The working of the Bitcoin market must nowadays be of interest even to non-specialists. At UPGRADE 2021, NTT Research Scientist Yuichiro Kamada (who is also an Associate Professor at the UC Berkeley Haas School of Business) presented a piece of joint work with Prof. Shunya Noda (University of Tokyo) looking at the future stability of the market and using game theory to model the behavior of users and miners under future conditions.

As is widely understood, Bitcoin transactions from users are recorded by miners, who use computing power to solve puzzles and are rewarded with the capacity to record transactions in blocks. Each block can hold a fixed number of transactions K; currently K=3000. Users pay a small fee to miners for each transaction recorded, and it is the user who decides the size of the fee. Naturally the user wants to have transactions recorded quickly and cheaply, while the miner will select the K most rewarding transactions to fill the block. Therefore, a market emerges.

A second reward to miners is the issue of extra Bitcoins for this work, but by design this reward is being reduced through time, and in about 120 years will reach zero. The question examined by Kamada and Noda is whether the market can be stable without this second reward.

As Kamada points out, the question is of more than academic interest: if the market is unstable after 120 years, nobody will want to be in the market in 119 years; if it is unstable after 119 years, nobody will want to be in the market in 118 years, and so on. There are real consequences for the present-day stability of Bitcoin.

By considering a small set of parameters (λ, the rate of success of all miners; W, the number of transactions processed to date; time t; and K), Kamada defines a function f describing users’ bidding behavior. Adding a parameter c, the cost to a miner of working, another function defines the reward to a miner. He states a theorem that (with c=0) there exists a perfect Bayesian equilibrium with such an f and shows that the payoff to the user has a unique stationary distribution as long as λK>1.

He also shows that as long as c>0 there will be periods when miners perceive it not to be worth working. This is significant because if no miners work, the market is susceptible to attacks. How λ and K affect the point at which miners become willing to work is stated as the subject of future work.