Crypto-Current (039)


State of Play

§4 — Humans are neither tigers, nor bees. Regardless of ethnic variation, or ideological faction, they are neither solitary, nor collective (eusocial[1]), but social, and societies are essentially middling, or ambiguous. The concepts of the social and the individual, or the public and the private, are reciprocal, and mutually compromised. Social beings are necessarily (always, but only) partially coordinated, through transactional bonds. They have neither group mentality nor perfect autonomy. The way they get along together is an ineluctable and perennial problem, resolved through precarious, transient, meta-stable solutions. All promises of definitive fusion or fission, perfected solidarity or independence, are strictly utopian. The perpetual tension of dynamic social arrangements is an unsurpassable human reality.[2] It occupies the zone of coordination.

§4.01 — The ineradicable ambivalence of the social animal is captured by the theory of games. A tiger does not play games with a prey animal, anymore than bees play games with each other. A game is a transactional integration, at once too intimate for a non-social animal, and too fractured for a consolidated collective.

§4.02 — Games, in the game-theoretical sense of the term – the one relevant here – are always played in the wild. That is to say, they cannot be exited by cheating. If knocking over the table is a move that can be made (in reality) and doing so ends the game, it wasn’t a game of any seriousness to begin with. In any game that matters, cheating is a permitted move, as soon as it is possible at all. It might be said, more precisely, that any game which effectively prevents cheating is embedded within a greater game where such prevention is actualized, as an outcome. Any regulated game is carved out of the wild, and it is the outer game – that carves – which game theory attends to. In this lies its realism, distinguishing its objects from circumscribed, ludic amusements. Games merit social attention precisely because they contain cheating as integral options. Trust has to be internally processed, not extraneously presumed. There are no external referees.[3]

§4.03 — Due to its extreme elegance, and consequent generality of application, Prisoners’ Dilemma (PD) has come to achieve broad acceptance as the archetypal game. The scenario is elementary, by design. Two prisoners are held in noncommunicating cells. Each has the same, binary (or ‘Boolean’) strategic decision to make – to betray the other, or not. The entire game can therefore be represented by a 2×2 matrix. Finally, each space (or outcome) contains two numbers, representing the payoff to the players. In PD this aspect is perfectly symmetrical – the situation of each player exactly mirrors that of the other. Every payoff is a weighted negative utility – dramatized as a prospective period of jail time. All of the information on the outcome grid (or payoff table) is objective. It represent the dilemma facing each player as both, equally, would acknowledge it, without controversy, or perspectival inflection. In principle, it is accessible to both prisoners, and guides their choice of ‘move’.

§4.04 — PD has no well-coordinated solution, unless the game is multiplied – to become iterated,[4] and mnemonic. This is because there is no strictly rational alternative to defection (betrayal) in the absence of additional information, such as the kind that would be provided by the persistence of reputational positions through multiple cycles. In this respect, PD models coordination problems of the tragedy of the commons type, in which the optimization of collective interest is practically unobtainable.[5] ‘Free-rider’ problems are sub-components of the same dilemma, which indicates that it is generalizable to parasitic relations of all kinds.[6] Within all of these cases, rational individual decisions aggregate to a collective failure, expressed as systemic collapse in extreme cases, or – more typically – as a deadweight (negative sum) loss to the population as a whole.

§4.05 — It bears repeating – or reiterating – because it cannot be easily over-emphasized, that Prisoners’ Dilemma has extraordinarily general application to coordination problems. It would, indeed, be quite reasonable to characterize it as the model trust crisis. When concentrated into an atom, the pure element of the game is a double chance of treachery – subjective and objective – arising from the ineliminable hazard, on both sides, of betrayal. What Bitcoin acknowledges, from the beginning, is that to escape the prison-house of distrust is no easy thing, once mere moral exhortation in the direction of altruism is theoretically shelved. The recognition of this problem as a problem is socio-political realism itself. It is at this fork in the road that almost everything is decided.

§4.06 — PD is a close analog of a number of other game theoretical dilemmas, of which the best known is ‘Chicken’ – itself based upon an abstract model of bipolar geopolitical conflict in the context of nuclear deterrence. Chicken has several variants, distinguished primarily by dramatization. In one, competitors wrestle at the edge of a cliff, and double ‘defection’ pushes both over the edge. Another version of Chicken sets two drivers accelerating towards each other in automobiles. The contestant who swerves, loses. If neither swerves, a common calamity results (equivalent to the double defection – or collective pessimal – equilibrium in PD). An important difference between classic PD and Chicken, however, is that in the latter scenario(s) the contestants are not held to be strictly non-communicating. While the final decision of each antagonist remains a black box to the other, thus preserving the core of the game-theoretical dilemma, preliminary expressions of commitment are permissible.[7] Chicken thus permits strategies that involve signaling.

§4.07 — The DSP tells us that signs are cheap. Communication of commitment, therefore, is no trivial matter. Semantically and syntactically flawless statements of exceptional rhetorical quality still commonly – and even typically – mean nothing.[8] To repeat the essential, in the ways that matter most they are easy to say (and their repetition is cheaper still). Unless a cost is credibly attached to them, their flourishes make no additional contribution. The problem of credible commitment, as it arises within the theory of games, thus closely tracks that of the contract in crypto-economics. In both cases the strength (or value) of the signal is directly proportional to a conspicuous contraction of discretionary power, corresponding to an irreversible operation. Only when it is impossible – or at least infeasible – to back-down, recant, or renege, does a signal acquire game-theoretical significance. Burning bridges behind oneself signals something that no rhetorical flight is able to match. Even the importance of precedent – or reputation – in iterated PD is based on the status of the past as an irrevocable commitment. If what had been done could be taken back, like a fumbled move in a friendly game of chess, it would count for nothing. The irrevocable consumption of freedom provides the content for strategic signs.

§4.08 — Bitcoin is a game, in the strong or technical sense, because it does not control cheating through a transcendent rule (upheld by a “trusted third party”), but rather through an immanent principle (Nakamoto Consensus). Its immediate ancestry, within the game-theoretic lineage, descends from the formulation of The Byzantine Generals’ Problem, dating back to the mid-1970s.[9] As Lamport, Shostak, and Pease explain the problem (with line breaks preserved from the original):

We imagine that several divisions of the Byzantine army are camped outside an enemy city, each division commanded by its own general. The generals can communicate with one another only by messenger. After observing the enemy, they must decide upon a common plan of action. However, some of the generals may be traitors, trying to prevent the loyal generals from reaching agreement.

The generals must have an algorithm to guarantee that

A. All loyal generals decide upon the same plan of action.

The loyal generals will all do what the algorithm says they should, but the traitors may do anything they wish. The algorithm must guarantee condition A regardless of what the traitors do.

The loyal generals should not only reach agreement, but should agree upon a reasonable plan. We therefore also want to insure that

B. A small number of traitors cannot cause the loyal generals to adopt a bad plan.

§4.09 — ‘Byzantine failures’ arise when parties distributed within a communication network, containing unreliable nodes, are obstructed from reaching agreement, because they cannot confidently establish among themselves what has in fact been communicated, or from which agents messages have been received. A global perspective appears unobtainable, and local perspective is vulnerable to compromise. The extreme difficulty involved in Byzantine communications makes them a model coordination problem, of special relevance to Internet-connected agencies. Crucially, for our purposes here, and beyond, the problem follows upon an assertion of immanence (a critique), since it is defined primarily by the absence of a transcendent tribunal with global insight. None of the ‘generals’ are able to stand outside the system, call upon an authoritative criterion from beyond it, or even direct their communications around it. Their relation to each other is technically flat (or peer-to-peer). Any solution has to be drawn from out of the system itself – which is to say, from the self-organizational resources inherent to sheer multiplicity.

§4.091 — Nakamoto Consensus, in game-theoretic context, is the name for a solution to the Byzantine Generals’ Problem, based upon proof-of-work. By including proof-of-work within each message (hashed block), the generals are able to make the measure of agreement reached – i.e. computational power committed – into an intrinsic property of their communications. Agreement about the message is folded into the message. As blocks are chained, securely, in strict succession, the signal of consensus strengthens. In meeting a reiterated proof-of-work criterion, the blockchain accumulates immanent credibility. It replaces an extrinsic – and intractable – question about the reliability of communications with an intrinsic communication of reliability. Trust is made into the message.

[1] Within the terrestrial biosphere eusociality is most vividly represented by the Hymenoptera (ants, bees, wasps) and by termites. Unsurprisingly, therefore, the concept has been advanced primarily by entomologists. Suzanne Batra and E.O. Wilson have been particularly significant in advancing the concept, based on insect models in both cases. Nevertheless, truly communistic mammals do exist, instantiated by two species of mole-rat. As with eusocial insects, mole-rat societies are rigidly segmented between fertile and infertile castes (a biological precondition for equilibrium communistic organization). Eusocial species incarnate the solution to a coordination problem. The games involved (searches for evolutionarily stable strategies) have been resolved at the genetic level. That the pseudo-individuals within insect hives or colonies do not engage in competitive games with each other is precisely what eusociality means. Within (merely) social species, in contrast, genetics is under-determining, setting only general parameters for intra-social cooperative and competitive behavior. The execution of games is delegated to phenotypic performance, without access to any collective optimum state, or established strategic equilibrium. Such animals thus inherit the plasticity implied by ongoing (and uncompletable) games – which opens the sphere of culture, as a semi-autonomous domain of variation and emergent outcomes.  

[2] The same set of distinctions between the social, the a-social and the eusocial, is invoked by James A. Donald in his path-breaking study on the foundations of Natural Law,

The tripartite distinction echoes Aristotle’s classical statement, from the Politics: “Man is by nature a social animal; an individual who is unsocial naturally and not accidentally is either beneath our notice or more than human. Society is something that precedes the individual. Anyone who either cannot lead the common life or is so self-sufficient as not to need to, and therefore does not partake of society, is either a beast or a god. ”

[3] We can say, more precisely, that any game overseen by an external referee is embedded within a greater game, perhaps recursively, until reaching the transcendental plane which isn’t subject to adjudication by anything beyond itself.

[4] The ubiquity of the PD coordination model does not escape Venkatesh Rao, who observes: “… the well-known Iterated Prisoner’s Dilemma (IPD) model [is] sometimes called the e. coli of social science research.” In the words of Simon Dedeo: “As a tool for the mathematical study of human behavior, [PD] is the equivalent of Galileo’s inclined plane, or Gregor Mendel’s pea plants.”

[5] Garrett Hardin’s ‘The Tragedy of the Commons’ (1968) first coined the term that now seems so indispensable. Despite its compelling simplicity, there is little sign of subsequent intellectual convergence upon what this model of overexploitation through coordination failure implies. At the political level, socialists and libertarians – equally – find their analyses and prescriptions supported by it. An ideological meta-tragedy has thus confirmed its insight in the very process of failing to draw common conclusions from it. Hardin’s classic essay can be found at:

[6] Radical coordination failure in biological systems is epitomized by the parasite that kills its host. Despite the difficulty of evaluating deep historical evidence, under natural conditions in which extinction is the fate of approximately all species, it nevertheless seems reasonable to interpret this extreme pessimal equilibrium as the exceptional case. It is widely recognized that diseases tend to decline in malignancy over time, as self-destructively extravagant forms of parasitism are weeded from the biological record. Epistemological and ontological selection effects here converge, as the ‘phenomenon’ of coordination failure is edited from the realm of evidence. (That we will tend to see what works is Darwinism itself.) As with the tragedy of the commons, parasitical relations – enveloping every kind of predator-prey interaction – are vulnerable to overexploitation failures. The attendant arms races are important drivers of biological diversity, and phenotypical extravagance. The effects of competition for light among trees – roughly, trees themselves – are only the most vivid example of the way biological form is dominated by the outcome of a long history of default to non-coordination.

[7] In The Strategy of Conflict (1960) Thomas Schelling emphasizes the importance of ‘credible commitment’ to classically-structured games. His insight is satirized – with great insight – in Kubrick’s Dr. Strangelove, which builds its plot around the understanding that the limit signal of commitment is strategic automation (or automatic retaliation). The strategic irrationality of making this extreme commitment without signaling it is a central comic device of the movie.  

[8] An entire poetics could be constructed in this space. Based upon the lacuna of credible commitments in the pure linguistic realm, it would reverse the game-theoretical problem into a source of creativity, by conceiving it as a rhetorical generator. (That is an undertaking for another occasion.)

[9] The Byzantine Generals’ Problem – which is the difficulty of achieving ‘Byzantine coordination’ – was initially named ‘The Two Generals Paradox’ upon its formulation by Jim Gray (in his ‘Notes on Data Base Operating Systems’, 1978), and was then generalized – to larger multiple agent systems – by Leslie Lamport, Marshall Pease, Robert Shostak (in 1980).

As humorously reformulated by Satoshi Nakamoto, in a post on the Cryptography mail list that scrupulously preserves the critical abstract properties of the problem: “A number of Byzantine Generals each have a computer and want to attack the King’s wi-fi by brute forcing the password, which they’ve learned is a certain number of characters in length. Once they stimulate the network to generate a packet, they must crack the password within a limited time to break in and erase the logs, otherwise they will be discovered and get in trouble. They only have enough CPU power to crack it fast enough if a majority of them attack at the same time. […] They don’t particularly care when the attack will be, just that they all agree. It has been decided that anyone who feels like it will announce a time, and whatever time is heard first will be the official attack time. The problem is that the network is not instantaneous, and if two generals announce different attack times at close to the same time, some may hear one first and others hear the other first.” The same post explains how a proof of work solution can be achieved:

It is especially important to note that the BGP formalizes the problem of coordination (in general) as synchronization. As already remarked (in Part One), it articulates a problem whose insolubility, in the context of cosmo-physical theory, coincides with general relativity, spacetime, and the renunciation of absolute succession. A solution to the BGP, therefore, is intrinsically post-relativistic. (Given the restoration of succession to the order of signs that follows from the innovation of the blockchain, the application of the ‘post-’ prefix in this case has exceptional – and reflexive – conceptual legitimacy.)

See also The Problem of Firing-Squad Synchronization, whose relevance is implicit in its name:

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