Duverger’s law for market concentration in Bitcoin mining


Bitcoin is perhaps the greatest innovations in economic design. I’m glad to see that despite the early predictions by many economists the currency is yet to die.  The value of Bitcoin has hovered around $550-$650 (USD) for a while and I remain confident that its value will stay close to the present marginal cost of mining Bitcoin.  In a previous post I identified scale economies in the Bitcoin mining protocol and predicted that this will eventually become a major issue.  Recently, the mining pool Ghash.io which is administered by the presumably Russian owned   CEX.io achieved 54% of computational power amongst all Bitcoin miners. The plurality lasted for a few hours and caused a great deal of `weeping and gnashing of teeth’ in the Bitcoin community. You see, anyone controlling more than 50% of mining power exercises complete control over the recording of Bitcoin transactions.

It is not surprising that a mining pool will occasionally achieve more than 50% of mining power, after all there are economies of scale that are built into the cryptographic mining contests in the Bitcoin protocol. But there are additional aspects of the Bitcoin protocol that will ensure that no persistent monopoly can emerge in Bitcoin mining. The protocol has democracy in built into it, and the plurality rule in the system combined with the fact that mining is costly ensures that we will not see a persistent monopoly. Indeed, given the economies of scale in the mining protocol I predict that the eventual stable market structure for Bitcoin mining will be two large mining pools of equal size.  By equal size I mean two mining consortiums that will each frequently cross the 50% computational power line and have temporary control of the recording of Bitcoin transactions. And that, unlike a persistent monopoly, need not be a bad thing for the longevity of the currency.

The relationship between two-party systems and majority-rule elections is called “Duverger’s law” in political science. In a theory paper that I wrote some time ago (before the release of Bitcoin)  with Martin Osborne, we identified economies of scale  in a plurality-rule election system as one possible explanation for   “Duverger’s law.” My thinking now is that the argument in that paper is rather compelling for predicting the eventual agglomeration that we will see in Bitcoin mining. Simply, because of economies of scale a stable outcome cannot involve more than two miners: there is always an incentive for miners to agglomerate into a pool with more than 50% computational power. Now it is also clear that a persistent monopolist is not a stable outcome. as the monopolist will have an incentive to reduce mining cost by remaining at just over 50% of computational power. After all, by way of market power there is no difference between having 51% of power and 52% of computational power. The non-monopolist, on the other hand,  will have an incentive to increase their mining power or simply drop out (49% with a persistent monopoly is the same as having %0). Of course, there is another possibility: no miners. But that is also not possible, as in the absence of miners anyone can use the computational power of a smart watch to mine Bitcoin, just for fun.


7 Responses to "Duverger’s law for market concentration in Bitcoin mining"
  1. Excellent application of theory, but it still fails to address the controlling power of a 51% monopoly. Perhaps the paradigm sought here is Mutually Assured Destruction Duopoly. But I think that it is not a stable outcome as why wouldn’t a monopolist seek to retain their (temporary) monopoly power by disallowing their competitors transactions.

    • They would try to disallow their competitor’s transactions. But that can’t last long if their competitor is actively seeking to regain control. Remember that mining is also about luck, so if two companies are vying for 50%, then luck becomes the great decider at any given moment. Having a persistent 51% is much harder than it sounds, especially when luck factors in.

    • I agree. The fact that two pools could collude to gain 51 pct monopoly at any point means that the problem still exists. This is not a stable enough fix.

    • Ben’s argument is the correct. Persistent 51% is not going to happen, because the other miners will actively compete.

  2. The currency is not dead, but as I predicted to you, the authorities in many countries have moved against it because of all the criminality surrounding this currency, limiting its potential use. And having a Russian owned computing company own half of it also sounds exactly what I predicted to you about the real users of this currency.
    Still, its survival does show there is a cohesive group still backing it and that there is real demand for an internet currency.

    • Paul, Paul, Paul…I haven’t read your follow-up post to my Bitcoin post. I’ll read it now, though I can predict what you wrote.

  3. The Bitcoin story is reminiscent of some agricultural experiments. A number of people tried to establish a cashmere growing industry here. For a long time there was lots of profit in it due to the breeding and selling so-called stud animals. However, beyond this there was little supportive trading of the actual fibre or the meat. Eventually the industry collapsed to a hobby farm interest.

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