This article is featured in Bitcoin Magazine\u2019s<\/em> \u201cThe Primary Issue\u201d. Click <\/em>here<\/a><\/em> to get your Annual Bitcoin Magazine Subscription.<\/strong><\/p>\n Click here<\/a> to download a PDF of this article.<\/strong><\/p>\n \u201cEconomics I think is sort of like accounting \u2014 you know, it doesn\u2019t immediately have any morals. You could go into welfare economics, you try to think of some human values or you go into variations.\u201d<\/em> \u2013 John F. Nash Jr., The University of Scranton, November, 2011<\/a>.<\/p>\n This quotation from John Forbes Nash Jr. is taken from a lecture Nash gave on \u201cIdeal Money and the Motivations of Savings and Thrift\u201d, some 61 years after the publication of his first game theory paper simply named \u201cThe Bargaining Problem\u201d (1950).<\/p>\n \u201cThe Bargaining Problem\u201d is significant because it is believed to be one of the first examples where an axiomatic approach is introduced into the social sciences. Nash introduces \u201cThe Bargaining Problem\u201d as a new treatment of a classical economic problem \u2014 regarding it as a nonzero-sum, two-person game, where a few general assumptions and \u201ccertain idealizations\u201d are made so that values are found for the game.<\/p>\n The genealogy from \u201cThe Bargaining Problem\u201d to Nash\u2019s later works on Ideal Money is established, where in \u201cThe Bargaining Problem\u201d Nash remarks upon the utility of money:<\/p>\n \u201cWhen the bargainers have a common medium of exchange the problem may take on an especially simple form. In many cases the money equivalent of a good will serve as a satisfactory approximate utility function.\u201d <\/em>John F. Nash Jr., The Bargaining Problem (1950)<\/a>.<\/p>\n <\/a><\/p>\n Click the image above to subscribe!<\/p>\n Nash\u2019s bargaining proposal is essentially asking about the fairest way to split $1 between participants in a financial transaction or contract, where each side has a range of interests and preferences and where there must be agreement, or else both sides will get nothing. The axioms which are introduced for a Nash bargain go on to define a unique solution.<\/p>\n Nash Equilibrium versus Nash Bargaining<\/p>\n In The Essential John Nash <\/em>(2007), Harold Kuhn describes Nash\u2019s subsequent \u201cNon-Cooperative Games\u201d (1950)<\/a> <\/em>paper, and what later became known as Nash equilibria, as a \u201cclumsy, if totally original, application of the Brouwer fixed point theorem\u201d. Yet it was Nash\u2019s equilibrium idea which bestowed him a public profile through a Nobel prize in the economic sciences. Nash\u2019s life was later dramatized in the Hollywood film A Beautiful Mind<\/em>.<\/p>\n In \u201cNon-Cooperative Games\u201d, Nash\u2019s theory is based on the \u201cabsence of coalitions, in that it is assumed each participant acts independently, without collaboration or communication with any of the others\u201d. In Adam Curtis\u2019s television documentary The Trap <\/em>(2007), Nash describes his equilibria as social adjustment:<\/p>\n \u201c\u2026this equilibrium which is used, is that what I do is perfectly adjusted in relation to what you\u2019re doing, and what you\u2019re doing or what any other person is doing is perfectly adjusted to what I am doing or what all other people are doing. They are seeking separate optimisations, just like poker players.\u201d<\/em> John F. Nash Jr., The Trap<\/em> (2007, Adam Curtis), F*ck You, Buddy<\/a>.<\/p>\n The difference between Nash equilibrium<\/em> and Nash bargaining<\/em> is that axiomatic bargaining (or reaching a Nash bargain<\/em>) assumes no equilibrium. Instead, it states the desired properties of a solution. Nash bargaining<\/em> is regarded as cooperative game theory because of its nonzero-sum characteristic and the existence of contracts. Nash extended the axiomatic treatment of The Bargaining Problem<\/em> in \u201cTwo-Person Cooperative Games\u201d (1953)<\/a>, <\/em>introducing a threat approach in which there is an umpire to enforce contracts \u2014 in the process discounting \u201cstrategies\u201d as not containing special qualities and rather focusing on formal representation of a determined game.<\/p>\n Ideal Money and Asymptotically Ideal Money<\/p>\n Just before the turn of the century, John Nash starts writing and lecturing on an evolving thesis called Ideal Money<\/em>. It assumed different iterations over the years, but Nash defined it as money intrinsically free of inflation or inflationary decadence. Nash isn\u2019t so much critical of Keynes the economist or person, but of the psychology of what\u2019s become known as Keynesianism; Nash regarded it a Machiavellian scheme of continual inflation and currency devaluation. Nash believed if central banks are to target inflation, they should target a zero rate for \u201cwhat is called inflation\u201d:<\/p>\n \u201cIt is only really respectable that there should not be an arbitrary or capricious pattern of inflation, but how should a proper and desirable form of money value stability be defined?\u201d<\/em> John F. Nash Jr., \u201cIdeal Money and Asymptotically Ideal Money\u201d, 2010<\/a>. <\/p>\n In \u201cIdeal Money\u201d, Nash returns to the axiomatic approach he first establishes in his inchoate game theory. Ideal Money therefore becomes critical of Keynesian macroeconomics:<\/p>\n \u201cSo I feel that the macroeconomics of the Keynesians is comparable to a scientific study of a mathematical area which is carried out with an insufficient set of axioms.\u201d<\/em> John F. Nash Jr., \u201cIdeal Money and Asymptotically Ideal Money\u201d, 2008<\/a>.<\/p>\n Nash defines the missing axiom:<\/p>\n \u201cThe missing axiom is simply an accepted axiom that the money being put into circulation by the central authorities should be so handled as to maintain, over long terms of time, a stable value.\u201d<\/em> John F. Nash Jr., \u201cIdeal Money and Asymptotically Ideal Money\u201d, 2008<\/a>.<\/p>\n In 2002, in the Southern Journal<\/em><\/a> version of Ideal Money, Nash realizes an ideal money can\u2019t be completely free of inflation (or too \u201cgood\u201d), as it will have problems circulating and could be exploited by parties who wish to safely deposit a store of wealth. Nash then introduces a steady and constant rate of inflation (or asymptote) which could be added to lending and borrowing contracts.<\/p>\n Indeed, Nash describes the purpose of Ideal Money in a cooperative game and microeconomic context:<\/p>\n \u201cA concept that we thought of later than at the time of developing our first ideas about Ideal Money is that of the importance of the comparative quality of the money used in an economic society to the possible precision, as an indicator of quality, of the contracts for performances of future contractual obligations.\u201d<\/em> John F. Nash Jr., \u201cIdeal Money and Asymptotically Ideal Money\u201d, 2008<\/a>.<\/p>\n Bitcoin as an Axiomatic Design<\/p>\n If Nash\u2019s view of economics was that it lacks any immediate morals \u2014 and that values, assumptions, axioms, variations, or idealizations can be introduced to determine a nonzero-sum or determined game which provides welfare for all participants \u2014 then it is worth considering if these axioms are present in the Bitcoin system, given that Nash, together with Satoshi, were both critical of the arbitrary (or undetermined) nature of centrally managed currencies.<\/p>\n Pareto Efficiency<\/p>\n The presence of Pareto efficiency is perhaps the most demonstrative Nash bargaining axiom (see illustration) in Bitcoin with respect to the cumulative supply density and distribution: The majority of coins are mined relatively early in the Bitcoin lifespan (loosely following the Pareto 80\/20 power law). <\/p>\n Scale Invariance<\/p>\n The scale invariance is present through the difficulty adjustment mechanism which keeps bitcoin supply \u201csteady and constant\u201d (a phrase both Nash and Satoshi use). No matter how popular or unpopular bitcoin becomes to mine, the scale invariance should mean players can form realistic expectations on the value of bitcoin, and that their underlying preferences shouldn\u2019t change regarding this. The internal divisibility of bitcoin also means the value a coin is expressed in (whether the U.S. dollar or other currency) shouldn\u2019t matter over shorter or immediate time frames \u2014 just as room temperature can be expressed as Celsius or Fahrenheit without affecting the actual temperature. These differences should become clear only over the longer term or in intertemporal transactions.<\/p>\n The adjustment mechanism also keeps total bitcoin supply at just under 21 million, due to a side effect of the system data structure, and therefore introduces the asymptote.<\/p>\n Symmetry<\/p>\n Nash\u2019s symmetry axiom is present in the pseudonymity and decentralization of the Bitcoin network, which provides for equality of bargaining skill (a phrase Nash introduces in \u201cThe Bargaining Problem\u201d) through not having to prove first-person identity in participating in the core or primary network. It means there isn\u2019t a centralized or trusted principal responsible for minting the coins, a \u201cgrand pardoner\u201d in Nash\u2019s words. In relation to Nash bargaining, two players should get the same amount if they have the same utility function, and are therefore indistinguishable. Alvin Roth (1977)<\/a> summarizes this as the label of players not mattering: \u201cIf switching the labels of players leaves the bargaining problem unchanged, then it should leave the solution unchanged.\u201d<\/p>\n Independence of Irrelevant Alternatives (IIA)<\/p>\n Finally, there is Nash\u2019s most controversial bargaining axiom: the Independence of Irrelevant Alternatives. In simple terms, this means adding a third (or non-winning candidate) to an election between two players shouldn\u2019t alter the outcome to the election (third parties become irrelevant). If peer-to-peer is referring to a two-player game, with the Bitcoin software acting as a third-party arbitrator or umpire to \u201cthe game\u201d with the software designed to a set of values or axioms, then it\u2019s possible that IIA is present in Bitcoin\u2019s proof-of-work. This speaks to a social group preference context: The proof-of-work says it solves the problem of the determination of representation in majority decision-making<\/em>, and that Nash\u2019s axiomatic bargaining (in both \u201cThe Bargaining Problem\u201d and \u201cTwo-Person Cooperative Games\u201d) explicitly addresses formal representation in determinative games.<\/p>\n Characteristics and Benefits of Cooperation<\/p>\n Generally speaking, there are believed to be three conditions required for a cooperative game:<\/p>\n Reduced participants, as there is less room for verbal complications, i.e., two players.Contracts, where participants are able to agree on a rational joint plan of action, enforceable by an external authority such as a court.Participants are able to communicate and collaborate on the basis of trusted information and have full access to the structure of the game (such as the Bitcoin blockchain<\/a>).<\/p>\n In respect of a nonzero sum game and the money preference, John Nash reflects on how money can facilitate transferable utility by way of \u201clubrication\u201d, and makes this observation:<\/p>\n \u201cIn Game Theory there is generally the concept of \u2018pay-offs\u2019, if the game is not simply a game of win or lose (or win, lose, or draw). The game may be concerned with actions all to be taken like at the same time so that the utility measure for defining the payoffs could be taken to be any practical currency with good divisibility and measurability properties at the relevant instant of time.<\/em>\u201d <\/em>John F. Nash Jr., \u201cIdeal Money and the Motivation of Savings and Thrift\u201d, 2011<\/a>.<\/p>\n <\/a><\/p>\n Click the image above to download a PDF of the article.\u00a0<\/p>\n The benefits of cooperation reduce the need for mediation or dispute resolution as contracts and agreements become more trustworthy; less border friction in trading; a nonzero-sum outcome (win-win bargaining or welfare economics); more intuitive, informal decision-making; and the possibility for coalition formation<\/em> which John Nash ultimately defines as a world empire context<\/em>. The latter makes resolutions to difficult problems like net zero (or any other problem requiring multilateral coordination) more realistic. Nash likens his Ideal Money proposal to old-fashioned sovereigns:<\/p>\n \u201cAny version of ideal money (money intrinsically not subject to inflation) would be necessarily comparable to classical \u201cSovereigns\u201d or \u201cSeigneurs\u201d who have provided practical media for use in traders\u2019 exchanges.\u201d<\/em> John F. Nash Jr., \u201cIdeal Money and the Motivation of Savings and Thrift\u201d, 2011<\/a>.<\/p>\n Nash also reflects in 2011 on a \u201cgame\u201d of contract signatures, as if Ideal Money<\/em> is the contract:<\/p>\n \u201cIt is as if there is another player in the game of the contract signers and this player is the Sovereign who provides the medium of currency in terms of which the contract is to be expressed.<\/em>\u201d John F. Nash Jr., \u201cIdeal Money and the Motivation of Savings and Thrift\u201d, 2011<\/a><\/p>\n Concluding Remarks<\/p>\n It\u2019s plausible to describe the Bitcoin system as a cooperative game in a non-cooperative setting, and while it may be that the axioms present in Bitcoin are not limited to just those required for a Nash bargain, it would appear there are ingredients in the system design that give Bitcoin a deterministic characteristic. At the very least, they contain certain morals as Nash remarked as desirable in his Scranton lecture.<\/p>\n Finally, John Nash first conceived his bargaining solution in 1950. It is perhaps fitting therefore he provides a simpler context to framing the question of money as that of \u201chonesty\u201d in one of his final lectures on the subject delivered to the Oxford Union<\/a> shortly before his death in 2015. <\/p>\n References<\/p>\n A Beautiful Mind<\/em> – S Nasar<\/p>\n \u201cThe Bargaining Problem\u201d – J Nash<\/p>\n \u201cNon-Cooperative Games\u201d – J Nash<\/p>\n \u201cTwo-Person Cooperative Games\u201d – J Nash<\/p>\n The Essential John Nash<\/em> – H Kuhn & S Nasar<\/p>\n Nash Bargaining Solution – Game Theory Tuesdays – P Talwalkar<\/p>\n This article is featured in Bitcoin Magazine\u2019s<\/em> \u201cThe Primary Issue\u201d. Click <\/em>here<\/a><\/em> to get your Annual Bitcoin Magazine Subscription.<\/strong><\/p>\n