カント的均衡 How We Cooperate: A Theory of Kantian Optimization | YaleNews
How We Cooperate: A Theory of Kantian Optimization
John E. Roemer, the Elizabeth S. and A. Varick Stout Professor of Political Science and Economics
(Yale University Press)
Game theory explains competitive behavior by working from the premise that people are self-interested. People don't just compete, however; they also cooperate. In "How We Cooperate," John Roemer argues that attempts by orthodox game theorists to account for cooperation leave much to be desired. Unlike competing players, cooperating players take those actions that they would like others to take — which Roemer calls "Kantian optimization." Through reasoning and modeling, Roemer demonstrates a simpler theory of cooperative behavior than the standard model provides.
資本主義分析の基礎理論研究の現状及び 「新しい福祉社会」モデルの探求
吉原直毅
2013
Roemer, J. E. (2010) Kantian equilibrium, Scandinavian Journal of Economics, Vol. 112, No. 1, pp. 1-24.
16）カント的均衡，及び経済行動のカント的アプローチについての一連の諸研究に関する最新の展望論文としては，奥島・吉原（2012）を参照せよ．
参考文献 稲葉振一郎・松尾匡・吉原直毅（2006）『マルクスの使いみち』太田出版．
奥島真一郎・吉原直毅（2012）｢非経済的動機を導入した経済理論の可能性：カント的アプローチ｣『経済研究』第63巻，第 4 号，pp.346－364．
鈴村興太郎・吉原直毅（2000）｢責任と補償：厚生経済学の新しいパラダイム｣『経済研究』第51巻，第2号，pp.162－184． 高増明・松井暁編（1999）『アナリティカル・マルキシズム』ナカニシヤ出版． 吉原直毅（2008）『労働搾取の厚生理論序説』岩波書店． 吉原直毅（2009 a）「 21世紀における労働搾取理論の新展開」『経済研究』第60巻，第 3 号，pp.205227． 吉原直毅（2009b）｢連載『福祉社会の経済学』：その10：ベーシック・インカムの実行可能性｣『経済セミナー』2009年2・3月号． 吉原直毅（2010）「古典派及びマルクスの経済理論：一般均衡理論アプローチ」丸山徹編『経済学のエピメーテウス』知泉書院，pp.105－160． Bowles, S. and H. Gintis (1981) Structure and practice in the labor theory of value, Review of Radical Political Economics, Vol. 12, No. 4, pp. 1-26. Duménil, G. (1980) De la Valeur aux Prix de Production. Paris: Economica. Foley, D. K. (1982) The Value of Money, the Value of labour Power, and the Marxian Transformation Problem, Review of Radical Political Economics, Vol. 14, No. 2, pp. 37-47. Fujimoto, T. and A. Opocher (2010) Commodity content in a general input-output model, Metroeconomica, Vol. 61, No. 3, pp. 442-453. Matsuo, T. (2009) Generalized Commodity Exploitation Theorem and the Net-production Concept, Bulletin of Political Economy, Vol. 3, No. 1, pp. 1-11. Mayer, T. F. (1991) Analytical Marxism, Sage.（瀬戸岡紘監訳『アナリティカル・マルクシズム』桜井書店，2005年） Morishima, M. (1973) Marx's Economics. Cambridge: Cambridge University Press. Morishima, M. (1974) Marx in the Light of Modern Economic Theory, Econometrica, Vol. 42, No. 4, pp. 611-632. Okishio, N. (1963) A mathematical note on Marxian theorems, Weltwirtschaftliches Archiv, Vol. 91, pp. 287-299. Van Parijs, P. (1995) Real Freedom for All: What (if Anything) can Justify Capitalism, Oxford University Press, Oxford.（後藤玲子・斉藤拓訳『ベーシック・インカムの哲学：すべての人にリアルな自由を』勁草書房，2009年） Rawls, J. (1971) A Theory of Justice, Cambridge: Harvard University Press. R
John Roemer on Kantian Equilibrium 2020
keeping them explicit may be important for agent implementations. The purpose of this paper is to contribute to the emerging literature on non-Nashian, morally inspired game theoretic concepts and, equally important, to bring its concerns and methods to the attention of the various communities represented in TARK. We are inspired by what we believe is one of the most intriguing classes of equilibrium concepts that can be seen as morally grounded: Kantian (a.k.a. Hofstadter) equilibria [54]. This notion emerged from three separate lines of research converging on an identical mathematical definition, but justifying it, however, from several very different perspectives: superrationality [38, 25], team reasoning [4], and Kantian optimization, respectively [54]. The common framework (most crisply developed for symmetric coordination games) only cons
しかし、それらを明示的にしておくことは、エージェントの実装にとって重要である。この論文の目的は、非梨園的で道徳的に触発されたゲーム理論的概念に関する新たな文献に貢献することであり、同様に重要なこととして、TARKに代表される様々なコミュニティにその関心と方法をもたらすことである。私たちは、道徳的に根拠のある均衡概念の中でも最も興味をそそられるクラスの一つに触発されています。Kantian (a.k.a. Hofstadter) equilibria [54]です。この概念は、同一の数学的定義に収束する3つの独立した研究ラインから生まれたものであるが、しかし、それを正当化するのは、それぞれ、超越性[38, 25]、チーム推論[4]、カント的最適化という、非常に異なる視点からである[54]。共通のフレームワーク（対称的なコーディネーションゲームのために最も明確に開発された）は、以下の点のみを考慮しています。
www.DeepL.com/Translator（無料版）で翻訳しました。
I'm a neoclassical economist in terms of general equilibrium theory and what determines prices I think they're determined by supply and demand and preferences and technology so I disagree with Marx about the falling rate of his theory of the falling rate of profit so for leftists I want to make distinctions between what I'm what I believe or what I think and what Marx thought so it's not really wrong to call me a Marxist but I did not to do that among people that I'm interested in having left-wing conversations too I want to emphasize the important that that for instance in economics I think that using the neoclassical tools of price theory and general equilibrium theory extremely important for understanding reality Romans has told me that he's spent some time teaching you the theory that I've developed about optimization that I call content equilibrium I'm going to spend their various versions of this kind of optimization I'm going to only talk today about the simplest kind the simplest version of it because it's the clearest it's pedagogically the easiest thing to try to teach to teach you what's a symmetric game a symmetric game is a game where all the players are identical except for where they're seated around the table think of it that way they have the same preferences in the same payoffs just subject to changing the names of people so if you think of a payoff matrix for a two-by-two game like the prisoner's dilemma or the stag hunt or the battle of the sexes these are represented by payoff matrices that are two by two symmetric matrices on the diagonal.
players have exactly identical preferences for which which profile along the diagonal of the matrix they would like and the off-diagonal elements are are symmetric so as I said the your you've studied a number of these I think the prisoner's dilemma of the stag hunt and so on now let me give an example of a symmetric game in a production economy that's a lot more complicated than a two-by-two game suppose we have a bunch of fishers on a lake and they all have the same preferences over fish caught and labour expended they want to catch more fish and they want to work less right so their utility is increasing in fiction efficient decreasing in labor very standard utility function but the more people who fish on the lake the harder it is to catch a fish because they're they're only a finite number of fish in the lake and they're congestion problems if a lot of people are fishing the probability that you'll catch a fish goes down with lots of people who are working on the lake so that's a monotone decreasing game where the contributions of people I'm going to call the strategy of a person his contribution that is to say how much he chooses to fish the labor that he expends on the lake and my payoff function is a decreasing function of the if we're all have the same preferences that's a perfectly symmetric game that's all I have to say at the moment another example is voting if you think it'd take a very simple view of voting and everybody values the outcome in the same way then everybody who has your politics who would like to who would like a certain you know candidate a to win they have the same preferences in a very simple model they get a certain value from the candidate winning and and their whether the candidate wins or not depends upon how many people come out to vote with our politics that's a symmetric game another example is signing the Declaration of Independence in the United States and I'll talk about this example more the politically active.
people who were fighting the British were thinking of starting a war against the British to get independence for the United States we're called together to discuss whether they should sign this declaration of independence asserting their asserting their freedom from the British but more other people sign the better the better I like the outcome because the probability of winning independence is going to depend upon the the probabilities of everybody signing so the payoff there are what's the probability of winning independence with however a certain risk involved in signing the signing the Declaration so that both a payoff and a positive benefit from signing and a negative and a positive cost also from signing the probability that you'll get captured by the British and thrown in in jail or or hanged abstractly we can represent the payoff function of a person in a symmetric game as a function of the contributions II won through en think effort efore effort some contribution it can be money or labor or any kind of positive number your contribution is a positive or zero number.
and you get a payoff which is a function of everybody's contribution now in many symmetric games I mean that a simple an example of a symmetric game this is a completely general form these functions can be different for different people but suppose everybody can write his or her payoff function as a function of his own contribution and then the contributions of all the other people I mean that's one way of writing this but if they have the same function so my fish pot depends upon how much labor I expend and let's say the total labor of everybody else and if we have the same payoffs with respect to those two arguments that would be an example of a symmetric game now a game is monotone increasing if every player's payoff is increasing in the contributions of the other players so I'll say it again I'm not saying anything about how my payoff changes with respect to my own contribution but I am gonna say I'm saying that in a monotone game my utility or payoff has to be an increasing function of what everybody else contributes so what's an example of that game of a monotone increasing game it would be building a bridge producing any kind of public good so each member of the village has to chip in some money to pay for the bridge and the better the more that everybody else chips in the bigger the bridge is gonna be and that's good for me with my suspect.
my own contribution it's a cost for me to contribute so my utility may not be increasing in my own contribution but it's certainly increasing in the contributions of others so building a bridge production of any public good is a monotone increasing game another example is recycling so we each have to decide whether to recycle there's a slight cost to recycling nobody observes whether you recycle or not you do it in your own kitchen if I value the a clean environment let's suppose everybody values to clean an environment then my payoff is an increasing function of how much other people recycle so that's a monotone decreasing game it may be increasing or decreasing in my own recycling I'm not so concerned about that paying taxes and other idea another example of a monotone increasing game the more taxes other people pay the better because that means we'll have more good provided by the by the government more public goods more transfer payments and so on so that's a monotone increasing game now often people don't think about that they only think about the cost of their paying taxes themselves but you really have to think about the fact that you know you're paying taxes may be a slight may be a cost to you may be significant.
but you have to also consider the fact that when everybody else pays taxes that's very good for you so there's a labor supply game with taxation in which each workers utility is an increasing function of the labor supplies of other workers because the more other workers contribute more they work the more taxes they pay and hence the greater will be the value of public goods and transfer payments that I may get signing the Declaration of Independence was a very interesting example Benjamin Franklin was the hero of that meeting I don't know if you guys have heard of Benjamin Franklin he was an American founding father so to speak and he gave a speech at that meeting he saw people were hesitant about signing the declaration that had been written why because when you sign the Declaration it's gonna be publicly announced you sign it'll be in all the newspapers and the British are gonna maybe come after you they're gonna put out a wanted poster for you so Franklin gave a speech in which he said the following he said if we don't hang together then most assuredly we will each hang separately so that expression depends upon the fact that hanging together in English means being solid heuristic and working together so the idea is and it's a cute phrase because there's a pun on hang right the second hanging in that statement will all hang separately it said the very different kind of hanging so he was urging people to sign the Declaration of Independence that was a monotone increasing game because the more that other people signed the better it is for me because I value independence example of amount decreasing game is fishing on the lake as I said when fish are scarce in the lake the more that other people fish the worse that is for me because it'll be lower my probability of catching a fish another example another example is robber neck rubbernecking the accident and the other Lane you're driving on the on the highway there's an accident in the other Lane everybody slows down to look at the accident right and that slows you down so that's a also a monotone decreasing game the more that others look at the accident that's their contribution looking at the accident the more that other people do that the worse it is for you emitting carbon in the atmosphere is the biggest example today of a monotone decreasing game I personally my country I might the more carbon that my country emits it has two effects it has some some effect on the global climate but if I'm a small country it might not be much of an effect emitting carbon means I can produce more at this point because production requires carbon emissions as long as we don't have completely non fossil fuels providing energy so but as far as other people are emitting that's a negative thing for me because it affects the climate of everybody including me so the contributions here are climate emissions or carbon emissions monotone decreasing game and I've said what a monotone increasing game is now here's the let's remember what a Nash equilibrium is a Nash equilibrium is a profile of contributions to the game such that no player would desire to alter his contribution given the contributions of others and this idea is the foundation of non cooperative game theory now here's a very important fact that you may not know Nash equilibria of monotone games either monotone increasing monotone decreasing it's true for both kinds of monotone games are almost always Pareto inefficient almost always Pareto efficient now this fact has the name has a name when the game is strictly increasing what is that name the name for the pareto and efficiency of a monotone increasing game is the free-rider problem it's got that popular name in popular currents monotone decreasing games also the Nash equilibria are always Preto efficient inefficient sorry Oh almost always Pareto efficient videos did : that's the tragedy of the Commons very good so the tragedy of Commons is the name the popular name for the Pareto and efficiency of monotone decreasing games and the free rider problem is the popular name for Pareto and efficiency in monotone increasing games those are very very important problems which afflict there they're often called market failures if you have a market economy okay now how would we model cooperation instead of competition between players so the Nash equilibrium players are competing with each other okay one proposal is this a contribution profile in which everybody contributes a certain number of amount each star of a game is a simple content equilibrium if everybody if every player prefers this profile to any other constant contribution profile so you ask yourself each person asks himself suppose we all contribute the same thing what would I like that thing to be if everybody answers the same number that's a simple content equilibrium I'm talking only about symmetric games now because everybody will have the same answer to that question in a symmetric game everybody has the same answer to that question is the same amount contribution that everybody would like everybody to make so in words that got it in red here he star is the contribution that each would like all to make and the reason I call that a simple content equilibrium is that Immanuel Kant's famous ethical position was called the categorical imperative and it said a person should take the action that he would will be universalized he should take the action he would like to see universalized so that's exactly what this is now the the big theorem is that the simple content equilibrium of any monotone game is Pareto efficient so in other words if people optimized in the content manner if they ask themselves the Contin question rather than the nash question there would be no tragedy the commons and there would be no free-rider problems they would all vanish well that would certainly be very nice that would certainly solve a lot of Pareto deficiencies in the real world if people are Nash optimizing so why doesn't everybody think this way well maybe people do a lot of time but our non cooperative game theory does not teach us to look for this behavior why because it models rationality as Nash optimization but I say that's a very narrow viewpoint Nash optimization is a formal model of going it alone what why I take the behavior of other people as fixed I assume they're simply parameters of my own decision problem I'm the only one who's thinking of thinking about the decision I simply assume other people are fixed that's going it alone whereas content optimization is a formal model of cooperation or solid heuristic behavior let's look at the prisoner's dilemma so here's the payoff matrix of the prisoner's dilemma the row player can play either C or D and the common player can play either C or D and if we play CC they both get one unit of utility if row plays C and column gets Steve and roguettes - two units column gets three if they both defect they get 0-0 the unique Nash equilibrium of this game is zero zero but notice it's Pareto dominated by cc however CC is not a Nash equilibrium why because suppose wrote plays CC and column thinks well I can either take this column or this column if I play C I get 1 but if I play D I get 3 so if if row player plays the first row column is going to play the second column what about if row player plays the second row well then columns choice is between again this or this but 0 is greater than minus 2 so again column will play D since this is a symmetric matrix the same argument holds for row so this is actually something that's a stronger than a Nash equilibrium it's called a dominant strategy equilibrium ok no matter what the other fellow does the best strategy for me is d so Nash players are caught here what is what a Content players do they simply say if we were both to play the same thing what would I prefer what I prefer we both play C or what I prefer we both play D well I'd prefer we both clacey because I'll get a utility of 1 which is bigger than 0 and column will reason the same way so if they ask that question what is the strategy I'd like both of us to play they'll agree this that's the simple content equilibrium and as you see it's Pareto efficient it can't be dominated by any of these other any of these other choices why doesn't everybody do this why in the prisoner's dilemma doesn't everybody they just cooperate and play cc because row what happens if row plays C then column if he doesn't want to cooperate can do better by playing D because 3 is better than one is bigger than 1 and then rogue says well if he's gonna do that I'm gonna get screwed I'm gonna get minus 2 but if I play D if you place T I'll get 0 which is bigger than minus 2 so that's how if you don't trust the other player to cooperate then that'll be you'll you'll decide not to be a Content player so that's the key thing ro must trust column to cooperate to make cooperation a good choice for him that's the key problem is there enough trust among the players of the game that they will agree not to play nash against other players but to cooperate with other players suppose we feel solidarity with other people we have an experience of acting in concert to solve problems perhaps I think you and I are very similar we grew up in the same culture my reason whatever I end up deciding to do with the prisoner's dilemma you're gonna come to the same conclusion therefore I need only ask on the main diagonal of the payoff matrix what profile do I prefer well I prefer CC to DD I know you'll come to the same conclusion so I play C and you simply reason that way too and you play C so that's how a common culture can make it possible for people to trust each other and end up better off than they would be in the Nash equilibrium here are some examples I've given you this already recycling voting and paying taxes I gave you those three examples now let me do a little economic example for you with taxation we have a set of identical workers all are earning the same wage each has a preferences modeled by a utility function represented by utility function you over consumption and labor a worker's net income with taxation is 1 minus T times the wage times his labor think of this as the real wage so this is the amount of the good that there's one good that he can buy with his labor earnings but with taxation each worker also receives what's called the demo grant they receive one end of the total tax revenues back as a as a check in the mail from the from the Internal Revenue Service so this is total income in the society it's a total wage bill this is the taxes paid on by those workers and each person gets back one end of it so the utility of the worker is a function of his consumption which is the first argument here that's his after-tax income plus his share of the Democrat Al assist means the sum of all the else and then of course the second argument is his labor supply so I've just written that again up here now how does a nash player decide upon his labor supply well he balances his utility from the take-home income against the disutility of Labor so what he does is I'm gonna do a little calculus here he think he says what is the L well there should be there's an L missing here so what the worker does is he has his take-home income and then he has his share of the demo grant and then this is his labor argument if he takes if he holds the other labor contributions fixed and then he chooses the L that maximizes his utility the L wan you take the derivative of this with respect to the first argument times the derivative of the first argument with respect to L 1 which is just this remember there should be an L 1 here and then plus the only place that out 1 appears is in the first argument here so when he takes to the root of this with respect to L wanna gets T over n times W and then plus the derivative of U with respect to L 1 that's just YouTube and you can rewrite that in this way notice that the sum of these two things is essentially just equal to 1 minus T over W suppose an is a million and we can just ignore this term it's going to be very close to zero so the consequence of these of this first-order condition is that the worker sets what's called his marginal rate of substitution equals to 1 minus T times W but Pareto efficiency requires that you set the marginal rate of substitution equal to your wage not your after-tax wage and the result so this is not Pareto efficient nice optimization with taxation is not Pareto efficient and the fact that this is smaller than this is called the deadweight loss of Taxation now what is the content do the content says what's the L I would like all of us to contribute well then my utility would be this would be my after-tax wage now everybody's contributing the same L so the sum of the elves will just be the sum of the Oh I will just be NL and here I have an L and if you take the derivative of this with respect to L notice what you get here the derivative of this first argument with respect to L is 1 minus TW plus TW the ends cancel out and this is just L so you get that but what is the sum of these two things its W so we get the formula which is the condition for Pareto efficiency so what this shows is if workers were optimizing in the content manner then you'd get Pareto efficiency at any tax rate that's hard to believe any tax rate even a tax rate of 1 all that happens when you change the tax rate is you change the distribution of income but you don't hurt efficiency so the content solution is Pareto efficient it solves the deadweight loss of Taxation well the deadweight loss of Taxation is just another name for the free rider problem see here when people Nash optimize in the labor supply game they're not taking account of the positive externality of other people's labor for their own consumption so what happens just to use this externality language content optimization internalizes the positive externality of income taxation now what if players have different preferences well all of this generalizes in a fairly sensible way to utility functions that are different across people the content question becomes more difficult it becomes more complicated so I'm not gonna go into that here I think you've covered that with Romans I think he's given you some examples now today the biggest negative externality is global warming created by greenhouse gas emissions there are about 200 countries each country would be better off if all the others reduce their emissions so it's just like the fishing game it's a tragedy of the Commons so this is a monotone decreasing game among heterogeneous players because people have different different GDPs have different relationship of carbon emissions to their own consumption in the different countries and so on it's no longer a symmetric game the Nash equilibrium leads to huge prey to an efficiency if we're essentially at a kind of a Nash equilibrium now because there's not much cooperation going on if this continues climate problems are gonna massively increase we're gonna have Wars when people in Bangladesh try to move to India because they're because their country is flooding there'll be millions or billions of live loss due to climate change but the content equilibrium is Pareto efficient so it would be massively important for people to learn to play that to play that content equilibrium I view the annual international meetings what are called the the conferences of the parties as an attempt to create solidarity and Trust that are needed to reach the content solution so let's think of Donald Trump he's the perfect example of a nash player he wants to dissolve all cooperative ventures in which the u.s. is involved his proto was belligerently non-cooperative think of his slogan America first because of his optimization protocol the world is now in the most dangerous place it's been since World War two learning to cooperate is now a matter of life and death for billions of people economic theory can help economists should teach their students that Nash equilibrium is not the theory of rationality cooperation is another kind of rationality having a way to model it will teach us to see cooperation as much more prevalent than we've been taught to believe thank you I would like to hear from you if you think that what you've heard of Mexican current policies and socialism in general can be consistent with kansian equilibrium okay so that's a very good question very complicated question I've actually written a long paper which is called what can socialism be in the 21st century and it applies content equilibrium to discussing different kinds of property relations that we could have which would be socialists the main thing we should be doing now is improving the lives of the disadvantaged in society most people are poor due to no fault of their own and most people who were rich are also rich due to that the fact that they had very good luck luck and in the families they were born into it particular if you're born into a well-off family a highly educated family this values education and can give you a lot of resources probability is our gonna do pretty well in life if you're born to an uneducated family people who are very poor who don't understand the value of education you're probably not going to do very well in life so I think that injustice is one of the main things we should care about my view is there are three pillars on which any economic system stands one is a set of institutions and property relations the second is of behavioral ethos that is to say a theory of how people should make decisions and the third is a distributive ethic that is to say a a moral view of how resources should be distributed an ethical view so under capitalism property relations are what you know firms are privately owned by individuals corporations and families and people sell resources on the labor market or on all markets capital market labor market and so on commodity markets the behavioral ethos is going it alone do the best you can given your own resources and the luck that you were born with do the best you can don't worry particularly about other people other than your family so that's going it alone and that's modeled by Nash equilibrium Nash equilibrium is a formalization of the deceive your thoughts of capitalism and the distributive ethic of capitalism is it's all right for you to get whatever you can get as long as you don't break the law now what about socialism the property relations of socialism there can be many kinds but they're not gonna be they don't they don't necessarily have to be let's put it that way private ownership of firms firms can be owned collectively by groups of people they can be owned by the workers who contribute labor they can even be owned by the investors also who contribute investment but there won't be a stock market in that model for buying becoming an owner of a firm the only way you'll get a share of the income of the firm is by contributing something to it labor or investment so that's the those are the property relations the distributive the behavioral ethos I say is cooperation rather than going alone the behavioral ethos is cooperation and that's mob by Content equilibrium by content optimization and finally the distributive ethic is well equality of opportunity its massive equality of deep equality of opportunity which means that we try to compensate people for bad luck that they have mainly in the birth lottery by having institutions that chiefly education and redistribution which will insure people against the bad luck of being born the birth lottery so very briefly what I do is I integrate the behavioral ethos into the theory of socialism and I contrast that with capitalism and the big story is that you get you will you solve all these Pareto inefficiencies that exist under capitalism because of free-rider problems and tragedies of the comments so it's basically just a further articulation of what I've talked about today how would the taxation problem change if agents had different incomes so if you use linear taxation but people have different wages because some people are more skilled than others then you can still get the theorem that you get Pareto efficiency regardless of the tax rate if people content optimized but you have to use what I call additive content optimization you don't have a homogeneous society again you don't have a symmetric gang you have an asymmetric game and they're basically two kinds of content optimization you can use in an asymmetric game to get Pareto efficiency one is multiplicative content optimization the other is additive so in the taxation problem if people optimize in the additive content manner you get prade efficiency independent of the tax rate now what does this require in a society it requires that people think solid heuristically that they're acting in concert with other people doesn't actually require you be altruistic doesn't you still evaluate the outcomes from your own viewpoint terms of your own utility but you think of acting in concert with other people if there are way to cooperating something where people think really different in the sense of some people see it as problem other people don't okay here's a it's a good question here's the here's the way that you have to think to solve the climate change problem so suppose that we have a proposal which is an amount of emissions from every country in the world or every region of the world say say you have 15 regions in the world and suppose the proposal is on the is on the bargaining table which proposes how much each region should be allowed to emit in carbon a multiplicative content equilibrium has the property that nobody no country or no region would like to rescale that vector of emissions as to say nobody would like that you can't say oh I want to cut my emissions I want to increase my emissions by 10% you can't say that you can only propose to increase everybody's emissions by 10% or you could propose to decrease everybody's emissions by 10% or increase everybody's emissions by 4% whatever but the only acceptable proposals are to rescale the whole vector by multiplying it by a constant if nobody wants to rescale the vector that's been proposed that's what I call a multiplicative content equilibrium and if you find such a such a vector of emissions which you can always calculate if you know all the technologies of the countries and so on it's a complicated calculation but you can calculate that if if nobody know region wants to rescale that vector it's pretty efficient which means it's really about as as good as we can do right it'll in particular we will avoid huge climate increases in temperature because that's going to be bad for everybody so that's the way that you can't in optimize their and that takes account of the fact that people have different preferences so some countries will get to emit more than others but nobody will want to rescale the whole bit if content equilibrium is supposed to make everyone to take East our action but given that it's like intertemporal problem if our grandparents or the previous generation already didn't take the East our action does it still hold yeah making the problem a problem for every generation makes it a much more complicated problem but suppose you say the citizens of every country compare care about their descendants they compare about the future right so their utility function does not only include their own personal utility but the utility of their family going down into the future of their descendants so then the content equilibrium but they have to make this decision today about how much to emit in the next 10 years to actually do the details of the intergenerational problem is complicated but the general principle is still there the general principle is that there will be a vector which nobody will want to alter rescale and that vector will bring about Pareto efficiency in the sense that you can't possibly improve every country's utility but now the utility is not just the utility of the present generation it's some welfare function of utility of the present generation and all their descendants if there are already differences in Ingham I just keep thinking of this solution of this period or optimal solution that they teaches where one individual has everything and the other one has nothing I guess Canton behavior is not enough what you're saying is Preto efficiency is not the be-all in the end all that's correct we have to be worried about equity as well as efficiency so here's the here's one answer to that question if you have a completely symmetric game a homogeneous society then there's no question that the Pareto equal if the content equilibrium is going to Pareto dominate the Nash equilibrium it'll make everything will not only be efficient but it'll make everybody better off and that will hold as long as people are fairly close to being heterogeneous but the more homogeneous the more heterogeneity you introduce in the population the less likely it is that everybody will be made better off in the content equilibrium the content equilibrium will be Pareto efficient but it might make some people worse off in the games that we actually consider in real life you won't have this terrible solution where one person gets everything but I can't guarantee that everybody will be medic better off from the content equilibrium than them but I've done simulations showing that in standard sort of tax models almost everybody will be better off as long as tax rates aren't really close to one if tax rates get really close to one and the rich will be worse off than they were in the Nash equilibrium so typically what happens in real economic problems is that the very richest people will be hurt by content equilibrium but the core but the benefit is you'll have massive improvements in efficiency so as to say most people will be made much better off the rich will never want to lose money so direct cooperative behavior would not be enough to redistribute income right maybe like in the tax problem if you set a tax rate of 95% that'll make the very very rich worse off but the poor will be massively better off than they were before in fact the bottom 95% will be much better off so I've got simulations of these examples which show what happens with taxation and with redistribution of wealth but the distribution of wealth we have now and in the kind of capitalism we have today in most countries including both Mexico and the United States is so terribly terribly unequal that if we introduce high taxation we will with content optimization get Pareto efficiency but the very very rich will be worse off than they are now they won't be worse off than the poor they'll be they'll still be very rich but they'll be worse off I'm a little sceptic about the trust mechanisms you talk about the culture being the trust factor there but what if they're two individuals or the two players cannot find a common ground through which they can build a trust relationship if the common factor isn't that obvious like culture then how can we trust that the other person will want to get to the content equilibrium that's right that's the big problem and heterogeneity makes it difficult to build trust but let me give you an example of what's happened in the 20th century in terms of cooperative behavior if you look at the most highly developed countries in the world let's say the OECD countries on average the government takes about between 30 and 50 percent of the national income in taxes and it spends that money on public goods and redistribution of through transfer payments that's a huge form of cooperation the each country is pooling between a third and a half of its total income to be used for redistribution or for public goods in the Scandinavian countries and in the northern European countries it's about one-half about fifty percent of national income is redistributed through taxation and invested in public goods that's a huge form of cooperation that wasn't true in the nineteenth century because it only came about with income taxation which began use in most countries in the early 20th century so you have to see that societies have made huge progress in being solid heuristic to the extent that they've decided to pool a lot of their income in that way now how did that happen it happened through democracy it happened through the extension of the franchise so that ordinary working-class people could vote and when that happened then people eventually voted to have a lot of redistribution it also happened because of various catastrophes that occurred in the 20th century the Great Depression in the 1930s and the to end the second world war people came back from the Second World War and they decided they were gonna have a more solid heuristic society than earlier and they voted for to form welfare states and to increase taxation so in the model you could include things like democracy that make Hitler Janey did not be like the limit that faith at the mobile phases that's right that's right I mean people have to recognize that although they have a lot of differences between them they also have a lot of similarities that's the important thing it's worth if you can visit a Scandinavian country Sweden or Denmark or Norway or Finland I mean which is a Nordic country you'll see that the society is much more cooperative and solid heuristic than any other country in the world they really have a huge degree of solidarity among their among their people and the reason that that happened was that they were fairly heterogeneous with respect to religion race language culture and it was relatively easy for them to be solid heuristic now they have a lot of people who have immigrated to those countries they're no longer as ethnically homogeneous as they were before but they've still maintained this solid heuristic economic policies do you think the current crisis will help people realize that we are all in the same boat and we should be more cooperative. I can't make any confident predictions about what will happen very very hard to predict. I mean I thought after the financial crisis in 2008 that people would learn that they have to be solid heuristic and they would pass universal health insurance but they didn't because the Republicans succeeded in convincing a lot of people that national health insurance would be socialism and that's a bad thing so I you know I I can't predict what's gonna happen I mean I'm sorry but I think there's no guarantee that we're gonna get to a better world out of this crisis I very much folk we will and a lot of people are talking about that but it's not clear it's not necessary and it will happen it seems to me..
返信削除John Roemer on Kantian Equilibrium 2020
https://youtu.be/hzucT13o_xo
参考
奥島真一郎・吉原直毅（2012）｢非経済的動機を導入した経済理論の可能性：カント的アプローチ｣『経済研究』第63巻，第 4 号，pp.346－364．
https://www.ier.hit-u.ac.jp/~yosihara/201208hikeizaidoukidounyukeizairiron.pdf