What is the essence of a zero-sum game?


A zero-sum game is a mathematical representation of a situation in which each participant’s gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero.

So, to proof bitcoin is a zero-sum game one has to prove that the total gains and losses of the participants will sum to zero. And you, at least, need an explanation for the surplus value of bitcoin over the amount of money that actually has been used to buy/mine the bitcoin outstanding in the light of a zero-sum game. Can the pie be increased or is the pie just redistributed? Or can the pie change in size while it remains a zero-sum game?

Mid-December 2017 bitcoin peaked at €16.000, double the value today: €135 billions of paper value evaporated… The pie obviously deflated 50% after a spectacular run last year. Participants have theoretically lost €8.000 per bitcoin in paper losses in only 1,5 months. So, obviously, the “the pie” can change in size?

If today (31/01/18) participant A is ready to pay €8.000 for one bitcoin to participant B, and B agrees, A will have the bitcoin while the money is exchanged from A to B. Other participants take this as a reference for their potential trades, which will lead them to conclude that their bitcoin is now worth €8.000 too. One can now argue that the total value of the bitcoin pool (“the pie”) its so-called market capitalization, by virtue of this one and latest trade, has become €135 billion [€8.000*16.8 mln outstanding bitcoins as of 31 Jan. 2018].

Almost all bitcoin has been bought or mined for a lower rate than the €16k mentioned. Only a very very small fraction of participants has bought into bitcoin at these high levels. If these participants were to sell their bitcoin today they would incur the real loss directly. While the participant(s) initially selling the bitcoin at the €16k rate made a windfall profit above the first amount they purchased/mined the bitcoin for. So, the paper value itself is not relevant to decide whether a participant made a gain or loss but only the real buying/mining rate of the bitcoin vs its actual selling rate is relevant. If you would add up all these real gains and losses this would amount to ZERO, regardless of what rate the bitcoin would reside. So, the proverbial pie is the net amount of money used to buy/mine the now available bitcoin. This pie can change in size by virtue of newly mined bitcoins and to the extent that the amount of money brought into the game is equal to holdings of the new participation in bitcoin exposure.

NB, I discard here from participants’ opportunity costs as bitcoin holdings do not give dividends or interest and having to pay capital tax based on the paper value of the bitcoin. This should be seen as a loss to the participants too and this would make bitcoin a negative non-zero-sum game. So, participants on average make a loss.

Let’s take a hypothetical average buying/mining rate for all present bitcoin of €80, the present value of money truly exposed in bitcoin is €1,35 billion. So current participants have paid this amount on a net basis to buy their bitcoin. So, the winners have pocketed €1,35 billion. While the current participants, the losers if you will, have bitcoin in their wallets or in their exchange accounts. These bitcoins have no value other than the hope/believe of the holders that sometime somebody else will buy this bitcoin from them, so the loss can be transferred to the next one. The participant is in the hope to earn a net gain in the process and with that increase the loss of the remainders still.

Investing in Bitcoin is all about the belief that somebody else will buy your bitcoin against current rates for real money or equivalents in goods/services believing the same ad infinitum. In liquid markets with enough abilities for arbitration between markets of commodities, stock, and currency in relatively normal and stable circumstances this is a valid assumption (for as long as it lasts). But bitcoin has no intrinsic value, other than being a value store and is not supported by institutions in case of market disruption. So, the question is whether this core belief underpinning bitcoin is a valid assumption by the participants.

As I have learned the hard way bitcoin market liquidity is not enough even at relevant marketplaces (Kraken in my case) to honor all trades for a given rate. After several times that my trade did not find a match while the market was trading at my desired execution price it made me stop trading bitcoin altogether. Also, arbitration between exchanges is notoriously cumbersome.

Bitcoin is at best a zero-sum game. One person’s loss is the others gain. There is no magical “feeding the multitude” here.

But that said; Bitcoin is a redistribution game: if you are lucky or smarter than others there is money to be gained out there. And of course this, by virtue of you being you, applies to you!