reparation of the destroyed economic infrastructure and the general damages created by the German army and 54 billion Euros for the forced loan that Greece took on behalf of the Nazi government . The 108 billion Euros was decided by International Peace Conference in Paris. As for the loan until now not even one German government denied it, but they deny to pay it. As you see being robbed by others is something that bothers me too. And this is the way I, as a Greek, feel when I think that Germany denied any compensation to Greece since the end of WWII. What was the explication that the German politicians gave to us for this denial; None. Is it fair, correct or moral ; No. Does the German people have any responsibility about this; No. And you know why; because no one asked them and no one told them that they still have obligations to other European countries. Instead of this we are suffering an unprecedented discrimination as we are the only devil in the paradise of EU. Why I am writing this to you; because I personally don’t like comments that tend to find cultural or ethnical explanations to what is going on with the eurozone crisis. And if you think that the German government or the German people have the moral right to say to the other Europeans what they should do with their mess you should first take a look to your history (I presume you are German ) , and you will find that Germany: a) during the Democracy of Weimar survived only because of the huge loans received from USA. Two plans the Dawes initially and the Young tried to ease the reparation debt of Germany. The Crash ended the American help and opened the road to Hitler. The German government since 1931 refused to pay any more rates. At the end of this story Germany paid only 1/8 of the “reparation” imposed from the Treaty of Versailles b) received an enormous haircut in 1953 (50% of the debt) from USA and other countries through the London Agreement on German External Debts. This agreement was extremely important because it allowed Germany to become the economic power of today and give us, the PIIGS, solid serious economic advices c)Also in 1953 many countries accepted to postpone war compensation until the reunification of Germany. Germany after the reunification simply denied to pay the war compensation declaring that instead of this is going to support financially EU.
      As for the nationalistic party, I am very sorry that we forced you to abandon your democratic beliefs and become a nationalist. I never realized that we have such a power.

  • geotentes, there is also the 4-5 outcome if the second player take two at his forth visit at the table.

    • Sakis, thank you so much for the comment, because it led me to the thread of thoughts that justifies yanisvaroufakis’ conclusion: finally both players realise that their most likely maximum is 2 and that they had better take it as fast as they can i.e. player 1 at round 1.


  • Dear Yanni.
    Thanks for the excellent illustration of fundamental problems in games. My personal interpretation, which I have not seen emphasized enough, is that the main issue is with the optimization objective. One can define two equally valid problems (a: beat the opponent, b: maximize holdings), even if in some cases solutions are not well-defined. However, a possible linguistic similarity of the objectives does not permit one to assume that the solution of one problem also produces a reasonable outcome for the other.
    In the same vein, Knut’s suggestion for legal boundaries etc will do little to change the outcome unless the boundaries are too strict (i.e., totalitarian governments).

    On the other hand, the Eurobond/Worldbond may be a way to smooth-out the objective and obtain sensible solutions to multi-objective problems. Whether this adjustment can be done now, or we require a general reset (war) because our politicians have been playing to win for too long, remains to be seen. Hopefully, we will learn to “be careful what we wish for”…

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