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Dynamic User Competition and Miner Behavior in the Bitcoin Market

Yuichiro Kamada, Shunya Noda

TL;DR

The paper develops a dynamic, decentralized model of Bitcoin-like markets where users set fees and miners decide when to operate in response to short-term congestion. It shows that congestion induces dynamic bidding, while miners may temporarily suspend mining when profits from fees are insufficient, reducing social welfare. A positive block reward is shown to align private incentives with social welfare by stabilizing mining activity and improving throughput. Moreover, the socially optimal block reward is strictly positive, suggesting that Bitcoin’s fixed halving schedule may be suboptimal in supporting welfare-enhancing mining activity.

Abstract

We develop a dynamic model of the Bitcoin market where users set fees themselves and miners decide whether to operate and whom to validate based on those fees. Our analysis reveals how, in equilibrium, users adjust their bids in response to short-term congestion (i.e., the amount of pending transactions), how miners decide when to start operating based on the level of congestion, and how the interplay between these two factors shapes the overall market dynamics. The miners hold off operating when the congestion is mild, which harms social welfare. However, we show that a block reward (a fixed reward paid to miners upon a block production) can mitigate these inefficiencies. We characterize the socially optimal block reward and demonstrate that it is always positive, suggesting that Bitcoin's halving schedule may be suboptimal.

Dynamic User Competition and Miner Behavior in the Bitcoin Market

TL;DR

The paper develops a dynamic, decentralized model of Bitcoin-like markets where users set fees and miners decide when to operate in response to short-term congestion. It shows that congestion induces dynamic bidding, while miners may temporarily suspend mining when profits from fees are insufficient, reducing social welfare. A positive block reward is shown to align private incentives with social welfare by stabilizing mining activity and improving throughput. Moreover, the socially optimal block reward is strictly positive, suggesting that Bitcoin’s fixed halving schedule may be suboptimal in supporting welfare-enhancing mining activity.

Abstract

We develop a dynamic model of the Bitcoin market where users set fees themselves and miners decide whether to operate and whom to validate based on those fees. Our analysis reveals how, in equilibrium, users adjust their bids in response to short-term congestion (i.e., the amount of pending transactions), how miners decide when to start operating based on the level of congestion, and how the interplay between these two factors shapes the overall market dynamics. The miners hold off operating when the congestion is mild, which harms social welfare. However, we show that a block reward (a fixed reward paid to miners upon a block production) can mitigate these inefficiencies. We characterize the socially optimal block reward and demonstrate that it is always positive, suggesting that Bitcoin's halving schedule may be suboptimal.

Paper Structure

This paper contains 48 sections, 32 theorems, 101 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Institutional Detail
  3. Related Literature
  4. User Competition
  5. Model
  6. Equilibrium
  7. Definition
  8. Characterization
  9. Comparative Statics
  10. Welfare
  11. User's Welfare
  12. Miner's Revenue
  13. Endogenous Operation
  14. Model
  15. Equilibrium
  16. ...and 33 more sections

Key Result

Theorem 1

In the UC model, if a bid function $\beta$ is an equilibrium, then the following conditions must be the case.

Figures (11)

  • Figure 1: Bid functions for various block arrival rate $\lambda$
  • Figure 2: Bid functions for various block capacity $K$
  • Figure 4: The shape of the equilibrium bid function $\beta^E(t, t')$ with varying threshold time $t'$.
  • Figure 5: The miner's surplus at threshold time $t$, $M^*(t)$
  • Figure 6: The equilibrium threshold time $t^E$
  • ...and 6 more figures

Theorems & Definitions (57)

  • Definition 1: Equilibrium, UC Model
  • Remark 1
  • Theorem 1
  • Theorem 2
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • Proposition 5
  • Definition 2: Equilibrium, EO Model
  • ...and 47 more